From 14b75fa304e72b694ea92991aab25307e97f47c8 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 24 Mar 2023 15:26:13 +0900 Subject: [PATCH 01/67] add qrao files --- .../algorithms/qrao/__init__.py | 65 ++ .../algorithms/qrao/encoding.py | 645 ++++++++++++++++++ .../algorithms/qrao/magic_rounding.py | 439 ++++++++++++ .../qrao/quantum_random_access_optimizer.py | 324 +++++++++ .../algorithms/qrao/rounding_common.py | 98 +++ .../qrao/semideterministic_rounding.py | 83 +++ qiskit_optimization/algorithms/qrao/utils.py | 87 +++ 7 files changed, 1741 insertions(+) create mode 100644 qiskit_optimization/algorithms/qrao/__init__.py create mode 100644 qiskit_optimization/algorithms/qrao/encoding.py create mode 100644 qiskit_optimization/algorithms/qrao/magic_rounding.py create mode 100644 qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py create mode 100644 qiskit_optimization/algorithms/qrao/rounding_common.py create mode 100644 qiskit_optimization/algorithms/qrao/semideterministic_rounding.py create mode 100644 qiskit_optimization/algorithms/qrao/utils.py diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py new file mode 100644 index 000000000..35a3d6851 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -0,0 +1,65 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2022. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +QRAO classes and functions +========================== + +Quantum Random Access Optimization. + +.. autosummary:: + :toctree: ../stubs/ + + encoding + rounding_common + SemideterministicRounding + MagicRounding + QuantumRandomAccessOptimizer + utils +""" + +from importlib_metadata import version as metadata_version, PackageNotFoundError + +from .encoding import QuantumRandomAccessEncoding + +from .rounding_common import RoundingScheme, RoundingContext, RoundingResult +from .semideterministic_rounding import ( + SemideterministicRounding, + SemideterministicRoundingResult, +) +from .magic_rounding import MagicRounding, MagicRoundingResult + +from .quantum_random_access_optimizer import ( + QuantumRandomAccessOptimizer, + QuantumRandomAccessOptimizationResult, +) + + +try: + __version__ = metadata_version("qrao") +except PackageNotFoundError: # pragma: no cover + # package is not installed + pass + + +__all__ = [ + "QuantumRandomAccessEncoding", + "RoundingScheme", + "RoundingContext", + "RoundingResult", + "SemideterministicRounding", + "SemideterministicRoundingResult", + "MagicRounding", + "MagicRoundingResult", + "QuantumRandomAccessOptimizer", + "QuantumRandomAccessOptimizationResult", +] diff --git a/qiskit_optimization/algorithms/qrao/encoding.py b/qiskit_optimization/algorithms/qrao/encoding.py new file mode 100644 index 000000000..454089458 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/encoding.py @@ -0,0 +1,645 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2019, 2022. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Quantum Random Access Encoding module. + +Contains code dealing with QRACs (quantum random access codes) and preparation +of such states. + +.. autosummary:: + :toctree: ../stubs/ + + z_to_31p_qrac_basis_circuit + z_to_21p_qrac_basis_circuit + qrac_state_prep_1q + qrac_state_prep_multiqubit + QuantumRandomAccessEncoding + +""" + +from typing import Tuple, List, Dict, Optional, Union +from collections import defaultdict +from functools import reduce +from itertools import chain + +import numpy as np +import rustworkx as rx + +from qiskit import QuantumCircuit +from qiskit.opflow import ( + I, + X, + Y, + Z, + PauliSumOp, + PrimitiveOp, + CircuitOp, + Zero, + One, + StateFn, + CircuitStateFn, +) +from qiskit.quantum_info import SparsePauliOp + +from qiskit_optimization.problems.quadratic_program import QuadraticProgram + + +def _ceildiv(n: int, d: int) -> int: + """Perform ceiling division in integer arithmetic + + >>> _ceildiv(0, 3) + 0 + >>> _ceildiv(1, 3) + 1 + >>> _ceildiv(3, 3) + 1 + >>> _ceildiv(4, 3) + 2 + """ + return (n - 1) // d + 1 + + +def z_to_31p_qrac_basis_circuit(basis: List[int]) -> QuantumCircuit: + """Return the basis rotation corresponding to the (3,1,p)-QRAC + + Args: + + basis: 0, 1, 2, or 3 for each qubit + + Returns: + The ``QuantumCircuit`` implementing the rotation. + """ + circ = QuantumCircuit(len(basis)) + BETA = np.arccos(1 / np.sqrt(3)) + for i, base in enumerate(reversed(basis)): + if base == 0: + circ.r(-BETA, -np.pi / 4, i) + elif base == 1: + circ.r(np.pi - BETA, np.pi / 4, i) + elif base == 2: + circ.r(np.pi + BETA, np.pi / 4, i) + elif base == 3: + circ.r(BETA, -np.pi / 4, i) + else: + raise ValueError(f"Unknown base: {base}") + return circ + + +def z_to_21p_qrac_basis_circuit(basis: List[int]) -> QuantumCircuit: + """Return the basis rotation corresponding to the (2,1,p)-QRAC + + Args: + + basis: 0 or 1 for each qubit + + Returns: + The ``QuantumCircuit`` implementing the rotation. + """ + circ = QuantumCircuit(len(basis)) + for i, base in enumerate(reversed(basis)): + if base == 0: + circ.r(-1 * np.pi / 4, -np.pi / 2, i) + elif base == 1: + circ.r(-3 * np.pi / 4, -np.pi / 2, i) + else: + raise ValueError(f"Unknown base: {base}") + return circ + + +def qrac_state_prep_1q(*m: int) -> CircuitStateFn: + """Prepare a single qubit QRAC state + + This function accepts 1, 2, or 3 arguments, in which case it generates a + 1-QRAC, 2-QRAC, or 3-QRAC, respectively. + + Args: + + m: The data to be encoded. Each argument must be 0 or 1. + + Returns: + + The circuit state function. + + """ + if len(m) not in (1, 2, 3): + raise TypeError( + f"qrac_state_prep_1q requires 1, 2, or 3 arguments, not {len(m)}." + ) + if not all(mi in (0, 1) for mi in m): + raise ValueError("Each argument to qrac_state_prep_1q must be 0 or 1.") + + if len(m) == 3: + # Prepare (3,1,p)-qrac + + # In the following lines, the input bits are XOR'd to match the + # conventions used in the paper. + + # To understand why this transformation happens, + # observe that the two states that define each magic basis + # correspond to the same bitstrings but with a global bitflip. + + # Thus the three bits of information we use to construct these states are: + # c0,c1 : two bits to pick one of four magic bases + # c2: one bit to indicate which magic basis projector we are interested in. + + c0 = m[0] ^ m[1] ^ m[2] + c1 = m[1] ^ m[2] + c2 = m[0] ^ m[2] + + base = [2 * c1 + c2] + cob = z_to_31p_qrac_basis_circuit(base) + # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf + # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| + sf = One if (c0) else Zero + # Apply the z_to_magic_basis circuit to either |0> or |1> + logical = CircuitOp(cob) @ sf + elif len(m) == 2: + # Prepare (2,1,p)-qrac + # (00,01) or (10,11) + c0 = m[0] + # (00,11) or (01,10) + c1 = m[0] ^ m[1] + + base = [c1] + cob = z_to_21p_qrac_basis_circuit(base) + # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf + # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| + sf = One if (c0) else Zero + # Apply the z_to_magic_basis circuit to either |0> or |1> + logical = CircuitOp(cob) @ sf + else: + assert len(m) == 1 + c0 = m[0] + sf = One if (c0) else Zero + + logical = sf + + return logical.to_circuit_op() + + +def qrac_state_prep_multiqubit( + dvars: Union[Dict[int, int], List[int]], + q2vars: List[List[int]], + max_vars_per_qubit: int, +) -> CircuitStateFn: + """ + Prepare a multiqubit QRAC state. + + Args: + dvars: state of each decision variable (0 or 1) + """ + remaining_dvars = set(dvars if isinstance(dvars, dict) else range(len(dvars))) + ordered_bits = [] + for qi_vars in q2vars: + if len(qi_vars) > max_vars_per_qubit: + raise ValueError( + "Each qubit is expected to be associated with at most " + f"`max_vars_per_qubit` ({max_vars_per_qubit}) variables, " + f"not {len(qi_vars)} variables." + ) + if not qi_vars: + # This probably actually doesn't cause any issues, but why support + # it (and test this edge case) if we don't have to? + raise ValueError( + "There is a qubit without any decision variables assigned to it." + ) + qi_bits: List[int] = [] + for dv in qi_vars: + try: + qi_bits.append(dvars[dv]) + except (KeyError, IndexError): + raise ValueError( + f"Decision variable not included in dvars: {dv}" + ) from None + try: + remaining_dvars.remove(dv) + except KeyError: + raise ValueError( + f"Unused decision variable(s) in dvars: {remaining_dvars}" + ) from None + # Pad with zeros if there are fewer than `max_vars_per_qubit`. + # NOTE: This results in everything being encoded as an n-QRAC, + # even if there are fewer than n decision variables encoded in the qubit. + # In the future, we plan to make the encoding "adaptive" so that the + # optimal encoding is used on each qubit, based on the number of + # decision variables assigned to that specific qubit. + # However, we cannot do this until magic state rounding supports 2-QRACs. + while len(qi_bits) < max_vars_per_qubit: + qi_bits.append(0) + + ordered_bits.append(qi_bits) + + if remaining_dvars: + raise ValueError(f"Not all dvars were included in q2vars: {remaining_dvars}") + + qracs = [qrac_state_prep_1q(*qi_bits) for qi_bits in ordered_bits] + logical = reduce(lambda x, y: x ^ y, qracs) + return logical + + +def q2vars_from_var2op(var2op: Dict[int, Tuple[int, PrimitiveOp]]) -> List[List[int]]: + """Calculate q2vars given var2op""" + num_qubits = max(qubit_index for qubit_index, _ in var2op.values()) + 1 + q2vars: List[List[int]] = [[] for i in range(num_qubits)] + for var, (q, _) in var2op.items(): + q2vars[q].append(var) + return q2vars + + +class QuantumRandomAccessEncoding: + """This class specifies a Quantum Random Access Code that can be used to encode + the binary variables of a QUBO (quadratic unconstrained binary optimization + problem). + + Args: + max_vars_per_qubit: maximum possible compression ratio. + Supported values are 1, 2, or 3. + + """ + + # This defines the convention of the Pauli operators (and their ordering) + # for each encoding. + OPERATORS = ( + (Z,), # (1,1,1) QRAC + (X, Z), # (2,1,p) QRAC, p ≈ 0.85 + (X, Y, Z), # (3,1,p) QRAC, p ≈ 0.79 + ) + + def __init__(self, max_vars_per_qubit: int = 3): + if max_vars_per_qubit not in (1, 2, 3): + raise ValueError("max_vars_per_qubit must be 1, 2, or 3") + self._ops = self.OPERATORS[max_vars_per_qubit - 1] + + self._qubit_op: Optional[PauliSumOp] = None + self._offset: Optional[float] = None + self._problem: Optional[QuadraticProgram] = None + self._var2op: Dict[int, Tuple[int, PrimitiveOp]] = {} + self._q2vars: List[List[int]] = [] + self._frozen = False + + @property + def num_qubits(self) -> int: + """Number of qubits""" + return len(self._q2vars) + + @property + def num_vars(self) -> int: + """Number of decision variables""" + return len(self._var2op) + + @property + def max_vars_per_qubit(self) -> int: + """Maximum number of variables per qubit + + This is set in the constructor and controls the maximum compression ratio + """ + + return len(self._ops) + + @property + def var2op(self) -> Dict[int, Tuple[int, PrimitiveOp]]: + """Maps each decision variable to ``(qubit_index, operator)``""" + return self._var2op + + @property + def q2vars(self) -> List[List[int]]: + """Each element contains the list of decision variable indice(s) encoded on that qubit""" + return self._q2vars + + @property + def compression_ratio(self) -> float: + """Compression ratio + + Number of decision variables divided by number of qubits + """ + return self.num_vars / self.num_qubits + + @property + def minimum_recovery_probability(self) -> float: + """Minimum recovery probability, as set by ``max_vars_per_qubit``""" + n = self.max_vars_per_qubit + return (1 + 1 / np.sqrt(n)) / 2 + + @property + def qubit_op(self) -> PauliSumOp: + """Relaxed Hamiltonian operator""" + if self._qubit_op is None: + raise AttributeError( + "No objective function has been provided from which a " + "qubit Hamiltonian can be constructed. Please use the " + "encode method if you wish to manually compile " + "this field." + ) + return self._qubit_op + + @property + def offset(self) -> float: + """Relaxed Hamiltonian offset""" + if self._offset is None: + raise AttributeError( + "No objective function has been provided from which a " + "qubit Hamiltonian can be constructed. Please use the " + "encode method if you wish to manually compile " + "this field." + ) + return self._offset + + @property + def problem(self) -> QuadraticProgram: + """The ``QuadraticProgram`` used as basis for the encoding""" + if self._problem is None: + raise AttributeError( + "No quadratic program has been associated with this object. " + "Please use the encode method if you wish to do so." + ) + return self._problem + + def _add_variables(self, variables: List[int]) -> None: + self.ensure_thawed() + # NOTE: If this is called multiple times, it *always* adds an + # additional qubit (see final line), even if aggregating them into a + # single call would have resulted in fewer qubits. + if self._qubit_op is not None: + raise RuntimeError( + "_add_variables() cannot be called once terms have been added " + "to the operator, as the number of qubits must thereafter " + "remain fixed." + ) + if not variables: + return + if len(variables) != len(set(variables)): + raise ValueError("Added variables must be unique") + for v in variables: + if v in self._var2op: + raise ValueError("Added variables cannot collide with existing ones") + # Modify the object now that error checking is complete. + n = len(self._ops) + old_num_qubits = len(self._q2vars) + num_new_qubits = _ceildiv(len(variables), n) + # Populate self._var2op and self._q2vars + for _ in range(num_new_qubits): + self._q2vars.append([]) + for i, v in enumerate(variables): + qubit, op = divmod(i, n) + qubit_index = old_num_qubits + qubit + assert v not in self._var2op # was checked above + self._var2op[v] = (qubit_index, self._ops[op]) + self._q2vars[qubit_index].append(v) + + def _add_term(self, w: float, *variables: int) -> None: + self.ensure_thawed() + # Eq. (31) in https://arxiv.org/abs/2111.03167v2 assumes a weight-2 + # Pauli operator. To generalize, we replace the `d` in that equation + # with `d_prime`, defined as follows: + d_prime = np.sqrt(self.max_vars_per_qubit) ** len(variables) + op = self.term2op(*variables).mul(w * d_prime) + # We perform the following short-circuit *after* calling term2op so at + # least we have confirmed that the user provided a valid variables list. + if w == 0.0: + return + if self._qubit_op is None: + self._qubit_op = op + else: + self._qubit_op += op + + def term2op(self, *variables: int) -> PauliSumOp: + """Construct a ``PauliSumOp`` that is a product of encoded decision ``variable``\\(s). + + The decision variables provided must all be encoded on different qubits. + """ + ops = [I] * self.num_qubits + done = set() + for x in variables: + pos, op = self._var2op[x] + if pos in done: + raise RuntimeError(f"Collision of variables: {variables}") + ops[pos] = op + done.add(pos) + pauli_op = reduce(lambda x, y: x ^ y, ops) + # Convert from PauliOp to PauliSumOp + return PauliSumOp(SparsePauliOp(pauli_op.primitive, coeffs=[pauli_op.coeff])) + + @staticmethod + def _generate_ising_terms( + problem: QuadraticProgram, + ) -> Tuple[float, np.ndarray, np.ndarray]: + num_vars = problem.get_num_vars() + + # set a sign corresponding to a maximized or minimized problem: + # 1 is for minimized problem, -1 is for maximized problem. + sense = problem.objective.sense.value + + # convert a constant part of the objective function into Hamiltonian. + offset = problem.objective.constant * sense + + # convert linear parts of the objective function into Hamiltonian. + linear = np.zeros(num_vars) + for idx, coef in problem.objective.linear.to_dict().items(): + assert isinstance(idx, int) # hint for mypy + weight = coef * sense / 2 + linear[idx] -= weight + offset += weight + + # convert quadratic parts of the objective function into Hamiltonian. + quad = np.zeros((num_vars, num_vars)) + for (i, j), coef in problem.objective.quadratic.to_dict().items(): + assert isinstance(i, int) # hint for mypy + assert isinstance(j, int) # hint for mypy + weight = coef * sense / 4 + if i == j: + linear[i] -= 2 * weight + offset += 2 * weight + else: + quad[i, j] += weight + linear[i] -= weight + linear[j] -= weight + offset += weight + + return offset, linear, quad + + @staticmethod + def _find_variable_partition(quad: np.ndarray) -> Dict[int, List[int]]: + num_nodes = quad.shape[0] + assert quad.shape == (num_nodes, num_nodes) + graph = rx.PyGraph() + graph.add_nodes_from(range(num_nodes)) + graph.add_edges_from_no_data(list(zip(*np.where(quad != 0)))) + node2color = rx.graph_greedy_color(graph) + color2node: Dict[int, List[int]] = defaultdict(list) + for node, color in sorted(node2color.items()): + color2node[color].append(node) + return color2node + + def encode(self, problem: QuadraticProgram) -> None: + """Encode the (n,1,p) QRAC relaxed Hamiltonian of this problem. + + We associate to each binary decision variable one bit of a + (n,1,p) Quantum Random Access Code. This is done in such a way that the + given problem's objective function commutes with the encoding. + + After being called, the object will have the following attributes: + qubit_op: The qubit operator encoding the input QuadraticProgram. + offset: The constant value in the encoded Hamiltonian. + problem: The ``problem`` used for encoding. + + Inputs: + problem: A QuadraticProgram object encoding a QUBO optimization problem + + Raises: + RuntimeError: if the ``problem`` isn't a QUBO or if the current + object has been used already + + """ + # Ensure fresh object + if self.num_qubits > 0: + raise RuntimeError( + "Must call encode() on an Encoding that has not been used already" + ) + + # if problem has variables that are not binary, raise an error + if problem.get_num_vars() > problem.get_num_binary_vars(): + raise RuntimeError( + "The type of all variables must be binary. " + "You can use `QuadraticProgramToQubo` converter " + "to convert integer variables to binary variables. " + "If the problem contains continuous variables, `qrao` " + "cannot handle it." + ) + + # if constraints exist, raise an error + if problem.linear_constraints or problem.quadratic_constraints: + raise RuntimeError( + "There must be no constraint in the problem. " + "You can use `QuadraticProgramToQubo` converter to convert " + "constraints to penalty terms of the objective function." + ) + + num_vars = problem.get_num_vars() + + # Generate the decision variable terms in terms of Ising variables (+1 or -1) + offset, linear, quad = self._generate_ising_terms(problem) + + # Find variable partition (a graph coloring is sufficient) + variable_partition = self._find_variable_partition(quad) + + # The other methods of the current class allow for the variables to + # have arbitrary integer indices [i.e., they need not correspond to + # range(num_vars)], and the tests corresponding to this file ensure + # that this works. However, the current method is a high-level one + # that takes a QuadraticProgram, which always has its variables + # numbered sequentially. Furthermore, other portions of the QRAO code + # base [most notably the assignment of variable_ops in solve_relaxed() + # and the corresponding result objects] assume that the variables are + # numbered from 0 to (num_vars - 1). So we enforce that assumption + # here, both as a way of documenting it and to make sure + # _find_variable_partition() returns a sensible result (in case the + # user overrides it). + assert sorted(chain.from_iterable(variable_partition.values())) == list( + range(num_vars) + ) + + # generate a Hamiltonian + for _, v in sorted(variable_partition.items()): + self._add_variables(sorted(v)) + for i in range(num_vars): + w = linear[i] + if w != 0: + self._add_term(w, i) + for i in range(num_vars): + for j in range(num_vars): + w = quad[i, j] + if w != 0: + self._add_term(w, i, j) + + self._offset = offset + self._problem = problem + + # This is technically optional and can wait until the optimizer is + # constructed, but there's really no reason not to freeze + # immediately. + self.freeze() + + def freeze(self): + """Freeze the object to prevent further modification. + + Once an instance of this class is frozen, ``_add_variables`` and ``_add_term`` + can no longer be called. + + This operation is idempotent. There is no way to undo it, as it exists + to allow another object to rely on this one not changing its state + going forward without having to make a copy as a distinct object. + """ + if self._frozen is False: + self._qubit_op = self._qubit_op.reduce() + self._frozen = True + + @property + def frozen(self) -> bool: + """``True`` if the object can no longer be modified, ``False`` otherwise.""" + return self._frozen + + def ensure_thawed(self) -> None: + """Raise a ``RuntimeError`` if the object is frozen and thus cannot be modified.""" + if self._frozen: + raise RuntimeError("Cannot modify an encoding that has been frozen") + + def state_prep(self, dvars: Union[Dict[int, int], List[int]]) -> CircuitStateFn: + """Prepare a multiqubit QRAC state.""" + return qrac_state_prep_multiqubit(dvars, self.q2vars, self.max_vars_per_qubit) + + +class EncodingCommutationVerifier: + """Class for verifying that the relaxation commutes with the objective function + + See also the "check encoding problem commutation" how-to notebook. + """ + + def __init__(self, encoding: QuantumRandomAccessEncoding): + self._encoding = encoding + + def __len__(self) -> int: + return 2**self._encoding.num_vars + + def __iter__(self): + for i in range(len(self)): + yield self[i] + + def __getitem__(self, i: int) -> Tuple[str, float, float]: + if i not in range(len(self)): + raise IndexError(f"Index out of range: {i}") + + encoding = self._encoding + str_dvars = ("{0:0" + str(encoding.num_vars) + "b}").format(i) + dvars = [int(b) for b in str_dvars] + encoded_bitstr = encoding.state_prep(dvars) + + # Offset accounts for the value of the encoded Hamiltonian's + # identity coefficient. This term need not be evaluated directly as + # Tr[I•rho] is always 1. + offset = encoding.offset + + # Evaluate Un-encoded Problem + # ======================== + # `sense` accounts for sign flips depending on whether + # we are minimizing or maximizing the objective function + problem = encoding.problem + sense = problem.objective.sense.value + obj_val = problem.objective.evaluate(dvars) * sense + + # Evaluate Encoded Problem + # ======================== + encoded_problem = encoding.qubit_op # H + encoded_obj_val = ( + np.real((~StateFn(encoded_problem) @ encoded_bitstr).eval()) + offset + ) + + return (str_dvars, obj_val, encoded_obj_val) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py new file mode 100644 index 000000000..eaabec82d --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -0,0 +1,439 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2022. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Magic bases rounding""" + +from typing import List, Dict, Tuple, Optional +from collections import defaultdict +import numbers +import time +import warnings + +import numpy as np + +from qiskit import QuantumCircuit +from qiskit.providers import Backend +from qiskit.opflow import PrimitiveOp +from qiskit.utils import QuantumInstance + +from .encoding import z_to_31p_qrac_basis_circuit, z_to_21p_qrac_basis_circuit +from .rounding_common import ( + RoundingSolutionSample, + RoundingScheme, + RoundingContext, + RoundingResult, +) + + +_invalid_backend_names = [ + "aer_simulator_unitary", + "aer_simulator_superop", + "unitary_simulator", + "pulse_simulator", +] + + +def _backend_name(backend: Backend) -> str: + """Return the backend name in a way that is agnostic to Backend version""" + # See qiskit.utils.backend_utils in qiskit-terra for similar examples + if backend.version <= 1: + return backend.name() + return backend.name + + +def _is_original_statevector_simulator(backend: Backend) -> bool: + """Return True if the original statevector simulator""" + return _backend_name(backend) == "statevector_simulator" + + +class MagicRoundingResult(RoundingResult): + """Result of magic rounding""" + + def __init__( + self, + samples: List[RoundingSolutionSample], + *, + bases=None, + basis_shots=None, + basis_counts=None, + time_taken=None, + ): + self._bases = bases + self._basis_shots = basis_shots + self._basis_counts = basis_counts + super().__init__(samples, time_taken=time_taken) + + @property + def bases(self): + return self._bases + + @property + def basis_shots(self): + return self._basis_shots + + @property + def basis_counts(self): + return self._basis_counts + + +class MagicRounding(RoundingScheme): + """ "Magic rounding" method + + This method is described in https://arxiv.org/abs/2111.03167v2. + + """ + + _DECODING = { + 3: ( # Eq. (8) + {"0": [0, 0, 0], "1": [1, 1, 1]}, # I mu+ I, I mu- I + {"0": [0, 1, 1], "1": [1, 0, 0]}, # X mu+ X, X mu- X + {"0": [1, 0, 1], "1": [0, 1, 0]}, # Y mu+ Y, Y mu- Y + {"0": [1, 1, 0], "1": [0, 0, 1]}, # Z mu+ Z, Z mu- Z + ), + 2: ( # Sec. VII + {"0": [0, 0], "1": [1, 1]}, # I xi+ I, I xi- I + {"0": [0, 1], "1": [1, 0]}, # X xi+ X, X xi- X + ), + 1: ({"0": [0], "1": [1]},), + } + + # Pauli op string to label index in ops + _OP_INDICES = {1: {"Z": 0}, 2: {"X": 0, "Z": 1}, 3: {"X": 0, "Y": 1, "Z": 2}} + + def __init__( + self, + quantum_instance: QuantumInstance, + *, + basis_sampling: str = "uniform", + seed: Optional[int] = None, + ): + """ + Args: + + quantum_instance: Provides the ``Backend`` for quantum execution + and the ``shots`` count (i.e., the number of samples to collect + from the magic bases). + + basis_sampling: Method to use for sampling the magic bases. Must + be either ``"uniform"`` (default) or ``"weighted"``. + ``"uniform"`` samples all magic bases uniformly, and is the + method described in https://arxiv.org/abs/2111.03167v2. + ``"weighted"`` attempts to choose bases strategically using the + Pauli expectation values from the minimum eigensolver. + However, the approximation bounds given in + https://arxiv.org/abs/2111.03167v2 apply only to ``"uniform"`` + sampling. + + seed: Seed for random number generator, which is used to sample the + magic bases. + + """ + if basis_sampling not in ("uniform", "weighted"): + raise ValueError( + f"'{basis_sampling}' is not an implemented sampling method. " + "Please choose either 'uniform' or 'weighted'." + ) + self.quantum_instance = quantum_instance + self.rng = np.random.RandomState(seed) + self._basis_sampling = basis_sampling + super().__init__() + + @property + def shots(self) -> int: + """Shots count as configured by the given ``quantum_instance``.""" + return self.quantum_instance.run_config.shots + + @property + def basis_sampling(self): + """Basis sampling method (either ``"uniform"`` or ``"weighted"``).""" + return self._basis_sampling + + @property + def quantum_instance(self) -> QuantumInstance: + """Provides the ``Backend`` and the ``shots`` (samples) count.""" + return self._quantum_instance + + @quantum_instance.setter + def quantum_instance(self, quantum_instance: QuantumInstance) -> None: + backend_name = _backend_name(quantum_instance.backend) + if backend_name in _invalid_backend_names: + raise ValueError(f"{backend_name} is not supported.") + if _is_original_statevector_simulator(quantum_instance.backend): + warnings.warn( + 'Use of "statevector_simulator" is discouraged because it effectively ' + "brute-forces all possible solutions. We suggest using the newer " + '"aer_simulator_statevector" instead.' + ) + self._quantum_instance = quantum_instance + + def _unpack_measurement_outcome( + self, + bits: str, + basis: List[int], + var2op: Dict[int, Tuple[int, PrimitiveOp]], + vars_per_qubit: int, + ) -> List[int]: + output_bits = [] + # iterate in order over decision variables + # (assumes variables are numbered consecutively beginning with 0) + for var in range(len(var2op)): # pylint: disable=consider-using-enumerate + q, op = var2op[var] + # get the decoding outcome index for the variable + # corresponding to this Pauli op. + op_index = self._OP_INDICES[vars_per_qubit][str(op)] + # get the bits associated to this magic basis' + # measurement outcomes + bit_outcomes = self._DECODING[vars_per_qubit][basis[q]] + # select which measurement outcome we observed + # this gives up to 3 bits of information + magic_bits = bit_outcomes[bits[q]] + # Assign our variable's value depending on + # which pauli our variable was associated to + variable_value = magic_bits[op_index] + output_bits.append(variable_value) + return output_bits + + @staticmethod + def _make_circuits( + circ: QuantumCircuit, bases: List[List[int]], measure: bool, vars_per_qubit: int + ) -> List[QuantumCircuit]: + circuits = [] + for basis in bases: + if vars_per_qubit == 3: + qc = circ.compose( + z_to_31p_qrac_basis_circuit(basis).inverse(), inplace=False + ) + elif vars_per_qubit == 2: + qc = circ.compose( + z_to_21p_qrac_basis_circuit(basis).inverse(), inplace=False + ) + elif vars_per_qubit == 1: + qc = circ.copy() + if measure: + qc.measure_all() + circuits.append(qc) + return circuits + + def _evaluate_magic_bases(self, circuit, bases, basis_shots, vars_per_qubit): + """ + Given a circuit you wish to measure, a list of magic bases to measure, + and a list of the shots to use for each magic basis configuration. + + Measure the provided circuit in the magic bases given and return the counts + dictionaries associated with each basis measurement. + + len(bases) == len(basis_shots) == len(basis_counts) + """ + measure = not _is_original_statevector_simulator(self.quantum_instance.backend) + circuits = self._make_circuits(circuit, bases, measure, vars_per_qubit) + + # Execute each of the rotated circuits and collect the results + + # Batch the circuits into jobs where each group has the same number of + # shots, so that you can wait for the queue as few times as possible if + # using hardware. + circuit_indices_by_shots: Dict[int, List[int]] = defaultdict(list) + assert len(circuits) == len(basis_shots) + for i, shots in enumerate(basis_shots): + circuit_indices_by_shots[shots].append(i) + + basis_counts: List[Optional[Dict[str, int]]] = [None] * len(circuits) + overall_shots = self.quantum_instance.run_config.shots + try: + for shots, indices in sorted( + circuit_indices_by_shots.items(), reverse=True + ): + self.quantum_instance.set_config(shots=shots) + result = self.quantum_instance.execute([circuits[i] for i in indices]) + counts_list = result.get_counts() + if not isinstance(counts_list, List): + # This is the only case where this should happen, and that + # it does at all (namely, when a single-element circuit + # list is provided) is a weird API quirk of Qiskit. + # https://github.com/Qiskit/qiskit-terra/issues/8103 + assert len(indices) == 1 + counts_list = [counts_list] + assert len(indices) == len(counts_list) + for i, counts in zip(indices, counts_list): + basis_counts[i] = counts + finally: + # We've temporarily modified quantum_instance; now we restore it to + # its initial state. + self.quantum_instance.set_config(shots=overall_shots) + assert None not in basis_counts + + # Process the outcomes and extract expectation of decision vars + + # The "statevector_simulator", unlike all the others, returns + # probabilities instead of integer counts. So if probabilities are + # detected, we rescale them. + if any( + any(not isinstance(x, numbers.Integral) for x in counts.values()) + for counts in basis_counts + ): + basis_counts = [ + {key: val * basis_shots[i] for key, val in counts.items()} + for i, counts in enumerate(basis_counts) + ] + + return basis_counts + + def _compute_dv_counts(self, basis_counts, bases, var2op, vars_per_qubit): + """ + Given a list of bases, basis_shots, and basis_counts, convert + each observed bitstrings to its corresponding decision variable + configuration. Return the counts of each decision variable configuration. + """ + dv_counts = {} + for i, counts in enumerate(basis_counts): + base = bases[i] + # For each measurement outcome... + for bitstr, count in counts.items(): + + # For each bit in the observed bitstring... + soln = self._unpack_measurement_outcome( + bitstr, base, var2op, vars_per_qubit + ) + soln = "".join([str(int(bit)) for bit in soln]) + if soln in dv_counts: + dv_counts[soln] += count + else: + dv_counts[soln] = count + return dv_counts + + def _sample_bases_uniform(self, q2vars, vars_per_qubit): + bases = [ + self.rng.choice(2 ** (vars_per_qubit - 1), size=len(q2vars)).tolist() + for _ in range(self.shots) + ] + bases, basis_shots = np.unique(bases, axis=0, return_counts=True) + return bases, basis_shots + + def _sample_bases_weighted(self, q2vars, trace_values, vars_per_qubit): + """Perform weighted sampling from the expectation values. + + The goal is to make smarter choices about which bases to measure in + using the trace values. + """ + # First, we make sure all Pauli expectation values have absolute value + # at most 1. Otherwise, some of the probabilities computed below might + # be negative. + tv = np.clip(trace_values, -1, 1) + # basis_probs will have num_qubits number of elements. + # Each element will be a list of length 4 specifying the + # probability of picking the corresponding magic basis on that qubit. + basis_probs = [] + for dvars in q2vars: + if vars_per_qubit == 3: + x = 0.5 * (1 - tv[dvars[0]]) + y = 0.5 * (1 - tv[dvars[1]]) if (len(dvars) > 1) else 0 + z = 0.5 * (1 - tv[dvars[2]]) if (len(dvars) > 2) else 0 + # ppp: mu± = .5(I ± 1/sqrt(3)( X + Y + Z)) + # pmm: X mu± X = .5(I ± 1/sqrt(3)( X - Y - Z)) + # mpm: Y mu± Y = .5(I ± 1/sqrt(3)(-X + Y - Z)) + # mmp: Z mu± Z = .5(I ± 1/sqrt(3)(-X - Y + Z)) + # fmt: off + ppp_mmm = x * y * z + (1-x) * (1-y) * (1-z) + pmm_mpp = x * (1-y) * (1-z) + (1-x) * y * z + mpm_pmp = (1-x) * y * (1-z) + x * (1-y) * z + ppm_mmp = x * y * (1-z) + (1-x) * (1-y) * z + # fmt: on + basis_probs.append([ppp_mmm, pmm_mpp, mpm_pmp, ppm_mmp]) + elif vars_per_qubit == 2: + x = 0.5 * (1 - tv[dvars[0]]) + z = 0.5 * (1 - tv[dvars[1]]) if (len(dvars) > 1) else 0 + # pp: xi± = .5(I ± 1/sqrt(2)( X + Z )) + # pm: X xi± X = .5(I ± 1/sqrt(2)( X - Z )) + # fmt: off + pp_mm = x * z + (1-x) * (1-z) + pm_mp = x * (1-z) + (1-x) * z + # fmt: on + basis_probs.append([pp_mm, pm_mp]) + elif vars_per_qubit == 1: + basis_probs.append([1.0]) + bases = [ + [ + self.rng.choice(2 ** (vars_per_qubit - 1), p=probs) + for probs in basis_probs + ] + for _ in range(self.shots) + ] + bases, basis_shots = np.unique(bases, axis=0, return_counts=True) + return bases, basis_shots + + def round(self, ctx: RoundingContext) -> MagicRoundingResult: + """Perform magic rounding""" + + start_time = time.time() + trace_values = ctx.trace_values + circuit = ctx.circuit + + if circuit is None: + raise NotImplementedError( + "Magic rounding requires a circuit to be available. Perhaps try " + "semideterministic rounding instead." + ) + + # We've already checked that it is one of these two in the constructor + if self.basis_sampling == "uniform": + bases, basis_shots = self._sample_bases_uniform( + ctx.q2vars, ctx._vars_per_qubit + ) + elif self.basis_sampling == "weighted": + if trace_values is None: + raise NotImplementedError( + "Magic rounding with weighted sampling requires the trace values " + "to be available, but they are not." + ) + bases, basis_shots = self._sample_bases_weighted( + ctx.q2vars, trace_values, ctx._vars_per_qubit + ) + else: # pragma: no cover + raise NotImplementedError( + f'No such basis sampling method: "{self.basis_sampling}".' + ) + + assert self.shots == np.sum(basis_shots) + # For each of the Magic Bases sampled above, measure + # the appropriate number of times (given by basis_shots) + # and return the circuit results + + basis_counts = self._evaluate_magic_bases( + circuit, bases, basis_shots, ctx._vars_per_qubit + ) + # keys will be configurations of decision variables + # values will be total number of observations. + soln_counts = self._compute_dv_counts( + basis_counts, bases, ctx.var2op, ctx._vars_per_qubit + ) + + soln_samples = [ + RoundingSolutionSample( + x=np.asarray([int(bit) for bit in soln]), + probability=count / self.shots, + ) + for soln, count in soln_counts.items() + ] + + assert np.isclose( + sum(soln_counts.values()), self.shots + ), f"{sum(soln_counts.values())} != {self.shots}" + assert len(bases) == len(basis_shots) == len(basis_counts) + stop_time = time.time() + + return MagicRoundingResult( + samples=soln_samples, + bases=bases, + basis_shots=basis_shots, + basis_counts=basis_counts, + time_taken=stop_time - start_time, + ) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py new file mode 100644 index 000000000..5c1202b3d --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -0,0 +1,324 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2020, 2022. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Quantum Random Access Optimizer.""" + +from typing import Union, List, Tuple, Optional +import time + +import numpy as np + +from qiskit import QuantumCircuit +from qiskit.algorithms.minimum_eigensolvers import ( + MinimumEigensolver, + MinimumEigensolverResult, + NumPyMinimumEigensolver, +) +from qiskit.algorithms.minimum_eigen_solvers import ( + MinimumEigensolver as LegacyMinimumEigensolver, + MinimumEigensolverResult as LegacyMinimumEigensolverResult, + NumPyMinimumEigensolver as LegacyNumPyMinimumEigensolver, +) + +from qiskit_optimization.algorithms import ( + OptimizationAlgorithm, + OptimizationResult, + OptimizationResultStatus, + SolutionSample, +) +from qiskit_optimization.problems import QuadraticProgram, Variable + +from .encoding import QuantumRandomAccessEncoding +from .rounding_common import RoundingScheme, RoundingContext, RoundingResult +from .semideterministic_rounding import SemideterministicRounding + + +def _get_aux_operators_evaluated(relaxed_results): + try: + # Must be using the new "minimum_eigensolvers" + # https://github.com/Qiskit/qiskit-terra/blob/main/releasenotes/notes/0.22/add-eigensolvers-with-primitives-8b3a9f55f5fd285f.yaml + return relaxed_results.aux_operators_evaluated + except AttributeError: + # Must be using the old (deprecated) "minimum_eigen_solvers" + return relaxed_results.aux_operator_eigenvalues + + +class QuantumRandomAccessOptimizationResult(OptimizationResult): + """Result of Quantum Random Access Optimization procedure.""" + + def __init__( + self, + *, + x: Optional[Union[List[float], np.ndarray]], + fval: Optional[float], + variables: List[Variable], + status: OptimizationResultStatus, + samples: Optional[List[SolutionSample]], + relaxed_results: Union[ + MinimumEigensolverResult, LegacyMinimumEigensolverResult + ], + rounding_results: RoundingResult, + relaxed_results_offset: float, + sense: int, + ) -> None: + """ + Args: + x: the optimal value found by ``MinimumEigensolver``. + fval: the optimal function value. + variables: the list of variables of the optimization problem. + status: the termination status of the optimization algorithm. + min_eigen_solver_result: the result obtained from the underlying algorithm. + samples: the x values of the QUBO, the objective function value of the QUBO, + and the probability, and the status of sampling. + """ + super().__init__( + x=x, + fval=fval, + variables=variables, + status=status, + raw_results=None, + samples=samples, + ) + self._relaxed_results = relaxed_results + self._rounding_results = rounding_results + self._relaxed_results_offset = relaxed_results_offset + assert sense in (-1, 1) + self._sense = sense + + @property + def relaxed_results( + self, + ) -> Union[MinimumEigensolverResult, LegacyMinimumEigensolverResult]: + """Variationally obtained ground state of the relaxed Hamiltonian""" + return self._relaxed_results + + @property + def rounding_results(self) -> RoundingResult: + """Rounding results""" + return self._rounding_results + + @property + def trace_values(self): + """List of expectation values, one corresponding to each decision variable""" + trace_values = [ + v[0] for v in _get_aux_operators_evaluated(self._relaxed_results) + ] + return trace_values + + @property + def relaxed_fval(self) -> float: + """Relaxed function value, in the conventions of the original ``QuadraticProgram`` + + Restoring convertions may be necessary, for instance, if the provided + ``QuadraticProgram`` represents a maximization problem, as it will be + converted to a minimization problem when phrased as a Hamiltonian. + """ + return self._sense * ( + self._relaxed_results_offset + self.relaxed_results.eigenvalue.real + ) + + def __repr__(self) -> str: + lines = ( + "QRAO Result", + "-----------", + f"relaxed function value: {self.relaxed_fval}", + super().__repr__(), + ) + return "\n".join(lines) + + +class QuantumRandomAccessOptimizer(OptimizationAlgorithm): + """Quantum Random Access Optimizer.""" + + def __init__( + self, + min_eigen_solver: Union[MinimumEigensolver, LegacyMinimumEigensolver], + encoding: QuantumRandomAccessEncoding, + rounding_scheme: Optional[RoundingScheme] = None, + ): + """ + Args: + + min_eigen_solver: The minimum eigensolver to use for solving the + relaxed problem (typically an instance of ``VQE`` or ``QAOA``). + + encoding: The ``QuantumRandomAccessEncoding``, which must have + already been ``encode()``ed with a ``QuadraticProgram``. + + rounding_scheme: The rounding scheme. If ``None`` is provided, + ``SemideterministicRounding()`` will be used. + + """ + self.min_eigen_solver = min_eigen_solver + self.encoding = encoding + if rounding_scheme is None: + rounding_scheme = SemideterministicRounding() + self.rounding_scheme = rounding_scheme + + @property + def min_eigen_solver(self) -> Union[MinimumEigensolver, LegacyMinimumEigensolver]: + """The minimum eigensolver.""" + return self._min_eigen_solver + + @min_eigen_solver.setter + def min_eigen_solver( + self, min_eigen_solver: Union[MinimumEigensolver, LegacyMinimumEigensolver] + ) -> None: + """Set the minimum eigensolver.""" + if not min_eigen_solver.supports_aux_operators(): + raise TypeError( + f"The provided MinimumEigensolver ({type(min_eigen_solver)}) " + "does not support auxiliary operators." + ) + self._min_eigen_solver = min_eigen_solver + + @property + def encoding(self) -> QuantumRandomAccessEncoding: + """The encoding.""" + return self._encoding + + @encoding.setter + def encoding(self, encoding: QuantumRandomAccessEncoding) -> None: + """Set the encoding""" + if encoding.num_qubits == 0: + raise ValueError( + "The passed encoder has no variables associated with it; you probably " + "need to call `encode()` to encode it with a `QuadraticProgram`." + ) + # Instead of copying, we "freeze" the encoding to ensure it is not + # modified going forward. + encoding.freeze() + self._encoding = encoding + + def get_compatibility_msg(self, problem: QuadraticProgram) -> str: + if problem != self.encoding.problem: + return ( + "The problem passed does not match the problem used " + "to construct the QuantumRandomAccessEncoding." + ) + return "" + + def solve_relaxed( + self, + ) -> Tuple[ + Union[MinimumEigensolverResult, LegacyMinimumEigensolverResult], RoundingContext + ]: + """Solve the relaxed Hamiltonian given the ``encoding`` provided to the constructor.""" + # Get the ordered list of operators that correspond to each decision + # variable. This line assumes the variables are numbered consecutively + # starting with 0. Note that under this assumption, the following + # range is equivalent to `sorted(self.encoding.var2op.keys())`. See + # encoding.py for more commentary on this assumption, which always + # holds when starting from a `QuadraticProgram`. + variable_ops = [self.encoding.term2op(i) for i in range(self.encoding.num_vars)] + + # solve relaxed problem + start_time_relaxed = time.time() + relaxed_results = self.min_eigen_solver.compute_minimum_eigenvalue( + self.encoding.qubit_op, aux_operators=variable_ops + ) + stop_time_relaxed = time.time() + relaxed_results.time_taken = stop_time_relaxed - start_time_relaxed + + trace_values = [v[0] for v in _get_aux_operators_evaluated(relaxed_results)] + + # Collect inputs for rounding + # double check later that there's no funny business with the + # parameter ordering. + + # If the relaxed solution can be expressed as an explicit circuit + # then always express it that way - even if a statevector simulator + # was used and the actual wavefunction could be used. The only exception + # is the numpy eigensolver. If you wish to round the an explicit statevector, + # you must do so by manually rounding and passing in a QuantumCircuit + # initialized to the desired state. + if hasattr(self.min_eigen_solver, "ansatz"): + circuit = self.min_eigen_solver.ansatz.bind_parameters( + relaxed_results.optimal_point + ) + elif isinstance( + self.min_eigen_solver, + (NumPyMinimumEigensolver, LegacyNumPyMinimumEigensolver), + ): + statevector = relaxed_results.eigenstate + if isinstance(self.min_eigen_solver, LegacyNumPyMinimumEigensolver): + # statevector is a StateFn in this case, so we must convert it + # to a Statevector + statevector = statevector.primitive + circuit = QuantumCircuit(self.encoding.num_qubits) + circuit.initialize(statevector) + else: + circuit = None + + rounding_context = RoundingContext( + encoding=self.encoding, + trace_values=trace_values, + circuit=circuit, + ) + + return relaxed_results, rounding_context + + def solve(self, problem: Optional[QuadraticProgram] = None) -> OptimizationResult: + if problem is None: + problem = self.encoding.problem + else: + if problem != self.encoding.problem: + raise ValueError( + "The problem given must exactly match the problem " + "used to generate the encoded operator. Alternatively, " + "the argument to `solve` can be left blank." + ) + + # Solve relaxed problem + # ============================ + (relaxed_results, rounding_context) = self.solve_relaxed() + + # Round relaxed solution + # ============================ + rounding_results = self.rounding_scheme.round(rounding_context) + + # Process rounding results + # ============================ + # The rounding classes don't have enough information to evaluate the + # objective function, so they return a RoundingSolutionSample, which + # contains only part of the information in the SolutionSample. Here we + # fill in the rest. + samples: List[SolutionSample] = [] + for sample in rounding_results.samples: + samples.append( + SolutionSample( + x=sample.x, + fval=problem.objective.evaluate(sample.x), + probability=sample.probability, + status=self._get_feasibility_status(problem, sample.x), + ) + ) + + # TODO: rewrite this logic once the converters are integrated. + # we need to be very careful about ensuring that the problem + # sense is taken into account in the relaxed solution and the rounding + # this is likely only a temporary patch while we are sticking to a + # maximization problem. + fsense = {"MINIMIZE": min, "MAXIMIZE": max}[problem.objective.sense.name] + best_sample = fsense(samples, key=lambda x: x.fval) + + return QuantumRandomAccessOptimizationResult( + samples=samples, + x=best_sample.x, + fval=best_sample.fval, + variables=problem.variables, + status=OptimizationResultStatus.SUCCESS, + relaxed_results=relaxed_results, + rounding_results=rounding_results, + relaxed_results_offset=self.encoding.offset, + sense=problem.objective.sense.value, + ) diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py new file mode 100644 index 000000000..1689b8599 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -0,0 +1,98 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2022. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Common classes for rounding schemes""" + +from typing import Dict, List, Tuple, Optional +from abc import ABC, abstractmethod +from dataclasses import dataclass + +import numpy as np + +from qiskit.opflow import PrimitiveOp + +from .encoding import QuantumRandomAccessEncoding, q2vars_from_var2op + + +# pylint: disable=too-few-public-methods + + +@dataclass +class RoundingSolutionSample: + """Partial SolutionSample for use in rounding results""" + + x: np.ndarray + probability: float + + +class RoundingContext: + """Information that is provided for rounding""" + + def __init__( + self, + *, + encoding: Optional[QuantumRandomAccessEncoding] = None, + var2op: Optional[Dict[int, Tuple[int, PrimitiveOp]]] = None, + q2vars: Optional[List[List[int]]] = None, + trace_values=None, + circuit=None, + _vars_per_qubit: Optional[int] = None, + ): + if encoding is not None: + if var2op is not None or q2vars is not None: + raise ValueError( + "Neither var2op nor q2vars should be provided if encoding is" + ) + if _vars_per_qubit is not None: + raise ValueError( + "_vars_per_qubit should not be provided if encoding is" + ) + self.var2op = encoding.var2op + self.q2vars = encoding.q2vars + self._vars_per_qubit = encoding.max_vars_per_qubit + else: + if var2op is None: + raise ValueError("Either an encoding or var2ops must be provided") + if _vars_per_qubit is None: + raise ValueError( + "_vars_per_qubit must be provided if encoding is not provided" + ) + self.var2op = var2op + self.q2vars = q2vars_from_var2op(var2op) if q2vars is None else q2vars + self._vars_per_qubit = _vars_per_qubit + + self.trace_values = trace_values # TODO: rename me + self.circuit = circuit # TODO: rename me + + +class RoundingResult: + """Base class for a rounding result""" + + def __init__(self, samples: List[RoundingSolutionSample], *, time_taken=None): + self._samples = samples + self.time_taken = time_taken + + @property + def samples(self) -> List[RoundingSolutionSample]: + """List of samples""" + return self._samples + + +class RoundingScheme(ABC): + """Base class for a rounding scheme""" + + @abstractmethod + def round(self, ctx: RoundingContext) -> RoundingResult: + """Perform rounding + + Returns: an instance of RoundingResult + """ diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py new file mode 100644 index 000000000..64da99f05 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -0,0 +1,83 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2022. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Semideterministic rounding""" + +from typing import Optional + +import numpy as np + +from .rounding_common import ( + RoundingSolutionSample, + RoundingScheme, + RoundingContext, + RoundingResult, +) + + +# pylint: disable=too-few-public-methods + + +class SemideterministicRoundingResult(RoundingResult): + """Result of semideterministic rounding""" + + +class SemideterministicRounding(RoundingScheme): + """Semideterministic rounding scheme + + This is referred to as "Pauli rounding" in + https://arxiv.org/abs/2111.03167v2. + + """ + + def __init__(self, *, seed: Optional[int] = None): + """ + Args: + seed: Seed for random number generator, which is used to resolve + expectation values near zero to either +1 or -1. + """ + super().__init__() + self.rng = np.random.RandomState(seed) + + def round(self, ctx: RoundingContext) -> SemideterministicRoundingResult: + """Perform semideterministic rounding""" + + trace_values = ctx.trace_values + + if trace_values is None: + raise NotImplementedError( + "Semideterministic rounding requires that trace_values be available." + ) + + if len(trace_values) != len(ctx.var2op): + raise ValueError( + f"trace_values has length {len(trace_values)}, " + "but there are {len(ctx.var2op)} decision variables." + ) + + def sign(val) -> int: + return 0 if (val > 0) else 1 + + rounded_vars = [ + sign(e) if not np.isclose(0, e) else self.rng.randint(2) + for e in trace_values + ] + + soln_samples = [ + RoundingSolutionSample( + x=np.asarray(rounded_vars), + probability=1.0, + ) + ] + + result = SemideterministicRoundingResult(soln_samples) + return result diff --git a/qiskit_optimization/algorithms/qrao/utils.py b/qiskit_optimization/algorithms/qrao/utils.py new file mode 100644 index 000000000..b679f61a0 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/utils.py @@ -0,0 +1,87 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2021, 2022. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Utility functions related to Quantum Random Access Optimization""" + +from typing import Optional + +import numpy as np +import networkx as nx +from docplex.mp.model import Model + +from qiskit_optimization import QuadraticProgram +from qiskit_optimization.translators import from_docplex_mp + + +def get_random_maxcut_docplex_model( + *, + num_nodes: int = 6, + degree: int = 3, + seed: Optional[int] = None, + weight: int = 1, + draw: bool = False, +) -> Model: + """Prepare a random DOcplex max-cut model + + Args: + + num_nodes: The number of vertices in the graph + + degree: The degree of each node in the graph + + seed: The seed to use for randomness + + weight: If `-1`, each edge will randomly have weight `-1` or `1`. + Otherwise, each graph edge will have a random integer weight + between `1` and `weight`, inclusive. (It follows that if `weight + == 1`, all edge weights are `1`). + + draw: If `True`, will call `nx.draw()` on the generated graph before + returning. + + """ + rng = np.random.RandomState(seed) + graph = nx.random_regular_graph(d=degree, n=num_nodes, seed=rng) + edges = np.zeros((num_nodes, num_nodes)) + for i, j in graph.edges(): + if weight == 1: + w = 1 + elif weight == -1: + w = rng.choice((-1, 1)) + else: + w = rng.randint(1, weight + 1) + edges[i, j] = edges[j, i] = w + + mod = Model("maxcut") + nodes = list(range(num_nodes)) + var = [mod.binary_var(name="x" + str(i)) for i in nodes] + mod.maximize( + mod.sum( + edges[i, j] * (var[i] + var[j] - 2 * var[i] * var[j]) + for i in nodes + for j in nodes + ) + ) + + if draw: # pragma: no cover (tested by treon) + nx.draw(graph, with_labels=True, font_color="whitesmoke") + + return mod + + +def get_random_maxcut_qp(*args, **kwargs) -> QuadraticProgram: + """Prepare a random max-cut `QuadraticProgram`, using the same arguments as + :func:`get_random_maxcut_docplex_model`. + + """ + mod = get_random_maxcut_docplex_model(*args, **kwargs) + return from_docplex_mp(mod) From 837326b5c1a71f2ea2911b41da0926081712ca80 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 13 Apr 2023 19:39:35 +0900 Subject: [PATCH 02/67] support primitives and remove opflow --- .../algorithms/qrao/encoding.py | 43 ++++++++++--- .../algorithms/qrao/magic_rounding.py | 63 +++++++++++-------- 2 files changed, 70 insertions(+), 36 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/encoding.py b/qiskit_optimization/algorithms/qrao/encoding.py index 454089458..8115e9679 100644 --- a/qiskit_optimization/algorithms/qrao/encoding.py +++ b/qiskit_optimization/algorithms/qrao/encoding.py @@ -48,7 +48,10 @@ StateFn, CircuitStateFn, ) -from qiskit.quantum_info import SparsePauliOp + + + +from qiskit.quantum_info import SparsePauliOp, Pauli from qiskit_optimization.problems.quadratic_program import QuadraticProgram @@ -268,12 +271,18 @@ class QuantumRandomAccessEncoding: # This defines the convention of the Pauli operators (and their ordering) # for each encoding. + # OPERATORS = ( + # (Z,), # (1,1,1) QRAC + # (X, Z), # (2,1,p) QRAC, p ≈ 0.85 + # (X, Y, Z), # (3,1,p) QRAC, p ≈ 0.79 + # ) OPERATORS = ( - (Z,), # (1,1,1) QRAC - (X, Z), # (2,1,p) QRAC, p ≈ 0.85 - (X, Y, Z), # (3,1,p) QRAC, p ≈ 0.79 + (SparsePauliOp('Z'),), # (1,1,1) QRAC + (SparsePauliOp('X'), SparsePauliOp('Z')), # (2,1,p) QRAC, p ≈ 0.85 + (SparsePauliOp('X'), SparsePauliOp('Y'), SparsePauliOp('Z')), # (3,1,p) QRAC, p ≈ 0.79 ) + def __init__(self, max_vars_per_qubit: int = 3): if max_vars_per_qubit not in (1, 2, 3): raise ValueError("max_vars_per_qubit must be 1, 2, or 3") @@ -401,7 +410,7 @@ def _add_term(self, w: float, *variables: int) -> None: # Pauli operator. To generalize, we replace the `d` in that equation # with `d_prime`, defined as follows: d_prime = np.sqrt(self.max_vars_per_qubit) ** len(variables) - op = self.term2op(*variables).mul(w * d_prime) + op = self.term2op(*variables) * (w * d_prime) # We perform the following short-circuit *after* calling term2op so at # least we have confirmed that the user provided a valid variables list. if w == 0.0: @@ -416,7 +425,22 @@ def term2op(self, *variables: int) -> PauliSumOp: The decision variables provided must all be encoded on different qubits. """ - ops = [I] * self.num_qubits + # legacy code + # ops = [I] * self.num_qubits + # # ops = [SparsePauliOp(['I'])] * self.num_qubits + # done = set() + # for x in variables: + # pos, op = self._var2op[x] + # if pos in done: + # raise RuntimeError(f"Collision of variables: {variables}") + # ops[pos] = op + # done.add(pos) + # pauli_op = reduce(lambda x, y: x ^ y, ops) + # # Convert from PauliOp to PauliSumOp + # return PauliSumOp(SparsePauliOp(pauli_op.primitive, coeffs=[pauli_op.coeff])) + + # new code + ops = [SparsePauliOp('I')] * self.num_qubits done = set() for x in variables: pos, op = self._var2op[x] @@ -424,9 +448,10 @@ def term2op(self, *variables: int) -> PauliSumOp: raise RuntimeError(f"Collision of variables: {variables}") ops[pos] = op done.add(pos) - pauli_op = reduce(lambda x, y: x ^ y, ops) + pauli_op = reduce(lambda x, y: x.tensor(y), ops) # Convert from PauliOp to PauliSumOp - return PauliSumOp(SparsePauliOp(pauli_op.primitive, coeffs=[pauli_op.coeff])) + return pauli_op + @staticmethod def _generate_ising_terms( @@ -579,7 +604,7 @@ def freeze(self): going forward without having to make a copy as a distinct object. """ if self._frozen is False: - self._qubit_op = self._qubit_op.reduce() + self._qubit_op = self._qubit_op.simplify() self._frozen = True @property diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index eaabec82d..cf283aa67 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -21,6 +21,7 @@ import numpy as np from qiskit import QuantumCircuit +from qiskit.primitives import Sampler from qiskit.providers import Backend from qiskit.opflow import PrimitiveOp from qiskit.utils import QuantumInstance @@ -33,6 +34,8 @@ RoundingResult, ) +from qiskit.algorithms.exceptions import AlgorithmError + _invalid_backend_names = [ "aer_simulator_unitary", @@ -111,7 +114,7 @@ class MagicRounding(RoundingScheme): def __init__( self, - quantum_instance: QuantumInstance, + sampler: Sampler, *, basis_sampling: str = "uniform", seed: Optional[int] = None, @@ -142,7 +145,7 @@ def __init__( f"'{basis_sampling}' is not an implemented sampling method. " "Please choose either 'uniform' or 'weighted'." ) - self.quantum_instance = quantum_instance + self.sampler = sampler self.rng = np.random.RandomState(seed) self._basis_sampling = basis_sampling super().__init__() @@ -150,7 +153,7 @@ def __init__( @property def shots(self) -> int: """Shots count as configured by the given ``quantum_instance``.""" - return self.quantum_instance.run_config.shots + return self.sampler.options.get("shots") @property def basis_sampling(self): @@ -189,7 +192,7 @@ def _unpack_measurement_outcome( q, op = var2op[var] # get the decoding outcome index for the variable # corresponding to this Pauli op. - op_index = self._OP_INDICES[vars_per_qubit][str(op)] + op_index = self._OP_INDICES[vars_per_qubit][str(op.paulis[0])] # get the bits associated to this magic basis' # measurement outcomes bit_outcomes = self._DECODING[vars_per_qubit][basis[q]] @@ -233,7 +236,8 @@ def _evaluate_magic_bases(self, circuit, bases, basis_shots, vars_per_qubit): len(bases) == len(basis_shots) == len(basis_counts) """ - measure = not _is_original_statevector_simulator(self.quantum_instance.backend) + # measure = not _is_original_statevector_simulator(self.quantum_instance.backend) + measure = True circuits = self._make_circuits(circuit, bases, measure, vars_per_qubit) # Execute each of the rotated circuits and collect the results @@ -247,28 +251,33 @@ def _evaluate_magic_bases(self, circuit, bases, basis_shots, vars_per_qubit): circuit_indices_by_shots[shots].append(i) basis_counts: List[Optional[Dict[str, int]]] = [None] * len(circuits) - overall_shots = self.quantum_instance.run_config.shots - try: - for shots, indices in sorted( - circuit_indices_by_shots.items(), reverse=True - ): - self.quantum_instance.set_config(shots=shots) - result = self.quantum_instance.execute([circuits[i] for i in indices]) - counts_list = result.get_counts() - if not isinstance(counts_list, List): - # This is the only case where this should happen, and that - # it does at all (namely, when a single-element circuit - # list is provided) is a weird API quirk of Qiskit. - # https://github.com/Qiskit/qiskit-terra/issues/8103 - assert len(indices) == 1 - counts_list = [counts_list] - assert len(indices) == len(counts_list) - for i, counts in zip(indices, counts_list): - basis_counts[i] = counts - finally: - # We've temporarily modified quantum_instance; now we restore it to - # its initial state. - self.quantum_instance.set_config(shots=overall_shots) + overall_shots = self.shots + + for shots, indices in sorted( + circuit_indices_by_shots.items(), reverse=True + ): + # self.quantum_instance.set_config(shots=shots) + # result = self.quantum_instance.execute([circuits[i] for i in indices]) + # counts_list = result.get_counts() + try: + job = self.sampler.run([circuits[i] for i in indices], shots=shots) + result = job.result() + except Exception as exc: + raise AlgorithmError("The primitive job to evaluate the energy failed!") from exc + + counts_list = [dist.binary_probabilities() for dist in result.quasi_dists] + + if not isinstance(counts_list, List): + # This is the only case where this should happen, and that + # it does at all (namely, when a single-element circuit + # list is provided) is a weird API quirk of Qiskit. + # https://github.com/Qiskit/qiskit-terra/issues/8103 + assert len(indices) == 1 + counts_list = [counts_list] + assert len(indices) == len(counts_list) + for i, counts in zip(indices, counts_list): + basis_counts[i] = counts + assert None not in basis_counts # Process the outcomes and extract expectation of decision vars From 6e914ce1f8aa750c549c950b6f7420c724e3ae95 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Sun, 16 Apr 2023 16:21:33 +0900 Subject: [PATCH 03/67] update qrao --- .../algorithms/qrao/__init__.py | 60 +- .../algorithms/qrao/encoding.py | 670 ------------------ .../qrao/encoding_commutation_verifier.py | 63 ++ .../algorithms/qrao/magic_rounding.py | 248 ++++--- .../qrao/prototype-qrao.code-workspace | 23 + .../qrao/quantum_random_access_encoding.py | 584 +++++++++++++++ .../qrao/quantum_random_access_optimizer.py | 293 +++----- .../algorithms/qrao/rounding_common.py | 76 +- .../qrao/semideterministic_rounding.py | 30 +- 9 files changed, 998 insertions(+), 1049 deletions(-) delete mode 100644 qiskit_optimization/algorithms/qrao/encoding.py create mode 100644 qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py create mode 100644 qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace create mode 100644 qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index 35a3d6851..87056544f 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -1,6 +1,6 @@ # This code is part of Qiskit. # -# (C) Copyright IBM 2022. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -11,47 +11,53 @@ # that they have been altered from the originals. """ -QRAO classes and functions -========================== +Quantum Random Access Optimization (:mod:`qiskit_optimization.algorithms.qrao`) +======================================================================================= -Quantum Random Access Optimization. +.. currentmodule:: qiskit_optimization.algorithms.qrao + + +Quantum Random Access Encoding and Rounding +=========================================== .. autosummary:: :toctree: ../stubs/ + :nosignatures: - encoding - rounding_common - SemideterministicRounding - MagicRounding + EncodingCommutationVerifier + QuantumRandomAccessEncoding QuantumRandomAccessOptimizer - utils -""" + QuantumRandomAccessOptimizationResult -from importlib_metadata import version as metadata_version, PackageNotFoundError +Rounding schemes +================= -from .encoding import QuantumRandomAccessEncoding +.. autosummary:: + :toctree: ../stubs/ + :nosignatures: -from .rounding_common import RoundingScheme, RoundingContext, RoundingResult -from .semideterministic_rounding import ( - SemideterministicRounding, - SemideterministicRoundingResult, -) -from .magic_rounding import MagicRounding, MagicRoundingResult + MagicRounding + MagicRoundingResult + RoundingScheme + RoundingContext + RoundingResult + SemideterministicRounding + SemideterministicRoundingResult + +""" +from .encoding_commutation_verifier import EncodingCommutationVerifier +from .quantum_random_access_encoding import QuantumRandomAccessEncoding +from .magic_rounding import MagicRounding, MagicRoundingResult from .quantum_random_access_optimizer import ( - QuantumRandomAccessOptimizer, QuantumRandomAccessOptimizationResult, + QuantumRandomAccessOptimizer, ) - - -try: - __version__ = metadata_version("qrao") -except PackageNotFoundError: # pragma: no cover - # package is not installed - pass - +from .rounding_common import RoundingContext, RoundingResult, RoundingScheme +from .semideterministic_rounding import SemideterministicRounding, SemideterministicRoundingResult __all__ = [ + "EncodingCommutationVerifier", "QuantumRandomAccessEncoding", "RoundingScheme", "RoundingContext", diff --git a/qiskit_optimization/algorithms/qrao/encoding.py b/qiskit_optimization/algorithms/qrao/encoding.py deleted file mode 100644 index 8115e9679..000000000 --- a/qiskit_optimization/algorithms/qrao/encoding.py +++ /dev/null @@ -1,670 +0,0 @@ -# This code is part of Qiskit. -# -# (C) Copyright IBM 2019, 2022. -# -# This code is licensed under the Apache License, Version 2.0. You may -# obtain a copy of this license in the LICENSE.txt file in the root directory -# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. -# -# Any modifications or derivative works of this code must retain this -# copyright notice, and modified files need to carry a notice indicating -# that they have been altered from the originals. - -"""Quantum Random Access Encoding module. - -Contains code dealing with QRACs (quantum random access codes) and preparation -of such states. - -.. autosummary:: - :toctree: ../stubs/ - - z_to_31p_qrac_basis_circuit - z_to_21p_qrac_basis_circuit - qrac_state_prep_1q - qrac_state_prep_multiqubit - QuantumRandomAccessEncoding - -""" - -from typing import Tuple, List, Dict, Optional, Union -from collections import defaultdict -from functools import reduce -from itertools import chain - -import numpy as np -import rustworkx as rx - -from qiskit import QuantumCircuit -from qiskit.opflow import ( - I, - X, - Y, - Z, - PauliSumOp, - PrimitiveOp, - CircuitOp, - Zero, - One, - StateFn, - CircuitStateFn, -) - - - -from qiskit.quantum_info import SparsePauliOp, Pauli - -from qiskit_optimization.problems.quadratic_program import QuadraticProgram - - -def _ceildiv(n: int, d: int) -> int: - """Perform ceiling division in integer arithmetic - - >>> _ceildiv(0, 3) - 0 - >>> _ceildiv(1, 3) - 1 - >>> _ceildiv(3, 3) - 1 - >>> _ceildiv(4, 3) - 2 - """ - return (n - 1) // d + 1 - - -def z_to_31p_qrac_basis_circuit(basis: List[int]) -> QuantumCircuit: - """Return the basis rotation corresponding to the (3,1,p)-QRAC - - Args: - - basis: 0, 1, 2, or 3 for each qubit - - Returns: - The ``QuantumCircuit`` implementing the rotation. - """ - circ = QuantumCircuit(len(basis)) - BETA = np.arccos(1 / np.sqrt(3)) - for i, base in enumerate(reversed(basis)): - if base == 0: - circ.r(-BETA, -np.pi / 4, i) - elif base == 1: - circ.r(np.pi - BETA, np.pi / 4, i) - elif base == 2: - circ.r(np.pi + BETA, np.pi / 4, i) - elif base == 3: - circ.r(BETA, -np.pi / 4, i) - else: - raise ValueError(f"Unknown base: {base}") - return circ - - -def z_to_21p_qrac_basis_circuit(basis: List[int]) -> QuantumCircuit: - """Return the basis rotation corresponding to the (2,1,p)-QRAC - - Args: - - basis: 0 or 1 for each qubit - - Returns: - The ``QuantumCircuit`` implementing the rotation. - """ - circ = QuantumCircuit(len(basis)) - for i, base in enumerate(reversed(basis)): - if base == 0: - circ.r(-1 * np.pi / 4, -np.pi / 2, i) - elif base == 1: - circ.r(-3 * np.pi / 4, -np.pi / 2, i) - else: - raise ValueError(f"Unknown base: {base}") - return circ - - -def qrac_state_prep_1q(*m: int) -> CircuitStateFn: - """Prepare a single qubit QRAC state - - This function accepts 1, 2, or 3 arguments, in which case it generates a - 1-QRAC, 2-QRAC, or 3-QRAC, respectively. - - Args: - - m: The data to be encoded. Each argument must be 0 or 1. - - Returns: - - The circuit state function. - - """ - if len(m) not in (1, 2, 3): - raise TypeError( - f"qrac_state_prep_1q requires 1, 2, or 3 arguments, not {len(m)}." - ) - if not all(mi in (0, 1) for mi in m): - raise ValueError("Each argument to qrac_state_prep_1q must be 0 or 1.") - - if len(m) == 3: - # Prepare (3,1,p)-qrac - - # In the following lines, the input bits are XOR'd to match the - # conventions used in the paper. - - # To understand why this transformation happens, - # observe that the two states that define each magic basis - # correspond to the same bitstrings but with a global bitflip. - - # Thus the three bits of information we use to construct these states are: - # c0,c1 : two bits to pick one of four magic bases - # c2: one bit to indicate which magic basis projector we are interested in. - - c0 = m[0] ^ m[1] ^ m[2] - c1 = m[1] ^ m[2] - c2 = m[0] ^ m[2] - - base = [2 * c1 + c2] - cob = z_to_31p_qrac_basis_circuit(base) - # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf - # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| - sf = One if (c0) else Zero - # Apply the z_to_magic_basis circuit to either |0> or |1> - logical = CircuitOp(cob) @ sf - elif len(m) == 2: - # Prepare (2,1,p)-qrac - # (00,01) or (10,11) - c0 = m[0] - # (00,11) or (01,10) - c1 = m[0] ^ m[1] - - base = [c1] - cob = z_to_21p_qrac_basis_circuit(base) - # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf - # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| - sf = One if (c0) else Zero - # Apply the z_to_magic_basis circuit to either |0> or |1> - logical = CircuitOp(cob) @ sf - else: - assert len(m) == 1 - c0 = m[0] - sf = One if (c0) else Zero - - logical = sf - - return logical.to_circuit_op() - - -def qrac_state_prep_multiqubit( - dvars: Union[Dict[int, int], List[int]], - q2vars: List[List[int]], - max_vars_per_qubit: int, -) -> CircuitStateFn: - """ - Prepare a multiqubit QRAC state. - - Args: - dvars: state of each decision variable (0 or 1) - """ - remaining_dvars = set(dvars if isinstance(dvars, dict) else range(len(dvars))) - ordered_bits = [] - for qi_vars in q2vars: - if len(qi_vars) > max_vars_per_qubit: - raise ValueError( - "Each qubit is expected to be associated with at most " - f"`max_vars_per_qubit` ({max_vars_per_qubit}) variables, " - f"not {len(qi_vars)} variables." - ) - if not qi_vars: - # This probably actually doesn't cause any issues, but why support - # it (and test this edge case) if we don't have to? - raise ValueError( - "There is a qubit without any decision variables assigned to it." - ) - qi_bits: List[int] = [] - for dv in qi_vars: - try: - qi_bits.append(dvars[dv]) - except (KeyError, IndexError): - raise ValueError( - f"Decision variable not included in dvars: {dv}" - ) from None - try: - remaining_dvars.remove(dv) - except KeyError: - raise ValueError( - f"Unused decision variable(s) in dvars: {remaining_dvars}" - ) from None - # Pad with zeros if there are fewer than `max_vars_per_qubit`. - # NOTE: This results in everything being encoded as an n-QRAC, - # even if there are fewer than n decision variables encoded in the qubit. - # In the future, we plan to make the encoding "adaptive" so that the - # optimal encoding is used on each qubit, based on the number of - # decision variables assigned to that specific qubit. - # However, we cannot do this until magic state rounding supports 2-QRACs. - while len(qi_bits) < max_vars_per_qubit: - qi_bits.append(0) - - ordered_bits.append(qi_bits) - - if remaining_dvars: - raise ValueError(f"Not all dvars were included in q2vars: {remaining_dvars}") - - qracs = [qrac_state_prep_1q(*qi_bits) for qi_bits in ordered_bits] - logical = reduce(lambda x, y: x ^ y, qracs) - return logical - - -def q2vars_from_var2op(var2op: Dict[int, Tuple[int, PrimitiveOp]]) -> List[List[int]]: - """Calculate q2vars given var2op""" - num_qubits = max(qubit_index for qubit_index, _ in var2op.values()) + 1 - q2vars: List[List[int]] = [[] for i in range(num_qubits)] - for var, (q, _) in var2op.items(): - q2vars[q].append(var) - return q2vars - - -class QuantumRandomAccessEncoding: - """This class specifies a Quantum Random Access Code that can be used to encode - the binary variables of a QUBO (quadratic unconstrained binary optimization - problem). - - Args: - max_vars_per_qubit: maximum possible compression ratio. - Supported values are 1, 2, or 3. - - """ - - # This defines the convention of the Pauli operators (and their ordering) - # for each encoding. - # OPERATORS = ( - # (Z,), # (1,1,1) QRAC - # (X, Z), # (2,1,p) QRAC, p ≈ 0.85 - # (X, Y, Z), # (3,1,p) QRAC, p ≈ 0.79 - # ) - OPERATORS = ( - (SparsePauliOp('Z'),), # (1,1,1) QRAC - (SparsePauliOp('X'), SparsePauliOp('Z')), # (2,1,p) QRAC, p ≈ 0.85 - (SparsePauliOp('X'), SparsePauliOp('Y'), SparsePauliOp('Z')), # (3,1,p) QRAC, p ≈ 0.79 - ) - - - def __init__(self, max_vars_per_qubit: int = 3): - if max_vars_per_qubit not in (1, 2, 3): - raise ValueError("max_vars_per_qubit must be 1, 2, or 3") - self._ops = self.OPERATORS[max_vars_per_qubit - 1] - - self._qubit_op: Optional[PauliSumOp] = None - self._offset: Optional[float] = None - self._problem: Optional[QuadraticProgram] = None - self._var2op: Dict[int, Tuple[int, PrimitiveOp]] = {} - self._q2vars: List[List[int]] = [] - self._frozen = False - - @property - def num_qubits(self) -> int: - """Number of qubits""" - return len(self._q2vars) - - @property - def num_vars(self) -> int: - """Number of decision variables""" - return len(self._var2op) - - @property - def max_vars_per_qubit(self) -> int: - """Maximum number of variables per qubit - - This is set in the constructor and controls the maximum compression ratio - """ - - return len(self._ops) - - @property - def var2op(self) -> Dict[int, Tuple[int, PrimitiveOp]]: - """Maps each decision variable to ``(qubit_index, operator)``""" - return self._var2op - - @property - def q2vars(self) -> List[List[int]]: - """Each element contains the list of decision variable indice(s) encoded on that qubit""" - return self._q2vars - - @property - def compression_ratio(self) -> float: - """Compression ratio - - Number of decision variables divided by number of qubits - """ - return self.num_vars / self.num_qubits - - @property - def minimum_recovery_probability(self) -> float: - """Minimum recovery probability, as set by ``max_vars_per_qubit``""" - n = self.max_vars_per_qubit - return (1 + 1 / np.sqrt(n)) / 2 - - @property - def qubit_op(self) -> PauliSumOp: - """Relaxed Hamiltonian operator""" - if self._qubit_op is None: - raise AttributeError( - "No objective function has been provided from which a " - "qubit Hamiltonian can be constructed. Please use the " - "encode method if you wish to manually compile " - "this field." - ) - return self._qubit_op - - @property - def offset(self) -> float: - """Relaxed Hamiltonian offset""" - if self._offset is None: - raise AttributeError( - "No objective function has been provided from which a " - "qubit Hamiltonian can be constructed. Please use the " - "encode method if you wish to manually compile " - "this field." - ) - return self._offset - - @property - def problem(self) -> QuadraticProgram: - """The ``QuadraticProgram`` used as basis for the encoding""" - if self._problem is None: - raise AttributeError( - "No quadratic program has been associated with this object. " - "Please use the encode method if you wish to do so." - ) - return self._problem - - def _add_variables(self, variables: List[int]) -> None: - self.ensure_thawed() - # NOTE: If this is called multiple times, it *always* adds an - # additional qubit (see final line), even if aggregating them into a - # single call would have resulted in fewer qubits. - if self._qubit_op is not None: - raise RuntimeError( - "_add_variables() cannot be called once terms have been added " - "to the operator, as the number of qubits must thereafter " - "remain fixed." - ) - if not variables: - return - if len(variables) != len(set(variables)): - raise ValueError("Added variables must be unique") - for v in variables: - if v in self._var2op: - raise ValueError("Added variables cannot collide with existing ones") - # Modify the object now that error checking is complete. - n = len(self._ops) - old_num_qubits = len(self._q2vars) - num_new_qubits = _ceildiv(len(variables), n) - # Populate self._var2op and self._q2vars - for _ in range(num_new_qubits): - self._q2vars.append([]) - for i, v in enumerate(variables): - qubit, op = divmod(i, n) - qubit_index = old_num_qubits + qubit - assert v not in self._var2op # was checked above - self._var2op[v] = (qubit_index, self._ops[op]) - self._q2vars[qubit_index].append(v) - - def _add_term(self, w: float, *variables: int) -> None: - self.ensure_thawed() - # Eq. (31) in https://arxiv.org/abs/2111.03167v2 assumes a weight-2 - # Pauli operator. To generalize, we replace the `d` in that equation - # with `d_prime`, defined as follows: - d_prime = np.sqrt(self.max_vars_per_qubit) ** len(variables) - op = self.term2op(*variables) * (w * d_prime) - # We perform the following short-circuit *after* calling term2op so at - # least we have confirmed that the user provided a valid variables list. - if w == 0.0: - return - if self._qubit_op is None: - self._qubit_op = op - else: - self._qubit_op += op - - def term2op(self, *variables: int) -> PauliSumOp: - """Construct a ``PauliSumOp`` that is a product of encoded decision ``variable``\\(s). - - The decision variables provided must all be encoded on different qubits. - """ - # legacy code - # ops = [I] * self.num_qubits - # # ops = [SparsePauliOp(['I'])] * self.num_qubits - # done = set() - # for x in variables: - # pos, op = self._var2op[x] - # if pos in done: - # raise RuntimeError(f"Collision of variables: {variables}") - # ops[pos] = op - # done.add(pos) - # pauli_op = reduce(lambda x, y: x ^ y, ops) - # # Convert from PauliOp to PauliSumOp - # return PauliSumOp(SparsePauliOp(pauli_op.primitive, coeffs=[pauli_op.coeff])) - - # new code - ops = [SparsePauliOp('I')] * self.num_qubits - done = set() - for x in variables: - pos, op = self._var2op[x] - if pos in done: - raise RuntimeError(f"Collision of variables: {variables}") - ops[pos] = op - done.add(pos) - pauli_op = reduce(lambda x, y: x.tensor(y), ops) - # Convert from PauliOp to PauliSumOp - return pauli_op - - - @staticmethod - def _generate_ising_terms( - problem: QuadraticProgram, - ) -> Tuple[float, np.ndarray, np.ndarray]: - num_vars = problem.get_num_vars() - - # set a sign corresponding to a maximized or minimized problem: - # 1 is for minimized problem, -1 is for maximized problem. - sense = problem.objective.sense.value - - # convert a constant part of the objective function into Hamiltonian. - offset = problem.objective.constant * sense - - # convert linear parts of the objective function into Hamiltonian. - linear = np.zeros(num_vars) - for idx, coef in problem.objective.linear.to_dict().items(): - assert isinstance(idx, int) # hint for mypy - weight = coef * sense / 2 - linear[idx] -= weight - offset += weight - - # convert quadratic parts of the objective function into Hamiltonian. - quad = np.zeros((num_vars, num_vars)) - for (i, j), coef in problem.objective.quadratic.to_dict().items(): - assert isinstance(i, int) # hint for mypy - assert isinstance(j, int) # hint for mypy - weight = coef * sense / 4 - if i == j: - linear[i] -= 2 * weight - offset += 2 * weight - else: - quad[i, j] += weight - linear[i] -= weight - linear[j] -= weight - offset += weight - - return offset, linear, quad - - @staticmethod - def _find_variable_partition(quad: np.ndarray) -> Dict[int, List[int]]: - num_nodes = quad.shape[0] - assert quad.shape == (num_nodes, num_nodes) - graph = rx.PyGraph() - graph.add_nodes_from(range(num_nodes)) - graph.add_edges_from_no_data(list(zip(*np.where(quad != 0)))) - node2color = rx.graph_greedy_color(graph) - color2node: Dict[int, List[int]] = defaultdict(list) - for node, color in sorted(node2color.items()): - color2node[color].append(node) - return color2node - - def encode(self, problem: QuadraticProgram) -> None: - """Encode the (n,1,p) QRAC relaxed Hamiltonian of this problem. - - We associate to each binary decision variable one bit of a - (n,1,p) Quantum Random Access Code. This is done in such a way that the - given problem's objective function commutes with the encoding. - - After being called, the object will have the following attributes: - qubit_op: The qubit operator encoding the input QuadraticProgram. - offset: The constant value in the encoded Hamiltonian. - problem: The ``problem`` used for encoding. - - Inputs: - problem: A QuadraticProgram object encoding a QUBO optimization problem - - Raises: - RuntimeError: if the ``problem`` isn't a QUBO or if the current - object has been used already - - """ - # Ensure fresh object - if self.num_qubits > 0: - raise RuntimeError( - "Must call encode() on an Encoding that has not been used already" - ) - - # if problem has variables that are not binary, raise an error - if problem.get_num_vars() > problem.get_num_binary_vars(): - raise RuntimeError( - "The type of all variables must be binary. " - "You can use `QuadraticProgramToQubo` converter " - "to convert integer variables to binary variables. " - "If the problem contains continuous variables, `qrao` " - "cannot handle it." - ) - - # if constraints exist, raise an error - if problem.linear_constraints or problem.quadratic_constraints: - raise RuntimeError( - "There must be no constraint in the problem. " - "You can use `QuadraticProgramToQubo` converter to convert " - "constraints to penalty terms of the objective function." - ) - - num_vars = problem.get_num_vars() - - # Generate the decision variable terms in terms of Ising variables (+1 or -1) - offset, linear, quad = self._generate_ising_terms(problem) - - # Find variable partition (a graph coloring is sufficient) - variable_partition = self._find_variable_partition(quad) - - # The other methods of the current class allow for the variables to - # have arbitrary integer indices [i.e., they need not correspond to - # range(num_vars)], and the tests corresponding to this file ensure - # that this works. However, the current method is a high-level one - # that takes a QuadraticProgram, which always has its variables - # numbered sequentially. Furthermore, other portions of the QRAO code - # base [most notably the assignment of variable_ops in solve_relaxed() - # and the corresponding result objects] assume that the variables are - # numbered from 0 to (num_vars - 1). So we enforce that assumption - # here, both as a way of documenting it and to make sure - # _find_variable_partition() returns a sensible result (in case the - # user overrides it). - assert sorted(chain.from_iterable(variable_partition.values())) == list( - range(num_vars) - ) - - # generate a Hamiltonian - for _, v in sorted(variable_partition.items()): - self._add_variables(sorted(v)) - for i in range(num_vars): - w = linear[i] - if w != 0: - self._add_term(w, i) - for i in range(num_vars): - for j in range(num_vars): - w = quad[i, j] - if w != 0: - self._add_term(w, i, j) - - self._offset = offset - self._problem = problem - - # This is technically optional and can wait until the optimizer is - # constructed, but there's really no reason not to freeze - # immediately. - self.freeze() - - def freeze(self): - """Freeze the object to prevent further modification. - - Once an instance of this class is frozen, ``_add_variables`` and ``_add_term`` - can no longer be called. - - This operation is idempotent. There is no way to undo it, as it exists - to allow another object to rely on this one not changing its state - going forward without having to make a copy as a distinct object. - """ - if self._frozen is False: - self._qubit_op = self._qubit_op.simplify() - self._frozen = True - - @property - def frozen(self) -> bool: - """``True`` if the object can no longer be modified, ``False`` otherwise.""" - return self._frozen - - def ensure_thawed(self) -> None: - """Raise a ``RuntimeError`` if the object is frozen and thus cannot be modified.""" - if self._frozen: - raise RuntimeError("Cannot modify an encoding that has been frozen") - - def state_prep(self, dvars: Union[Dict[int, int], List[int]]) -> CircuitStateFn: - """Prepare a multiqubit QRAC state.""" - return qrac_state_prep_multiqubit(dvars, self.q2vars, self.max_vars_per_qubit) - - -class EncodingCommutationVerifier: - """Class for verifying that the relaxation commutes with the objective function - - See also the "check encoding problem commutation" how-to notebook. - """ - - def __init__(self, encoding: QuantumRandomAccessEncoding): - self._encoding = encoding - - def __len__(self) -> int: - return 2**self._encoding.num_vars - - def __iter__(self): - for i in range(len(self)): - yield self[i] - - def __getitem__(self, i: int) -> Tuple[str, float, float]: - if i not in range(len(self)): - raise IndexError(f"Index out of range: {i}") - - encoding = self._encoding - str_dvars = ("{0:0" + str(encoding.num_vars) + "b}").format(i) - dvars = [int(b) for b in str_dvars] - encoded_bitstr = encoding.state_prep(dvars) - - # Offset accounts for the value of the encoded Hamiltonian's - # identity coefficient. This term need not be evaluated directly as - # Tr[I•rho] is always 1. - offset = encoding.offset - - # Evaluate Un-encoded Problem - # ======================== - # `sense` accounts for sign flips depending on whether - # we are minimizing or maximizing the objective function - problem = encoding.problem - sense = problem.objective.sense.value - obj_val = problem.objective.evaluate(dvars) * sense - - # Evaluate Encoded Problem - # ======================== - encoded_problem = encoding.qubit_op # H - encoded_obj_val = ( - np.real((~StateFn(encoded_problem) @ encoded_bitstr).eval()) + offset - ) - - return (str_dvars, obj_val, encoded_obj_val) diff --git a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py new file mode 100644 index 000000000..76f6958e5 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py @@ -0,0 +1,63 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""The EncodingCommutationVerifier.""" + +from typing import Tuple + +from qiskit.primitives import Estimator + +from qiskit_optimization.exceptions import QiskitOptimizationError + +from .quantum_random_access_encoding import QuantumRandomAccessEncoding + + +class EncodingCommutationVerifier: + """Class for verifying that the relaxation commutes with the objective function.""" + + def __init__(self, encoding: QuantumRandomAccessEncoding): + self._encoding = encoding + self._estimator = Estimator() + + def __len__(self) -> int: + return 2**self._encoding.num_vars + + def __iter__(self): + for i in range(len(self)): + yield self[i] + + def __getitem__(self, i: int) -> Tuple[str, float, float]: + if i not in range(len(self)): + raise IndexError(f"Index out of range: {i}") + + encoding = self._encoding + str_dvars = f"{i:0{encoding.num_vars}b}" + dvars = [int(b) for b in str_dvars] + encoded_bitstr_qc = encoding.state_prep(dvars) + + # Evaluate the original objective function + problem = encoding.problem + sense = problem.objective.sense.value + obj_val = problem.objective.evaluate(dvars) * sense + + # Evaluate the encoded Hamiltonian + encoded_op = encoding.qubit_op + offset = encoding.offset + + job = self._estimator.run([encoded_bitstr_qc], [encoded_op]) + + try: + encoded_obj_val = job.result().values[0] + offset + except Exception as exc: + raise QiskitOptimizationError("Estimator job failed.") from exc + + return (str_dvars, obj_val, encoded_obj_val) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index cf283aa67..f02e95019 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -10,7 +10,7 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -"""Magic bases rounding""" +"""Magic basis rounding module""" from typing import List, Dict, Tuple, Optional from collections import defaultdict @@ -26,7 +26,7 @@ from qiskit.opflow import PrimitiveOp from qiskit.utils import QuantumInstance -from .encoding import z_to_31p_qrac_basis_circuit, z_to_21p_qrac_basis_circuit +from .quantum_random_access_encoding import z_to_31p_qrac_basis_circuit, z_to_21p_qrac_basis_circuit from .rounding_common import ( RoundingSolutionSample, RoundingScheme, @@ -89,10 +89,9 @@ def basis_counts(self): class MagicRounding(RoundingScheme): - """ "Magic rounding" method - - This method is described in https://arxiv.org/abs/2111.03167v2. + """Magic rounding scheme + This scheme is described in https://arxiv.org/abs/2111.03167v2. """ _DECODING = { @@ -145,100 +144,62 @@ def __init__( f"'{basis_sampling}' is not an implemented sampling method. " "Please choose either 'uniform' or 'weighted'." ) - self.sampler = sampler + self._sampler = sampler self.rng = np.random.RandomState(seed) self._basis_sampling = basis_sampling super().__init__() + @property + def sampler(self) -> Sampler: + """Returns the ``Sampler`` used to sample the magic bases.""" + return self._sampler + @property def shots(self) -> int: - """Shots count as configured by the given ``quantum_instance``.""" - return self.sampler.options.get("shots") + """Returns the number of samples to collect from each magic basis.""" + return self._sampler.options.get("shots") @property def basis_sampling(self): """Basis sampling method (either ``"uniform"`` or ``"weighted"``).""" return self._basis_sampling - @property - def quantum_instance(self) -> QuantumInstance: - """Provides the ``Backend`` and the ``shots`` (samples) count.""" - return self._quantum_instance - - @quantum_instance.setter - def quantum_instance(self, quantum_instance: QuantumInstance) -> None: - backend_name = _backend_name(quantum_instance.backend) - if backend_name in _invalid_backend_names: - raise ValueError(f"{backend_name} is not supported.") - if _is_original_statevector_simulator(quantum_instance.backend): - warnings.warn( - 'Use of "statevector_simulator" is discouraged because it effectively ' - "brute-forces all possible solutions. We suggest using the newer " - '"aer_simulator_statevector" instead.' - ) - self._quantum_instance = quantum_instance - - def _unpack_measurement_outcome( - self, - bits: str, - basis: List[int], - var2op: Dict[int, Tuple[int, PrimitiveOp]], - vars_per_qubit: int, - ) -> List[int]: - output_bits = [] - # iterate in order over decision variables - # (assumes variables are numbered consecutively beginning with 0) - for var in range(len(var2op)): # pylint: disable=consider-using-enumerate - q, op = var2op[var] - # get the decoding outcome index for the variable - # corresponding to this Pauli op. - op_index = self._OP_INDICES[vars_per_qubit][str(op.paulis[0])] - # get the bits associated to this magic basis' - # measurement outcomes - bit_outcomes = self._DECODING[vars_per_qubit][basis[q]] - # select which measurement outcome we observed - # this gives up to 3 bits of information - magic_bits = bit_outcomes[bits[q]] - # Assign our variable's value depending on - # which pauli our variable was associated to - variable_value = magic_bits[op_index] - output_bits.append(variable_value) - return output_bits @staticmethod def _make_circuits( - circ: QuantumCircuit, bases: List[List[int]], measure: bool, vars_per_qubit: int + circ: QuantumCircuit, bases: List[List[int]], vars_per_qubit: int ) -> List[QuantumCircuit]: circuits = [] for basis in bases: if vars_per_qubit == 3: - qc = circ.compose( - z_to_31p_qrac_basis_circuit(basis).inverse(), inplace=False - ) + qc = circ.compose(z_to_31p_qrac_basis_circuit(basis).inverse(), inplace=False) elif vars_per_qubit == 2: - qc = circ.compose( - z_to_21p_qrac_basis_circuit(basis).inverse(), inplace=False - ) + qc = circ.compose(z_to_21p_qrac_basis_circuit(basis).inverse(), inplace=False) elif vars_per_qubit == 1: qc = circ.copy() - if measure: - qc.measure_all() + qc.measure_all() circuits.append(qc) return circuits - def _evaluate_magic_bases(self, circuit, bases, basis_shots, vars_per_qubit): + def _evaluate_magic_bases( + self, circuit: QuantumCircuit, bases: np.array, basis_shots: np.array, vars_per_qubit: int + ) -> List[Dict[str, int]]: """ - Given a circuit you wish to measure, a list of magic bases to measure, - and a list of the shots to use for each magic basis configuration. + Given a quantum circuit to measure, a list of magic bases to measure, and a list of the + shots to use for each magic basis configuration, measure the provided circuit in the magic + bases given and return the counts dictionaries associated with each basis measurement. - Measure the provided circuit in the magic bases given and return the counts - dictionaries associated with each basis measurement. + Args: + circuit: The quantum circuit to measure. + bases: A list of magic bases to measure. + basis_shots: A list of shots to use for each magic basis configuration. + vars_per_qubit: The number of decision variables per qubit. - len(bases) == len(basis_shots) == len(basis_counts) + Returns: + List[Dict[str, int]]: A list of counts dictionaries associated with each basis measurement. """ # measure = not _is_original_statevector_simulator(self.quantum_instance.backend) - measure = True - circuits = self._make_circuits(circuit, bases, measure, vars_per_qubit) + circuits = self._make_circuits(circuit, bases, vars_per_qubit) # Execute each of the rotated circuits and collect the results @@ -251,29 +212,26 @@ def _evaluate_magic_bases(self, circuit, bases, basis_shots, vars_per_qubit): circuit_indices_by_shots[shots].append(i) basis_counts: List[Optional[Dict[str, int]]] = [None] * len(circuits) - overall_shots = self.shots - for shots, indices in sorted( - circuit_indices_by_shots.items(), reverse=True - ): + for shots, indices in sorted(circuit_indices_by_shots.items(), reverse=True): # self.quantum_instance.set_config(shots=shots) # result = self.quantum_instance.execute([circuits[i] for i in indices]) # counts_list = result.get_counts() try: - job = self.sampler.run([circuits[i] for i in indices], shots=shots) + job = self._sampler.run([circuits[i] for i in indices], shots=shots) result = job.result() except Exception as exc: raise AlgorithmError("The primitive job to evaluate the energy failed!") from exc counts_list = [dist.binary_probabilities() for dist in result.quasi_dists] - if not isinstance(counts_list, List): - # This is the only case where this should happen, and that - # it does at all (namely, when a single-element circuit - # list is provided) is a weird API quirk of Qiskit. - # https://github.com/Qiskit/qiskit-terra/issues/8103 - assert len(indices) == 1 - counts_list = [counts_list] + # if not isinstance(counts_list, List): + # # This is the only case where this should happen, and that + # # it does at all (namely, when a single-element circuit + # # list is provided) is a weird API quirk of Qiskit. + # # https://github.com/Qiskit/qiskit-terra/issues/8103 + # assert len(indices) == 1 + # counts_list = [counts_list] assert len(indices) == len(counts_list) for i, counts in zip(indices, counts_list): basis_counts[i] = counts @@ -285,17 +243,49 @@ def _evaluate_magic_bases(self, circuit, bases, basis_shots, vars_per_qubit): # The "statevector_simulator", unlike all the others, returns # probabilities instead of integer counts. So if probabilities are # detected, we rescale them. - if any( - any(not isinstance(x, numbers.Integral) for x in counts.values()) - for counts in basis_counts - ): - basis_counts = [ + basis_counts = [ {key: val * basis_shots[i] for key, val in counts.items()} for i, counts in enumerate(basis_counts) ] + # if any( + # any(not isinstance(x, numbers.Integral) for x in counts.values()) + # for counts in basis_counts + # ): + # basis_counts = [ + # {key: val * basis_shots[i] for key, val in counts.items()} + # for i, counts in enumerate(basis_counts) + # ] + return basis_counts + def _unpack_measurement_outcome( + self, + bits: str, + basis: List[int], + var2op: Dict[int, Tuple[int, PrimitiveOp]], + vars_per_qubit: int, + ) -> List[int]: + output_bits = [] + # iterate in order over decision variables + # (assumes variables are numbered consecutively beginning with 0) + for var in range(len(var2op)): # pylint: disable=consider-using-enumerate + q, op = var2op[var] + # get the decoding outcome index for the variable + # corresponding to this Pauli op. + op_index = self._OP_INDICES[vars_per_qubit][str(op.paulis[0])] + # get the bits associated to this magic basis' + # measurement outcomes + bit_outcomes = self._DECODING[vars_per_qubit][basis[q]] + # select which measurement outcome we observed + # this gives up to 3 bits of information + magic_bits = bit_outcomes[bits[q]] + # Assign our variable's value depending on + # which pauli our variable was associated to + variable_value = magic_bits[op_index] + output_bits.append(variable_value) + return output_bits + def _compute_dv_counts(self, basis_counts, bases, var2op, vars_per_qubit): """ Given a list of bases, basis_shots, and basis_counts, convert @@ -309,9 +299,7 @@ def _compute_dv_counts(self, basis_counts, bases, var2op, vars_per_qubit): for bitstr, count in counts.items(): # For each bit in the observed bitstring... - soln = self._unpack_measurement_outcome( - bitstr, base, var2op, vars_per_qubit - ) + soln = self._unpack_measurement_outcome(bitstr, base, var2op, vars_per_qubit) soln = "".join([str(int(bit)) for bit in soln]) if soln in dv_counts: dv_counts[soln] += count @@ -319,10 +307,38 @@ def _compute_dv_counts(self, basis_counts, bases, var2op, vars_per_qubit): dv_counts[soln] = count return dv_counts - def _sample_bases_uniform(self, q2vars, vars_per_qubit): + def _sample_bases_uniform( + self, q2vars: List[List[int]], vars_per_qubit: int + ) -> Tuple[np.ndarray, np.ndarray]: + """ + Sample measurement bases for each qubit uniformly at random. If the number of shots + is not specified, we default to 1024. + + Args: + q2vars: A list of lists of integers. Each inner list contains the indices of decision + variables mapped to a specific qubit. + vars_per_qubit: The maximum number of decision variables that can be mapped to a + single qubit.. + + Returns: + A tuple containing two arrays: + bases: A 2D numpy array of shape (num_bases, num_qubits), where each row + corresponds to a basis configuration. Each element of the array is an + integer in the range [0, 2 ** (vars_per_qubit - 1) - 1]. The integer + represents the index of the basis to measure in for the corresponding + qubit. + basis_shots: A 1D numpy array of shape (num_bases,), where each element + corresponds to the number of shots to use for the corresponding basis in + the bases array. + """ + # If the number of shots is not specified, we default to 1024. + if self.shots is None: + shots = 1024 + else: + shots = self.shots bases = [ self.rng.choice(2 ** (vars_per_qubit - 1), size=len(q2vars)).tolist() - for _ in range(self.shots) + for _ in range(shots) ] bases, basis_shots = np.unique(bases, axis=0, return_counts=True) return bases, basis_shots @@ -370,21 +386,31 @@ def _sample_bases_weighted(self, q2vars, trace_values, vars_per_qubit): elif vars_per_qubit == 1: basis_probs.append([1.0]) bases = [ - [ - self.rng.choice(2 ** (vars_per_qubit - 1), p=probs) - for probs in basis_probs - ] + [self.rng.choice(2 ** (vars_per_qubit - 1), p=probs) for probs in basis_probs] for _ in range(self.shots) ] bases, basis_shots = np.unique(bases, axis=0, return_counts=True) return bases, basis_shots def round(self, ctx: RoundingContext) -> MagicRoundingResult: - """Perform magic rounding""" + """Perform magic rounding using the given RoundingContext. + Args: + ctx: The context containing the information needed for the rounding. + + Returns: + MagicRoundingResult: The results of the magic rounding process. + + Raises: + NotImplementedError: If the circuit is not available for magic rounding. + + """ start_time = time.time() - trace_values = ctx.trace_values + expectation_values = ctx.expectation_values circuit = ctx.circuit + q2vars = ctx.encoding.q2vars + var2op = ctx.encoding.var2op + vars_per_qubit = ctx.encoding.max_vars_per_qubit if circuit is None: raise NotImplementedError( @@ -392,38 +418,29 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: "semideterministic rounding instead." ) - # We've already checked that it is one of these two in the constructor if self.basis_sampling == "uniform": - bases, basis_shots = self._sample_bases_uniform( - ctx.q2vars, ctx._vars_per_qubit - ) - elif self.basis_sampling == "weighted": - if trace_values is None: + # uniform sampling + bases, basis_shots = self._sample_bases_uniform(q2vars, vars_per_qubit) + else: + # weighted sampling + if expectation_values is None: raise NotImplementedError( "Magic rounding with weighted sampling requires the trace values " "to be available, but they are not." ) bases, basis_shots = self._sample_bases_weighted( - ctx.q2vars, trace_values, ctx._vars_per_qubit - ) - else: # pragma: no cover - raise NotImplementedError( - f'No such basis sampling method: "{self.basis_sampling}".' + q2vars, expectation_values, vars_per_qubit ) - assert self.shots == np.sum(basis_shots) + # assert self.shots == np.sum(basis_shots) # For each of the Magic Bases sampled above, measure # the appropriate number of times (given by basis_shots) # and return the circuit results - basis_counts = self._evaluate_magic_bases( - circuit, bases, basis_shots, ctx._vars_per_qubit - ) + basis_counts = self._evaluate_magic_bases(circuit, bases, basis_shots, vars_per_qubit) # keys will be configurations of decision variables # values will be total number of observations. - soln_counts = self._compute_dv_counts( - basis_counts, bases, ctx.var2op, ctx._vars_per_qubit - ) + soln_counts = self._compute_dv_counts(basis_counts, bases, var2op, vars_per_qubit) soln_samples = [ RoundingSolutionSample( @@ -439,6 +456,7 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: assert len(bases) == len(basis_shots) == len(basis_counts) stop_time = time.time() + # Create a MagicRoundingResult object to return return MagicRoundingResult( samples=soln_samples, bases=bases, diff --git a/qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace b/qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace new file mode 100644 index 000000000..d2de79c12 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace @@ -0,0 +1,23 @@ +{ + "folders": [ + { + "path": "../../../../prototype-qrao" + }, + { + "path": "../../.." + }, + { + "path": "../../../../terra" + } + ], + "settings": { + "cSpell.words": [ + "ndarray", + "QRAC", + "qrao", + "qubits", + "QUBO" + ], + "esbonio.sphinx.confDir": "" + } +} \ No newline at end of file diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py new file mode 100644 index 000000000..1e1f81633 --- /dev/null +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -0,0 +1,584 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""The Quantum Random Access Encoding module.""" + +from collections import defaultdict +from functools import reduce +from typing import Dict, List, Optional, Tuple + +import numpy as np +import rustworkx as rx +from qiskit import QuantumCircuit +from qiskit.quantum_info import SparsePauliOp + +from qiskit_optimization.exceptions import QiskitOptimizationError +from qiskit_optimization.problems.quadratic_program import QuadraticProgram + + +def z_to_31p_qrac_basis_circuit(basis: List[int], bit_flip: int = 0) -> QuantumCircuit: + """Return the circuit that implements the rotation to the (3,1,p)-QRAC. + + Args: + basis: The basis, 0, 1, 2, or 3, for the qubit. + bit_flip: Whether to flip the state of the qubit. 1 for flip, 0 for no flip. + + Returns: + The ``QuantumCircuit`` implementing the rotation to the (3,1,p)-QRAC. + + Raises: + ValueError: If the basis is not 0, 1, 2, or 3 + """ + circ = QuantumCircuit(len(basis)) + BETA = np.arccos(1 / np.sqrt(3)) # pylint: disable=invalid-name + + if bit_flip: + # if bit_flip == 1: then flip the state of the first qubit to |1> + circ.x(0) + + for i, base in enumerate(reversed(basis)): + if base == 0: + circ.r(-BETA, -np.pi / 4, i) + elif base == 1: + circ.r(np.pi - BETA, np.pi / 4, i) + elif base == 2: + circ.r(np.pi + BETA, np.pi / 4, i) + elif base == 3: + circ.r(BETA, -np.pi / 4, i) + else: + raise ValueError(f"Unknown basis: {base}. Basis must be 0, 1, 2, or 3.") + return circ + + +def z_to_21p_qrac_basis_circuit(basis: int, bit_flip: int = 0) -> QuantumCircuit: + """Return the circuit that implements the rotation to the (2,1,p)-QRAC. + + Args: + basis: The basis, 0, 1, for the qubit. + bit_flip: Whether to flip the state of the qubit. 1 for flip, 0 for no flip. + + Returns: + The ``QuantumCircuit`` implementing the rotation to the (2,1,p)-QRAC. + + Raises: + ValueError: if the basis is not 0 or 1 + """ + circ = QuantumCircuit(1) + + if bit_flip: + # if bit_flip == 1: then flip the state of the first qubit to |1> + circ.x(0) + + for i, base in enumerate(reversed(basis)): + if base == 0: + circ.r(-1 * np.pi / 4, -np.pi / 2, i) + elif base == 1: + circ.r(-3 * np.pi / 4, -np.pi / 2, i) + else: + raise ValueError(f"Unknown basis: {base}. Basis must be 0, 1.") + return circ + + +def qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: + """ + Return the circuit that prepares the state for a (1,1,p), (2,1,p), or (3,1,p)-QRAC. + + Args: + bit_list: The bitstring to prepare. If 1 argument is given, then a (1,1,p)-QRAC is generated. + If 2 arguments are given, then a (2,1,p)-QRAC is generated. If 3 arguments are given, + then a (3,1,p)-QRAC is generated. + + Returns: + The ``QuantumCircuit`` implementing the state preparation. + + Raises: + TypeError: if the number of arguments is not 1, 2, or 3 + ValueError: if any of the arguments are not 0 or 1 + """ + if len(bit_list) not in (1, 2, 3): + raise TypeError(f"qrac_state_prep_1q requires 1, 2, or 3 arguments, not {len(bit_list)}.") + if not all(bit in (0, 1) for bit in bit_list): + raise ValueError("Each argument to qrac_state_prep_1q must be 0 or 1.") + + if len(bit_list) == 3: + # Prepare (3,1,p)-qrac + # In the following lines, the input bits are XOR'd to match the + # conventions used in the paper. + # To understand why this transformation happens, + # observe that the two states that define each magic basis + # correspond to the same bitstrings but with a global bitflip. + # Thus the three bits of information we use to construct these states are: + # c0,c1 : two bits to pick one of four magic bases + # c2: one bit to indicate which magic basis projector we are interested in. + + c0 = bit_list[0] ^ bit_list[1] ^ bit_list[2] + c1 = bit_list[1] ^ bit_list[2] + c2 = bit_list[0] ^ bit_list[2] + + # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf + # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| + base = 2 * c1 + c2 + circ = z_to_31p_qrac_basis_circuit(base, c0) + + elif len(bit_list) == 2: + # Prepare (2,1,p)-qrac + # (00,01) or (10,11) + c0 = bit_list[0] + # (00,11) or (01,10) + c1 = bit_list[0] ^ bit_list[1] + + # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf + # # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| + base = c1 + circ = z_to_21p_qrac_basis_circuit(base, c0) + + else: + c0 = bit_list[0] + circ = QuantumCircuit(1) + if c0: + circ.x(0) + + return circ + + +def qrac_state_prep_multiqubit( + dvars: List[int], + q2vars: List[List[int]], + max_vars_per_qubit: int, +) -> QuantumCircuit: + """Prepares a multiqubit QRAC state. + + Args: + dvars: The state of each decision variable (0 or 1). + q2vars: A list of lists of integers. Each inner list contains the indices of decision variables + mapped to a specific qubit. + max_vars_per_qubit: The maximum number of decision variables that can be mapped to a + single qubit. + + Returns: + A QuantumCircuit object representing the prepared state. + + Raises: + ValueError: If any qubit is associated with more than ``max_vars_per_qubit`` variables. + ValueError: If a decision variable in ``q2vars`` is not included in ``dvars``. + ValueError: If there are unused decision variables in `dvars` after mapping to qubits. + """ + # Create a set of all remaining decision variables + remaining_dvars = set(range(len(dvars))) + # Create a list to store the binary mappings of each qubit to its corresponding decision variables + variable_mappings: List[List[int]] = [] + # Check that each qubit is associated with at most max_vars_per_qubit variables + for qi_vars in q2vars: + if len(qi_vars) > max_vars_per_qubit: + raise ValueError( + "Each qubit is expected to be associated with at most " + f"`max_vars_per_qubit` ({max_vars_per_qubit}) variables, " + f"not {len(qi_vars)} variables." + ) + # Create a list to store the binary mapping of the current qubit + qi_bits: List[int] = [] + + # Map each decision variable associated with the current qubit to a binary value and add it + # to the qubit bits + for dv in qi_vars: + try: + qi_bits.append(dvars[dv]) + except IndexError: + raise ValueError(f"Decision variable not included in dvars: {dv}") from None + try: + remaining_dvars.remove(dv) + except KeyError: + raise ValueError( + f"Unused decision variable(s) in dvars: {remaining_dvars}" + ) from None + + # Pad with zeros if necessary + while len(qi_bits) < max_vars_per_qubit: + qi_bits.append(0) + + variable_mappings.append(qi_bits) + + # Raise an error if not all decision variables are used + if remaining_dvars: + raise ValueError(f"Not all dvars were included in q2vars: {remaining_dvars}") + + # Prepare the individual qrac circuit and combine them into a multiqubit circuit + qracs = [qrac_state_prep_1q(qi_bits) for qi_bits in variable_mappings] + qrac_circ = reduce(lambda x, y: x.tensor(y), qracs) + return qrac_circ + + +def q2vars_from_var2op(var2op: Dict[int, Tuple[int, SparsePauliOp]]) -> List[List[int]]: + """ + Converts a dictionary mapping decision variables to qubits and Pauli operators to a list of + lists of decision variables. + + Args: + var2op: A dictionary mapping decision variables to qubits and Pauli operators. + + Returns: + A list of lists of decision variables. Each inner list contains the indices of decision + variables mapped to a specific qubit. + """ + num_qubits = max(qubit_index for qubit_index, _ in var2op.values()) + 1 + q2vars: List[List[int]] = [[] for i in range(num_qubits)] + for var, (q, _) in var2op.items(): + q2vars[q].append(var) + return q2vars + + +class QuantumRandomAccessEncoding: + """This class specifies a Quantum Random Access Code that can be used to encode + the binary variables of a QUBO (quadratic unconstrained binary optimization + problem). + + Args: + max_vars_per_qubit: maximum possible compression ratio. + Supported values are 1, 2, or 3. + + """ + + # This defines the convention of the Pauli operators (and their ordering) + # for each encoding. + OPERATORS = ( + (SparsePauliOp("Z"),), # (1,1,1) QRAC + (SparsePauliOp("X"), SparsePauliOp("Z")), # (2,1,p) QRAC, p ≈ 0.85 + (SparsePauliOp("X"), SparsePauliOp("Y"), SparsePauliOp("Z")), # (3,1,p) QRAC, p ≈ 0.79 + ) + + def __init__(self, max_vars_per_qubit: int = 3): + if max_vars_per_qubit not in (1, 2, 3): + raise ValueError("max_vars_per_qubit must be 1, 2, or 3") + self._ops = self.OPERATORS[max_vars_per_qubit - 1] + + self._qubit_op: Optional[SparsePauliOp] = None + self._offset: Optional[float] = None + self._problem: Optional[QuadraticProgram] = None + self._var2op: Dict[int, Tuple[int, SparsePauliOp]] = {} + self._q2vars: List[List[int]] = [] + self._frozen = False + + @property + def num_qubits(self) -> int: + """Number of qubits""" + return len(self._q2vars) + + @property + def num_vars(self) -> int: + """Number of decision variables""" + return len(self._var2op) + + @property + def max_vars_per_qubit(self) -> int: + """Maximum number of variables per qubit""" + return len(self._ops) + + @property + def var2op(self) -> Dict[int, Tuple[int, SparsePauliOp]]: + """Maps each decision variable to ``(qubit_index, operator)``""" + return self._var2op + + @property + def q2vars(self) -> List[List[int]]: + """Each element contains the list of decision variable indice(s) encoded on that qubit""" + return self._q2vars + + @property + def compression_ratio(self) -> float: + """Compression ratio. Number of decision variables divided by number of qubits""" + return self.num_vars / self.num_qubits + + @property + def minimum_recovery_probability(self) -> float: + """Minimum recovery probability, as set by ``max_vars_per_qubit``""" + n = self.max_vars_per_qubit + return (1 + 1 / np.sqrt(n)) / 2 + + @property + def qubit_op(self) -> SparsePauliOp: + """Relaxed Hamiltonian operator. + + Raises: + AttributeError: If no objective function has been provided yet, and + a qubit Hamiltonian cannot be constructed. Use the `encode` method + to manually compile this field. + """ + if self._qubit_op is None: + raise AttributeError( + "Cannot return the relaxed Hamiltonian operator: no objective function has been " + "provided yet. Please use the ``encode`` method to construct the Hamiltonian, or make " + "sure that the objective function has been set." + ) + return self._qubit_op + + @property + def offset(self) -> float: + """Relaxed Hamiltonian offset""" + if self._offset is None: + raise AttributeError( + "Cannot return the relaxed Hamiltonian offset: The offset attribute cannot be " + "accessed until the ``encode`` method has been called to generate the qubit " + "Hamiltonian. Please call ``encode`` first." + ) + return self._offset + + @property + def problem(self) -> QuadraticProgram: + """The ``QuadraticProgram`` encoding a QUBO optimization problem""" + if self._problem is None: + raise AttributeError( + "This object has not been associated with a ``QuadraticProgram``. " + "Please use the ``encode`` method to set the problem." + ) + return self._problem + + def freeze(self): + """Freeze the object to prevent further modification. + + Once an instance of this class is frozen, ``encode`` can no longer be called. + """ + if self._frozen is False: + self._qubit_op = self._qubit_op.simplify() + self._frozen = True + + @property + def frozen(self) -> bool: + """Whether the object is frozen or not.""" + return self._frozen + + def _add_variables(self, variables: List[int]) -> None: + """Add variables to the Encoding object. + + Args: + variables: A list of variable indices to be added. + + Raises: + ValueError: If added variables are not unique. + ValueError: If added variables collide with existing ones. + + """ + # NOTE: If this is called multiple times, it *always* adds an + # additional qubit (see final line), even if aggregating them into a + # single call would have resulted in fewer qubits. + + # Check if variables is empty + if not variables: + return + + # Check if variables are unique + if len(variables) != len(set(variables)): + raise ValueError("Added variables must be unique") + + # Check if variables collide with existing ones + for v in variables: + if v in self._var2op: + raise ValueError("Added variables cannot collide with existing ones") + + # Calculate the number of new qubits required for the added variables. + n = len(self._ops) + old_num_qubits = len(self._q2vars) + num_new_qubits = int(np.ceil(len(variables) / n)) + # Add the new qubits to _q2vars. + for _ in range(num_new_qubits): + self._q2vars.append([]) + # Associate each added variable with a qubit and operator. + for i, v in enumerate(variables): + qubit, op = divmod(i, n) + qubit_index = old_num_qubits + qubit + self._var2op[v] = (qubit_index, self._ops[op]) + self._q2vars[qubit_index].append(v) + + def _add_term(self, w: float, *variables: int) -> None: + """Add a term to the Hamiltonian. + + Args: + weight: the coefficient for the term + *variables: the list of variables for the term + """ + # Eq. (31) in https://arxiv.org/abs/2111.03167v2 assumes a weight-2 + # Pauli operator. To generalize, we replace the `d` in that equation + # with `d_prime`, defined as follows: + d_prime = np.sqrt(self.max_vars_per_qubit) ** len(variables) + op = self._term2op(*variables) * (w * d_prime) + + if w == 0.0: + return + if self._qubit_op is None: + self._qubit_op = op + else: + self._qubit_op += op + + def _term2op(self, *variables: int) -> SparsePauliOp: + """Construct a ``SparsePauliOp`` that is a tensor product of encoded decision variables. + + Args: + *variables: The indices of the decision variables to encode. + + Returns: + The encoded ``SparsePauliOp`` representing the product of the provided variables. + + Raises: + QiskitOptimizationError: If any of the decision variables to be encoded collide in qubit + space. + + """ + ops = [SparsePauliOp("I")] * self.num_qubits + done = set() + for x in variables: + pos, op = self._var2op[x] + if pos in done: + raise QiskitOptimizationError(f"Collision of variables: {variables}") + ops[pos] = op + done.add(pos) + pauli_op = reduce(lambda x, y: x.tensor(y), ops) + return pauli_op + + @staticmethod + def _generate_ising_coefficients( + problem: QuadraticProgram, + ) -> Tuple[float, np.ndarray, np.ndarray]: + """Generate coefficients of Hamiltonian from a given problem.""" + num_vars = problem.get_num_vars() + + # set a sign corresponding to a maximized or minimized problem: + # 1 is for minimized problem, -1 is for maximized problem. + sense = problem.objective.sense.value + + # convert a constant part of the objective function into Hamiltonian. + offset = problem.objective.constant * sense + + # convert linear parts of the objective function into Hamiltonian. + linear = np.zeros(num_vars) + for idx, coef in problem.objective.linear.to_dict().items(): + assert isinstance(idx, int) # hint for mypy + weight = coef * sense / 2 + linear[idx] -= weight + offset += weight + + # convert quadratic parts of the objective function into Hamiltonian. + quad = np.zeros((num_vars, num_vars)) + for (i, j), coef in problem.objective.quadratic.to_dict().items(): + assert isinstance(i, int) # hint for mypy + assert isinstance(j, int) # hint for mypy + weight = coef * sense / 4 + if i == j: + linear[i] -= 2 * weight + offset += 2 * weight + else: + quad[i, j] += weight + linear[i] -= weight + linear[j] -= weight + offset += weight + + return offset, linear, quad + + @staticmethod + def _find_variable_partition(quad: np.ndarray) -> Dict[int, List[int]]: + """Find the variable partition of the quad based on the node coloring of the graph + + Args: + quad: coefficients of the quadratic part of the Hamiltonian. + + Returns: + Dict: a dictionary of the variable partition of the quad based on the node coloring. + """ + color2node: Dict[int, List[int]] = defaultdict(list) + num_nodes = quad.shape[0] + graph = rx.PyGraph() + graph.add_nodes_from(range(num_nodes)) + graph.add_edges_from_no_data(list(zip(*np.where(quad != 0)))) + node2color = rx.graph_greedy_color(graph) + for node, color in sorted(node2color.items()): + color2node[color].append(node) + return color2node + + def encode(self, problem: QuadraticProgram) -> None: + """ + Encodes a given ``QuadraticProgram`` as a (n,1,p) Quantum Random Access Code (QRAC) + relaxed Hamiltonian. It accomplishes this by mapping each binary decision variable to one + qubit of the QRAC. The encoding is designed to ensure that the problem's objective function + commutes with the QRAC encoding. + + After the function is called, it sets the following attributes: + - qubit_op: The qubit operator that encodes the input ``QuadraticProgram``. + - offset: The constant value in the encoded Hamiltonian. + - problem: The original ``QuadraticProgram`` used for encoding. + + Inputs: + problem: A ``QuadraticProgram`` encoding a QUBO optimization problem + + Raises: + QiskitOptimizationError: If this method is called more than once on the same object. + QiskitOptimizationError: If the problem contains non-binary variables. + QiskitOptimizationError: If the problem contains constraints. + """ + # Ensure the Encoding object is not already used + if self._frozen: + raise QiskitOptimizationError( + "Cannot reuse an Encoding object that has already been used. " + "Please create a new Encoding object and call encode() on it." + ) + + # Check for non-binary variables + if problem.get_num_vars() > problem.get_num_binary_vars(): + raise QiskitOptimizationError( + "All variables must be binary. " + "Please convert integer variables to binary variables using the" + "``QuadraticProgramToQubo`` converter. " + "Continuous variables are not supported by the QRAO algorithm." + ) + + # Check for constraints + if problem.linear_constraints or problem.quadratic_constraints: + raise QiskitOptimizationError( + "The problem cannot contain constraints. " + "Please convert constraints to penalty terms of the objective function using the " + "``QuadraticProgramToQubo`` converter." + ) + + num_vars = problem.get_num_vars() + + # Generate the coefficients of the Hamiltonian + offset, linear, quad = self._generate_ising_coefficients(problem) + + # Find the partition of the variables into groups + variable_partition = self._find_variable_partition(quad) + + # Add variables and generate the Hamiltonian + for _, v in sorted(variable_partition.items()): + self._add_variables(sorted(v)) + for i in range(num_vars): + w = linear[i] + if w != 0: + self._add_term(w, i) + for i in range(num_vars): + for j in range(num_vars): + w = quad[i, j] + if w != 0: + self._add_term(w, i, j) + + self._offset = offset + self._problem = problem + + self.freeze() + + def state_prep(self, dvars: List[int]) -> QuantumCircuit: + """ + Generate a circuit that prepares the state corresponding to the given binary string. + + Args: + dvars: A list of binary values to be encoded into the state. + + Returns: + A QuantumCircuit that prepares the state corresponding to the given binary string. + """ + return qrac_state_prep_multiqubit(dvars, self.q2vars, self.max_vars_per_qubit) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 5c1202b3d..c8b3119e9 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -1,6 +1,6 @@ # This code is part of Qiskit. # -# (C) Copyright IBM 2020, 2022. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -10,46 +10,25 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -"""Quantum Random Access Optimizer.""" +"""Quantum Random Access Optimizer class.""" -from typing import Union, List, Tuple, Optional import time +from typing import List, Optional, Tuple, Union import numpy as np - from qiskit import QuantumCircuit -from qiskit.algorithms.minimum_eigensolvers import ( - MinimumEigensolver, - MinimumEigensolverResult, - NumPyMinimumEigensolver, -) -from qiskit.algorithms.minimum_eigen_solvers import ( - MinimumEigensolver as LegacyMinimumEigensolver, - MinimumEigensolverResult as LegacyMinimumEigensolverResult, - NumPyMinimumEigensolver as LegacyNumPyMinimumEigensolver, -) - -from qiskit_optimization.algorithms import ( - OptimizationAlgorithm, - OptimizationResult, - OptimizationResultStatus, - SolutionSample, -) -from qiskit_optimization.problems import QuadraticProgram, Variable - -from .encoding import QuantumRandomAccessEncoding -from .rounding_common import RoundingScheme, RoundingContext, RoundingResult -from .semideterministic_rounding import SemideterministicRounding +from qiskit.algorithms.minimum_eigensolvers import (MinimumEigensolver, + MinimumEigensolverResult, + NumPyMinimumEigensolver) +from qiskit_optimization.algorithms import (OptimizationResult, + OptimizationResultStatus, + SolutionSample) +from qiskit_optimization.problems import Variable -def _get_aux_operators_evaluated(relaxed_results): - try: - # Must be using the new "minimum_eigensolvers" - # https://github.com/Qiskit/qiskit-terra/blob/main/releasenotes/notes/0.22/add-eigensolvers-with-primitives-8b3a9f55f5fd285f.yaml - return relaxed_results.aux_operators_evaluated - except AttributeError: - # Must be using the old (deprecated) "minimum_eigen_solvers" - return relaxed_results.aux_operator_eigenvalues +from .quantum_random_access_encoding import QuantumRandomAccessEncoding +from .rounding_common import RoundingContext, RoundingResult, RoundingScheme +from .semideterministic_rounding import SemideterministicRounding class QuantumRandomAccessOptimizationResult(OptimizationResult): @@ -63,22 +42,19 @@ def __init__( variables: List[Variable], status: OptimizationResultStatus, samples: Optional[List[SolutionSample]], - relaxed_results: Union[ - MinimumEigensolverResult, LegacyMinimumEigensolverResult - ], + relaxed_fval: float, + relaxed_results: MinimumEigensolverResult, rounding_results: RoundingResult, - relaxed_results_offset: float, - sense: int, ) -> None: """ Args: - x: the optimal value found by ``MinimumEigensolver``. - fval: the optimal function value. - variables: the list of variables of the optimization problem. - status: the termination status of the optimization algorithm. - min_eigen_solver_result: the result obtained from the underlying algorithm. - samples: the x values of the QUBO, the objective function value of the QUBO, - and the probability, and the status of sampling. + x: The optimal value found by ``MinimumEigensolver``. + fval: The optimal function value. + variables: The list of variables of the optimization problem. + status: The termination status of the optimization algorithm. + samples: The list of ``SolutionSample`` obtained from the optimization algorithm. + relaxed_results: The result obtained from the underlying minimum eigensolver. + rounding_results: The rounding results. """ super().__init__( x=x, @@ -88,91 +64,61 @@ def __init__( raw_results=None, samples=samples, ) + self._relaxed_fval = relaxed_fval self._relaxed_results = relaxed_results self._rounding_results = rounding_results - self._relaxed_results_offset = relaxed_results_offset - assert sense in (-1, 1) - self._sense = sense @property def relaxed_results( self, - ) -> Union[MinimumEigensolverResult, LegacyMinimumEigensolverResult]: - """Variationally obtained ground state of the relaxed Hamiltonian""" + ) -> MinimumEigensolverResult: + """The result obtained from the underlying minimum eigensolver.""" return self._relaxed_results @property def rounding_results(self) -> RoundingResult: - """Rounding results""" + """The rounding results.""" return self._rounding_results @property def trace_values(self): """List of expectation values, one corresponding to each decision variable""" - trace_values = [ - v[0] for v in _get_aux_operators_evaluated(self._relaxed_results) - ] + trace_values = [v[0] for v in self._relaxed_results.aux_operators_evaluated] return trace_values @property def relaxed_fval(self) -> float: - """Relaxed function value, in the conventions of the original ``QuadraticProgram`` - - Restoring convertions may be necessary, for instance, if the provided - ``QuadraticProgram`` represents a maximization problem, as it will be - converted to a minimization problem when phrased as a Hamiltonian. - """ - return self._sense * ( - self._relaxed_results_offset + self.relaxed_results.eigenvalue.real - ) - - def __repr__(self) -> str: - lines = ( - "QRAO Result", - "-----------", - f"relaxed function value: {self.relaxed_fval}", - super().__repr__(), - ) - return "\n".join(lines) + """Relaxed function value, in the conventions of the original ``QuadraticProgram``.""" + return self._relaxed_fval -class QuantumRandomAccessOptimizer(OptimizationAlgorithm): - """Quantum Random Access Optimizer.""" +class QuantumRandomAccessOptimizer: + """Quantum Random Access Optimizer class.""" def __init__( self, - min_eigen_solver: Union[MinimumEigensolver, LegacyMinimumEigensolver], - encoding: QuantumRandomAccessEncoding, + min_eigen_solver: MinimumEigensolver, rounding_scheme: Optional[RoundingScheme] = None, ): """ Args: - - min_eigen_solver: The minimum eigensolver to use for solving the - relaxed problem (typically an instance of ``VQE`` or ``QAOA``). - - encoding: The ``QuantumRandomAccessEncoding``, which must have - already been ``encode()``ed with a ``QuadraticProgram``. - + min_eigen_solver: The minimum eigensolver to use for solving the relaxed problem. rounding_scheme: The rounding scheme. If ``None`` is provided, ``SemideterministicRounding()`` will be used. """ self.min_eigen_solver = min_eigen_solver - self.encoding = encoding if rounding_scheme is None: rounding_scheme = SemideterministicRounding() self.rounding_scheme = rounding_scheme @property - def min_eigen_solver(self) -> Union[MinimumEigensolver, LegacyMinimumEigensolver]: - """The minimum eigensolver.""" + def min_eigen_solver(self) -> MinimumEigensolver: + """Return the minimum eigensolver.""" return self._min_eigen_solver @min_eigen_solver.setter - def min_eigen_solver( - self, min_eigen_solver: Union[MinimumEigensolver, LegacyMinimumEigensolver] - ) -> None: + def min_eigen_solver(self, min_eigen_solver: MinimumEigensolver) -> None: """Set the minimum eigensolver.""" if not min_eigen_solver.supports_aux_operators(): raise TypeError( @@ -181,144 +127,115 @@ def min_eigen_solver( ) self._min_eigen_solver = min_eigen_solver - @property - def encoding(self) -> QuantumRandomAccessEncoding: - """The encoding.""" - return self._encoding - - @encoding.setter - def encoding(self, encoding: QuantumRandomAccessEncoding) -> None: - """Set the encoding""" - if encoding.num_qubits == 0: + def solve_relaxed( + self, + encoding: QuantumRandomAccessEncoding, + ) -> Tuple[MinimumEigensolverResult, RoundingContext]: + """Solve the relaxed Hamiltonian given by the encoding. + + Args: + encoding: The ``QuantumRandomAccessEncoding``, which must have already been ``encode()``ed + with a ``QuadraticProgram``. + + Returns: + The result of the minimum eigensolver, and the rounding context. + + Raises: + ValueError: If the encoding has not been encoded with a ``QuadraticProgram``. + """ + if not encoding.frozen: raise ValueError( - "The passed encoder has no variables associated with it; you probably " - "need to call `encode()` to encode it with a `QuadraticProgram`." - ) - # Instead of copying, we "freeze" the encoding to ensure it is not - # modified going forward. - encoding.freeze() - self._encoding = encoding - - def get_compatibility_msg(self, problem: QuadraticProgram) -> str: - if problem != self.encoding.problem: - return ( - "The problem passed does not match the problem used " - "to construct the QuantumRandomAccessEncoding." + "The encoding must call ``encode()`` with a ``QuadraticProgram`` before being passed" + "to the QuantumRandomAccessOptimizer." ) - return "" - def solve_relaxed( - self, - ) -> Tuple[ - Union[MinimumEigensolverResult, LegacyMinimumEigensolverResult], RoundingContext - ]: - """Solve the relaxed Hamiltonian given the ``encoding`` provided to the constructor.""" - # Get the ordered list of operators that correspond to each decision - # variable. This line assumes the variables are numbered consecutively - # starting with 0. Note that under this assumption, the following - # range is equivalent to `sorted(self.encoding.var2op.keys())`. See - # encoding.py for more commentary on this assumption, which always - # holds when starting from a `QuadraticProgram`. - variable_ops = [self.encoding.term2op(i) for i in range(self.encoding.num_vars)] - - # solve relaxed problem + # Get the list of operators that correspond to each decision variable. + variable_ops = [encoding._term2op(i) for i in range(encoding.num_vars)] + + # Solve the relaxed problem start_time_relaxed = time.time() relaxed_results = self.min_eigen_solver.compute_minimum_eigenvalue( - self.encoding.qubit_op, aux_operators=variable_ops + encoding.qubit_op, aux_operators=variable_ops ) - stop_time_relaxed = time.time() - relaxed_results.time_taken = stop_time_relaxed - start_time_relaxed - - trace_values = [v[0] for v in _get_aux_operators_evaluated(relaxed_results)] + relaxed_results.time_taken = time.time() - start_time_relaxed - # Collect inputs for rounding - # double check later that there's no funny business with the - # parameter ordering. + # Get auxiliary trace values for rounding. + expectation_values = [v[0] for v in relaxed_results.aux_operators_evaluated] - # If the relaxed solution can be expressed as an explicit circuit - # then always express it that way - even if a statevector simulator - # was used and the actual wavefunction could be used. The only exception - # is the numpy eigensolver. If you wish to round the an explicit statevector, - # you must do so by manually rounding and passing in a QuantumCircuit - # initialized to the desired state. + # Get the circuit corresponding to the relaxed solution. if hasattr(self.min_eigen_solver, "ansatz"): - circuit = self.min_eigen_solver.ansatz.bind_parameters( - relaxed_results.optimal_point - ) - elif isinstance( - self.min_eigen_solver, - (NumPyMinimumEigensolver, LegacyNumPyMinimumEigensolver), - ): + circuit = self.min_eigen_solver.ansatz.bind_parameters(relaxed_results.optimal_point) + elif isinstance(self.min_eigen_solver, NumPyMinimumEigensolver): statevector = relaxed_results.eigenstate - if isinstance(self.min_eigen_solver, LegacyNumPyMinimumEigensolver): - # statevector is a StateFn in this case, so we must convert it - # to a Statevector - statevector = statevector.primitive - circuit = QuantumCircuit(self.encoding.num_qubits) + circuit = QuantumCircuit(encoding.num_qubits) circuit.initialize(statevector) else: circuit = None rounding_context = RoundingContext( - encoding=self.encoding, - trace_values=trace_values, + encoding=encoding, + expectation_values=expectation_values, circuit=circuit, ) return relaxed_results, rounding_context - def solve(self, problem: Optional[QuadraticProgram] = None) -> OptimizationResult: - if problem is None: - problem = self.encoding.problem - else: - if problem != self.encoding.problem: - raise ValueError( - "The problem given must exactly match the problem " - "used to generate the encoded operator. Alternatively, " - "the argument to `solve` can be left blank." - ) + def solve(self, encoding: QuantumRandomAccessEncoding) -> QuantumRandomAccessOptimizationResult: + """Solve the relaxed Hamiltonian given by the encoding and round the solution by the given + rounding scheme. - # Solve relaxed problem - # ============================ - (relaxed_results, rounding_context) = self.solve_relaxed() + Args: + encoding: The ``QuantumRandomAccessEncoding``, which must have already been encoded + with a ``QuadraticProgram``. + Returns: + The result of the quantum random access optimization. + + Raises: + ValueError: If the encoding has not been encoded with a ``QuadraticProgram``. + """ + if not encoding.frozen: + raise ValueError( + "The encoding must call ``encode()`` with a ``QuadraticProgram`` before being passed" + "to the QuantumRandomAccessOptimizer." + ) - # Round relaxed solution - # ============================ + # Solve the relaxed problem + (relaxed_results, rounding_context) = self.solve_relaxed(encoding) + + # Round the solution rounding_results = self.rounding_scheme.round(rounding_context) # Process rounding results - # ============================ - # The rounding classes don't have enough information to evaluate the - # objective function, so they return a RoundingSolutionSample, which - # contains only part of the information in the SolutionSample. Here we - # fill in the rest. samples: List[SolutionSample] = [] for sample in rounding_results.samples: + if encoding.problem.is_feasible(sample.x): + status = OptimizationResultStatus.SUCCESS + else: + status = OptimizationResultStatus.INFEASIBLE samples.append( SolutionSample( x=sample.x, - fval=problem.objective.evaluate(sample.x), + fval=encoding.problem.objective.evaluate(sample.x), probability=sample.probability, - status=self._get_feasibility_status(problem, sample.x), + status=status, ) ) - # TODO: rewrite this logic once the converters are integrated. - # we need to be very careful about ensuring that the problem - # sense is taken into account in the relaxed solution and the rounding - # this is likely only a temporary patch while we are sticking to a - # maximization problem. - fsense = {"MINIMIZE": min, "MAXIMIZE": max}[problem.objective.sense.name] + # Get the best sample + fsense = {"MINIMIZE": min, "MAXIMIZE": max}[encoding.problem.objective.sense.name] best_sample = fsense(samples, key=lambda x: x.fval) + relaxed_fval = encoding.problem.objective.sense.value * ( + encoding.offset + relaxed_results.eigenvalue.real + ) + return QuantumRandomAccessOptimizationResult( - samples=samples, x=best_sample.x, fval=best_sample.fval, - variables=problem.variables, + variables=encoding.problem.variables, status=OptimizationResultStatus.SUCCESS, + samples=samples, + relaxed_fval=relaxed_fval, relaxed_results=relaxed_results, rounding_results=rounding_results, - relaxed_results_offset=self.encoding.offset, - sense=problem.objective.sense.value, ) diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index 1689b8599..fcd6e2a3a 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -18,9 +18,10 @@ import numpy as np -from qiskit.opflow import PrimitiveOp +# from qiskit.opflow import PrimitiveOp +from qiskit.circuit import QuantumCircuit -from .encoding import QuantumRandomAccessEncoding, q2vars_from_var2op +from .quantum_random_access_encoding import QuantumRandomAccessEncoding, q2vars_from_var2op # pylint: disable=too-few-public-methods @@ -40,45 +41,47 @@ class RoundingContext: def __init__( self, *, - encoding: Optional[QuantumRandomAccessEncoding] = None, - var2op: Optional[Dict[int, Tuple[int, PrimitiveOp]]] = None, - q2vars: Optional[List[List[int]]] = None, - trace_values=None, - circuit=None, - _vars_per_qubit: Optional[int] = None, + encoding: QuantumRandomAccessEncoding, + # var2op: Optional[Dict[int, Tuple[int, PrimitiveOp]]] = None, + # q2vars: Optional[List[List[int]]] = None, + expectation_values, + circuit: Optional[QuantumCircuit] = None, + # _vars_per_qubit: Optional[int] = None, ): - if encoding is not None: - if var2op is not None or q2vars is not None: - raise ValueError( - "Neither var2op nor q2vars should be provided if encoding is" - ) - if _vars_per_qubit is not None: - raise ValueError( - "_vars_per_qubit should not be provided if encoding is" - ) - self.var2op = encoding.var2op - self.q2vars = encoding.q2vars - self._vars_per_qubit = encoding.max_vars_per_qubit - else: - if var2op is None: - raise ValueError("Either an encoding or var2ops must be provided") - if _vars_per_qubit is None: - raise ValueError( - "_vars_per_qubit must be provided if encoding is not provided" - ) - self.var2op = var2op - self.q2vars = q2vars_from_var2op(var2op) if q2vars is None else q2vars - self._vars_per_qubit = _vars_per_qubit - - self.trace_values = trace_values # TODO: rename me - self.circuit = circuit # TODO: rename me + # if encoding is not None: + # if var2op is not None or q2vars is not None: + # raise ValueError( + # "Neither var2op nor q2vars should be provided if encoding is" + # ) + # if _vars_per_qubit is not None: + # raise ValueError( + # "_vars_per_qubit should not be provided if encoding is" + # ) + # self.var2op = encoding.var2op + # self.q2vars = encoding.q2vars + # self._vars_per_qubit = encoding.max_vars_per_qubit + # else: + # if var2op is None: + # raise ValueError("Either an encoding or var2ops must be provided") + # if _vars_per_qubit is None: + # raise ValueError( + # "_vars_per_qubit must be provided if encoding is not provided" + # ) + # self.var2op = var2op + # self.q2vars = q2vars_from_var2op(var2op) if q2vars is None else q2vars + # self._vars_per_qubit = _vars_per_qubit + + self.encoding = encoding + self.expectation_values = expectation_values + self.circuit = circuit class RoundingResult: """Base class for a rounding result""" - def __init__(self, samples: List[RoundingSolutionSample], *, time_taken=None): + def __init__(self, samples: List[RoundingSolutionSample], expectation_values,*, time_taken=None): self._samples = samples + self._expectation_values = expectation_values self.time_taken = time_taken @property @@ -86,6 +89,11 @@ def samples(self) -> List[RoundingSolutionSample]: """List of samples""" return self._samples + @property + def expectation_values(self): + """Expectation values""" + return self._expectation_values + class RoundingScheme(ABC): """Base class for a rounding scheme""" diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 64da99f05..67f36f3ce 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -10,7 +10,7 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -"""Semideterministic rounding""" +"""Semideterministic rounding module""" from typing import Optional @@ -36,7 +36,6 @@ class SemideterministicRounding(RoundingScheme): This is referred to as "Pauli rounding" in https://arxiv.org/abs/2111.03167v2. - """ def __init__(self, *, seed: Optional[int] = None): @@ -51,25 +50,24 @@ def __init__(self, *, seed: Optional[int] = None): def round(self, ctx: RoundingContext) -> SemideterministicRoundingResult: """Perform semideterministic rounding""" - trace_values = ctx.trace_values + # # trace_values = ctx.expectation_values - if trace_values is None: - raise NotImplementedError( - "Semideterministic rounding requires that trace_values be available." - ) + # if trace_values is None: + # raise NotImplementedError( + # "Semideterministic rounding requires that trace_values be available." + # ) - if len(trace_values) != len(ctx.var2op): - raise ValueError( - f"trace_values has length {len(trace_values)}, " - "but there are {len(ctx.var2op)} decision variables." - ) + # if len(trace_values) != len(ctx.var2op): + # raise ValueError( + # f"trace_values has length {len(trace_values)}, " + # "but there are {len(ctx.var2op)} decision variables." + # ) def sign(val) -> int: return 0 if (val > 0) else 1 rounded_vars = [ - sign(e) if not np.isclose(0, e) else self.rng.randint(2) - for e in trace_values + sign(e) if not np.isclose(0, e) else self.rng.randint(2) for e in ctx.expectation_values ] soln_samples = [ @@ -79,5 +77,7 @@ def sign(val) -> int: ) ] - result = SemideterministicRoundingResult(soln_samples) + result = SemideterministicRoundingResult( + samples=soln_samples, expectation_values=ctx.expectation_values + ) return result From 32acacbd0bcbd95faa7c888308f55aa5ecf90a2b Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 17 Apr 2023 13:34:51 +0900 Subject: [PATCH 04/67] update qrao --- .../algorithms/qrao/__init__.py | 9 +- .../qrao/encoding_commutation_verifier.py | 15 +- .../algorithms/qrao/magic_rounding.py | 218 +++++++++--------- .../qrao/quantum_random_access_encoding.py | 40 ++-- .../algorithms/qrao/rounding_common.py | 57 ++--- .../qrao/semideterministic_rounding.py | 19 +- 6 files changed, 174 insertions(+), 184 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index 87056544f..ccfe8c283 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -12,14 +12,13 @@ """ Quantum Random Access Optimization (:mod:`qiskit_optimization.algorithms.qrao`) -======================================================================================= +=============================================================================== .. currentmodule:: qiskit_optimization.algorithms.qrao -Quantum Random Access Encoding and Rounding -=========================================== - +Quantum Random Access Encoding and Optimization +=============================================== .. autosummary:: :toctree: ../stubs/ :nosignatures: @@ -30,7 +29,7 @@ QuantumRandomAccessOptimizationResult Rounding schemes -================= +================ .. autosummary:: :toctree: ../stubs/ diff --git a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py index 76f6958e5..6a6fbe94d 100644 --- a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py +++ b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py @@ -24,9 +24,16 @@ class EncodingCommutationVerifier: """Class for verifying that the relaxation commutes with the objective function.""" - def __init__(self, encoding: QuantumRandomAccessEncoding): + def __init__(self, encoding: QuantumRandomAccessEncoding, estimator: Estimator = None): + """ + Args: + encoding: The encoding to verify. + """ self._encoding = encoding - self._estimator = Estimator() + if estimator is not None: + self._estimator = estimator + else: + self._estimator = Estimator() def __len__(self) -> int: return 2**self._encoding.num_vars @@ -58,6 +65,8 @@ def __getitem__(self, i: int) -> Tuple[str, float, float]: try: encoded_obj_val = job.result().values[0] + offset except Exception as exc: - raise QiskitOptimizationError("Estimator job failed.") from exc + raise QiskitOptimizationError( + "The primitive job to verify commutation failed!" + ) from exc return (str_dvars, obj_val, encoded_obj_val) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index f02e95019..fb9003741 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -1,6 +1,6 @@ # This code is part of Qiskit. # -# (C) Copyright IBM 2022. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -12,50 +12,18 @@ """Magic basis rounding module""" -from typing import List, Dict, Tuple, Optional -from collections import defaultdict -import numbers import time -import warnings +from collections import defaultdict +from typing import Dict, List, Optional, Tuple import numpy as np - from qiskit import QuantumCircuit -from qiskit.primitives import Sampler -from qiskit.providers import Backend -from qiskit.opflow import PrimitiveOp -from qiskit.utils import QuantumInstance - -from .quantum_random_access_encoding import z_to_31p_qrac_basis_circuit, z_to_21p_qrac_basis_circuit -from .rounding_common import ( - RoundingSolutionSample, - RoundingScheme, - RoundingContext, - RoundingResult, -) - from qiskit.algorithms.exceptions import AlgorithmError +from qiskit.primitives import Sampler +from qiskit.quantum_info import SparsePauliOp - -_invalid_backend_names = [ - "aer_simulator_unitary", - "aer_simulator_superop", - "unitary_simulator", - "pulse_simulator", -] - - -def _backend_name(backend: Backend) -> str: - """Return the backend name in a way that is agnostic to Backend version""" - # See qiskit.utils.backend_utils in qiskit-terra for similar examples - if backend.version <= 1: - return backend.name() - return backend.name - - -def _is_original_statevector_simulator(backend: Backend) -> bool: - """Return True if the original statevector simulator""" - return _backend_name(backend) == "statevector_simulator" +from .quantum_random_access_encoding import z_to_21p_qrac_basis_circuit, z_to_31p_qrac_basis_circuit +from .rounding_common import RoundingContext, RoundingResult, RoundingScheme, RoundingSolutionSample class MagicRoundingResult(RoundingResult): @@ -64,27 +32,39 @@ class MagicRoundingResult(RoundingResult): def __init__( self, samples: List[RoundingSolutionSample], - *, - bases=None, - basis_shots=None, - basis_counts=None, - time_taken=None, + expectation_values: List[float], + bases: np.ndarray, + basis_shots: int, + basis_counts: Dict[str, Dict[str, int]], + time_taken: Optional[float] = None, ): + """ + Args: + samples: List of samples of the rounding. + expectation_values: Expectation values of the encoding. + bases: The bases used for the magic rounding. + basis_shots: The number of shots used for each basis. + basis_counts: The counts for each basis. + time_taken: Time taken for the rounding. + """ self._bases = bases self._basis_shots = basis_shots self._basis_counts = basis_counts - super().__init__(samples, time_taken=time_taken) + super().__init__(samples, expectation_values, time_taken=time_taken) @property def bases(self): + """Return the bases used for the magic rounding.""" return self._bases @property def basis_shots(self): + """Return the number of shots used for each basis.""" return self._basis_shots @property def basis_counts(self): + """Return the counts for each basis.""" return self._basis_counts @@ -114,17 +94,12 @@ class MagicRounding(RoundingScheme): def __init__( self, sampler: Sampler, - *, basis_sampling: str = "uniform", seed: Optional[int] = None, ): """ Args: - - quantum_instance: Provides the ``Backend`` for quantum execution - and the ``shots`` count (i.e., the number of samples to collect - from the magic bases). - + sampler: Sampler to use for sampling the magic bases. basis_sampling: Method to use for sampling the magic bases. Must be either ``"uniform"`` (default) or ``"weighted"``. ``"uniform"`` samples all magic bases uniformly, and is the @@ -134,10 +109,11 @@ def __init__( However, the approximation bounds given in https://arxiv.org/abs/2111.03167v2 apply only to ``"uniform"`` sampling. - seed: Seed for random number generator, which is used to sample the magic bases. + Raises: + ValueError: If ``basis_sampling`` is not ``"uniform"`` or ``"weighted"``. """ if basis_sampling not in ("uniform", "weighted"): raise ValueError( @@ -164,11 +140,20 @@ def basis_sampling(self): """Basis sampling method (either ``"uniform"`` or ``"weighted"``).""" return self._basis_sampling - @staticmethod def _make_circuits( circ: QuantumCircuit, bases: List[List[int]], vars_per_qubit: int ) -> List[QuantumCircuit]: + """Make a list of circuits to measure in the given magic bases. + + Args: + circ: Quantum circuit to measure. + bases: List of magic bases to measure in. + vars_per_qubit: Number of variables per qubit. + + Returns: + List of quantum circuits to measure in the given magic bases. + """ circuits = [] for basis in bases: if vars_per_qubit == 3: @@ -197,80 +182,67 @@ def _evaluate_magic_bases( Returns: List[Dict[str, int]]: A list of counts dictionaries associated with each basis measurement. + + Raises: + AlgorithmError: If the primitive job failed. """ - # measure = not _is_original_statevector_simulator(self.quantum_instance.backend) circuits = self._make_circuits(circuit, bases, vars_per_qubit) - # Execute each of the rotated circuits and collect the results - # Batch the circuits into jobs where each group has the same number of # shots, so that you can wait for the queue as few times as possible if # using hardware. circuit_indices_by_shots: Dict[int, List[int]] = defaultdict(list) + basis_counts: List[Optional[Dict[str, int]]] = [None] * len(circuits) assert len(circuits) == len(basis_shots) for i, shots in enumerate(basis_shots): circuit_indices_by_shots[shots].append(i) - basis_counts: List[Optional[Dict[str, int]]] = [None] * len(circuits) - for shots, indices in sorted(circuit_indices_by_shots.items(), reverse=True): - # self.quantum_instance.set_config(shots=shots) - # result = self.quantum_instance.execute([circuits[i] for i in indices]) - # counts_list = result.get_counts() try: job = self._sampler.run([circuits[i] for i in indices], shots=shots) result = job.result() except Exception as exc: - raise AlgorithmError("The primitive job to evaluate the energy failed!") from exc + raise AlgorithmError( + "The primitive job to evaluate the magic state failed!" + ) from exc counts_list = [dist.binary_probabilities() for dist in result.quasi_dists] - - # if not isinstance(counts_list, List): - # # This is the only case where this should happen, and that - # # it does at all (namely, when a single-element circuit - # # list is provided) is a weird API quirk of Qiskit. - # # https://github.com/Qiskit/qiskit-terra/issues/8103 - # assert len(indices) == 1 - # counts_list = [counts_list] assert len(indices) == len(counts_list) for i, counts in zip(indices, counts_list): basis_counts[i] = counts assert None not in basis_counts - # Process the outcomes and extract expectation of decision vars - - # The "statevector_simulator", unlike all the others, returns - # probabilities instead of integer counts. So if probabilities are - # detected, we rescale them. basis_counts = [ - {key: val * basis_shots[i] for key, val in counts.items()} - for i, counts in enumerate(basis_counts) - ] - - # if any( - # any(not isinstance(x, numbers.Integral) for x in counts.values()) - # for counts in basis_counts - # ): - # basis_counts = [ - # {key: val * basis_shots[i] for key, val in counts.items()} - # for i, counts in enumerate(basis_counts) - # ] + {key: val * basis_shots[i] for key, val in counts.items()} + for i, counts in enumerate(basis_counts) + ] return basis_counts - def _unpack_measurement_outcome( + def _unpack_measurement_outcome( self, bits: str, basis: List[int], - var2op: Dict[int, Tuple[int, PrimitiveOp]], + var2op: Dict[int, Tuple[int, SparsePauliOp]], vars_per_qubit: int, ) -> List[int]: + """ + Given a measurement outcome, a magic basis, and a mapping from decision variables to + Pauli operators, return the values of the decision variables. + + Args: + bits: The measurement outcome. + basis: The magic basis used for the measurement. + var2op: A mapping from decision variables to Pauli operators. + vars_per_qubit: The number of decision variables per qubit. + + Returns: + List[int]: The values of the decision variables. + """ output_bits = [] # iterate in order over decision variables - # (assumes variables are numbered consecutively beginning with 0) - for var in range(len(var2op)): # pylint: disable=consider-using-enumerate - q, op = var2op[var] + for q, op in var2op.values(): # get the decoding outcome index for the variable # corresponding to this Pauli op. op_index = self._OP_INDICES[vars_per_qubit][str(op.paulis[0])] @@ -286,25 +258,35 @@ def _unpack_measurement_outcome( output_bits.append(variable_value) return output_bits - def _compute_dv_counts(self, basis_counts, bases, var2op, vars_per_qubit): + def _compute_dv_counts( + self, + basis_counts: Dict[str, Dict[str, int]], + bases: List[List[int]], + var2op: Dict[int, Tuple[int, SparsePauliOp]], + vars_per_qubit: int, + ): """ Given a list of bases, basis_shots, and basis_counts, convert each observed bitstrings to its corresponding decision variable configuration. Return the counts of each decision variable configuration. + + Args: + basis_counts: A list of counts dictionaries associated with each basis measurement. + bases: A list of magic bases to measure. + var2op: A mapping from decision variables to Pauli operators. + vars_per_qubit: The number of decision variables per qubit. + + Returns: + A dictionary of counts for each decision variable configuration. """ - dv_counts = {} - for i, counts in enumerate(basis_counts): - base = bases[i] + dv_counts = defaultdict(int) + for base, counts in zip(bases, basis_counts): # For each measurement outcome... for bitstr, count in counts.items(): - # For each bit in the observed bitstring... soln = self._unpack_measurement_outcome(bitstr, base, var2op, vars_per_qubit) - soln = "".join([str(int(bit)) for bit in soln]) - if soln in dv_counts: - dv_counts[soln] += count - else: - dv_counts[soln] = count + soln = "".join([str(bit) for bit in soln]) + dv_counts[soln] += count return dv_counts def _sample_bases_uniform( @@ -343,16 +325,35 @@ def _sample_bases_uniform( bases, basis_shots = np.unique(bases, axis=0, return_counts=True) return bases, basis_shots - def _sample_bases_weighted(self, q2vars, trace_values, vars_per_qubit): - """Perform weighted sampling from the expectation values. + def _sample_bases_weighted( + self, q2vars: List[List[int]], expectation_values: List[float], vars_per_qubit: int + ) -> Tuple[np.ndarray, np.ndarray]: + """ + Perform weighted sampling from the expectation values. The goal is to make smarter choices + about which bases to measure in using the expectation values. + + Args: + q2vars: A list of lists of integers. Each inner list contains the indices of decision + variables mapped to a specific qubit. + expectation_values: A list of expectation values for each decision variable. + vars_per_qubit: The maximum number of decision variables that can be mapped to a + single qubit. - The goal is to make smarter choices about which bases to measure in - using the trace values. + Returns: + A tuple containing two arrays: + bases: A 2D numpy array of shape (num_bases, num_qubits), where each row + corresponds to a basis configuration. Each element of the array is an + integer in the range [0, 2 ** (vars_per_qubit - 1) - 1]. The integer + represents the index of the basis to measure in for the corresponding + qubit. + basis_shots: A 1D numpy array of shape (num_bases,), where each element + corresponds to the number of shots to use for the corresponding basis in + the bases array. """ # First, we make sure all Pauli expectation values have absolute value # at most 1. Otherwise, some of the probabilities computed below might # be negative. - tv = np.clip(trace_values, -1, 1) + tv = np.clip(expectation_values, -1, 1) # basis_probs will have num_qubits number of elements. # Each element will be a list of length 4 specifying the # probability of picking the corresponding magic basis on that qubit. @@ -432,11 +433,9 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: q2vars, expectation_values, vars_per_qubit ) - # assert self.shots == np.sum(basis_shots) # For each of the Magic Bases sampled above, measure # the appropriate number of times (given by basis_shots) # and return the circuit results - basis_counts = self._evaluate_magic_bases(circuit, bases, basis_shots, vars_per_qubit) # keys will be configurations of decision variables # values will be total number of observations. @@ -459,6 +458,7 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: # Create a MagicRoundingResult object to return return MagicRoundingResult( samples=soln_samples, + expectation_values=expectation_values, bases=bases, basis_shots=basis_shots, basis_counts=basis_counts, diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 1e1f81633..655105769 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -25,11 +25,11 @@ from qiskit_optimization.problems.quadratic_program import QuadraticProgram -def z_to_31p_qrac_basis_circuit(basis: List[int], bit_flip: int = 0) -> QuantumCircuit: +def z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (3,1,p)-QRAC. Args: - basis: The basis, 0, 1, 2, or 3, for the qubit. + bases: The basis, 0, 1, 2, or 3, for the qubit. bit_flip: Whether to flip the state of the qubit. 1 for flip, 0 for no flip. Returns: @@ -38,14 +38,14 @@ def z_to_31p_qrac_basis_circuit(basis: List[int], bit_flip: int = 0) -> QuantumC Raises: ValueError: If the basis is not 0, 1, 2, or 3 """ - circ = QuantumCircuit(len(basis)) + circ = QuantumCircuit(len(bases)) BETA = np.arccos(1 / np.sqrt(3)) # pylint: disable=invalid-name if bit_flip: # if bit_flip == 1: then flip the state of the first qubit to |1> circ.x(0) - for i, base in enumerate(reversed(basis)): + for i, base in enumerate(reversed(bases)): if base == 0: circ.r(-BETA, -np.pi / 4, i) elif base == 1: @@ -59,11 +59,11 @@ def z_to_31p_qrac_basis_circuit(basis: List[int], bit_flip: int = 0) -> QuantumC return circ -def z_to_21p_qrac_basis_circuit(basis: int, bit_flip: int = 0) -> QuantumCircuit: +def z_to_21p_qrac_basis_circuit(bases: int, bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (2,1,p)-QRAC. Args: - basis: The basis, 0, 1, for the qubit. + bases: The basis, 0, 1, for the qubit. bit_flip: Whether to flip the state of the qubit. 1 for flip, 0 for no flip. Returns: @@ -78,7 +78,7 @@ def z_to_21p_qrac_basis_circuit(basis: int, bit_flip: int = 0) -> QuantumCircuit # if bit_flip == 1: then flip the state of the first qubit to |1> circ.x(0) - for i, base in enumerate(reversed(basis)): + for i, base in enumerate(reversed(bases)): if base == 0: circ.r(-1 * np.pi / 4, -np.pi / 2, i) elif base == 1: @@ -117,34 +117,34 @@ def qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: # observe that the two states that define each magic basis # correspond to the same bitstrings but with a global bitflip. # Thus the three bits of information we use to construct these states are: - # c0,c1 : two bits to pick one of four magic bases - # c2: one bit to indicate which magic basis projector we are interested in. + # base_index0,base_index1 : two bits to pick one of four magic bases + # bit_flip: one bit to indicate which magic basis projector we are interested in. - c0 = bit_list[0] ^ bit_list[1] ^ bit_list[2] - c1 = bit_list[1] ^ bit_list[2] - c2 = bit_list[0] ^ bit_list[2] + bit_flip = bit_list[0] ^ bit_list[1] ^ bit_list[2] + base_index0 = bit_list[1] ^ bit_list[2] + base_index1 = bit_list[0] ^ bit_list[2] # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| - base = 2 * c1 + c2 - circ = z_to_31p_qrac_basis_circuit(base, c0) + base = 2 * base_index0 + base_index1 + circ = z_to_31p_qrac_basis_circuit(base, bit_flip) elif len(bit_list) == 2: # Prepare (2,1,p)-qrac # (00,01) or (10,11) - c0 = bit_list[0] + bit_flip = bit_list[0] # (00,11) or (01,10) - c1 = bit_list[0] ^ bit_list[1] + base_index0 = bit_list[0] ^ bit_list[1] # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf # # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| - base = c1 - circ = z_to_21p_qrac_basis_circuit(base, c0) + base = base_index0 + circ = z_to_21p_qrac_basis_circuit(base, bit_flip) else: - c0 = bit_list[0] + bit_flip = bit_list[0] circ = QuantumCircuit(1) - if c0: + if bit_flip: circ.x(0) return circ diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index fcd6e2a3a..0e5ccefe7 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -1,6 +1,6 @@ # This code is part of Qiskit. # -# (C) Copyright IBM 2022. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -12,16 +12,15 @@ """Common classes for rounding schemes""" -from typing import Dict, List, Tuple, Optional +from typing import List, Optional from abc import ABC, abstractmethod from dataclasses import dataclass import numpy as np -# from qiskit.opflow import PrimitiveOp from qiskit.circuit import QuantumCircuit -from .quantum_random_access_encoding import QuantumRandomAccessEncoding, q2vars_from_var2op +from .quantum_random_access_encoding import QuantumRandomAccessEncoding # pylint: disable=too-few-public-methods @@ -40,37 +39,16 @@ class RoundingContext: def __init__( self, - *, encoding: QuantumRandomAccessEncoding, - # var2op: Optional[Dict[int, Tuple[int, PrimitiveOp]]] = None, - # q2vars: Optional[List[List[int]]] = None, - expectation_values, + expectation_values: List[float], circuit: Optional[QuantumCircuit] = None, - # _vars_per_qubit: Optional[int] = None, ): - # if encoding is not None: - # if var2op is not None or q2vars is not None: - # raise ValueError( - # "Neither var2op nor q2vars should be provided if encoding is" - # ) - # if _vars_per_qubit is not None: - # raise ValueError( - # "_vars_per_qubit should not be provided if encoding is" - # ) - # self.var2op = encoding.var2op - # self.q2vars = encoding.q2vars - # self._vars_per_qubit = encoding.max_vars_per_qubit - # else: - # if var2op is None: - # raise ValueError("Either an encoding or var2ops must be provided") - # if _vars_per_qubit is None: - # raise ValueError( - # "_vars_per_qubit must be provided if encoding is not provided" - # ) - # self.var2op = var2op - # self.q2vars = q2vars_from_var2op(var2op) if q2vars is None else q2vars - # self._vars_per_qubit = _vars_per_qubit - + """ + Args: + encoding: Encoding containing the problem information. + expectation_values: Expectation values of the encoding. + circuit: circuit corresponding to the encoding and expectation values. + """ self.encoding = encoding self.expectation_values = expectation_values self.circuit = circuit @@ -79,14 +57,25 @@ def __init__( class RoundingResult: """Base class for a rounding result""" - def __init__(self, samples: List[RoundingSolutionSample], expectation_values,*, time_taken=None): + def __init__( + self, + samples: List[RoundingSolutionSample], + expectation_values: List[float], + time_taken: Optional[float] = None, + ): + """ + Args: + samples: List of samples of the rounding. + expectation_values: Expectation values of the encoding. + time_taken: Time taken for rounding. + """ self._samples = samples self._expectation_values = expectation_values self.time_taken = time_taken @property def samples(self) -> List[RoundingSolutionSample]: - """List of samples""" + """List of samples for the rounding""" return self._samples @property diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 67f36f3ce..6977e915a 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -23,7 +23,6 @@ RoundingResult, ) - # pylint: disable=too-few-public-methods @@ -48,20 +47,14 @@ def __init__(self, *, seed: Optional[int] = None): self.rng = np.random.RandomState(seed) def round(self, ctx: RoundingContext) -> SemideterministicRoundingResult: - """Perform semideterministic rounding""" - - # # trace_values = ctx.expectation_values + """Perform semideterministic rounding - # if trace_values is None: - # raise NotImplementedError( - # "Semideterministic rounding requires that trace_values be available." - # ) + Args: + ctx: Rounding context containing information about the problem and solution. - # if len(trace_values) != len(ctx.var2op): - # raise ValueError( - # f"trace_values has length {len(trace_values)}, " - # "but there are {len(ctx.var2op)} decision variables." - # ) + Returns: + Result containing the rounded solution. + """ def sign(val) -> int: return 0 if (val > 0) else 1 From 31507c18b484dcbe9eb9bc998371569e6b5bafbd Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 17 Apr 2023 17:35:55 +0900 Subject: [PATCH 05/67] add expecation_values getter --- .../algorithms/qrao/quantum_random_access_optimizer.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index c8b3119e9..f84f962ef 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -81,10 +81,10 @@ def rounding_results(self) -> RoundingResult: return self._rounding_results @property - def trace_values(self): + def expectation_values(self): """List of expectation values, one corresponding to each decision variable""" - trace_values = [v[0] for v in self._relaxed_results.aux_operators_evaluated] - return trace_values + expectation_values = [v[0] for v in self._relaxed_results.aux_operators_evaluated] + return expectation_values @property def relaxed_fval(self) -> float: From 11a5e40ec57ebbb3ba71ecd1a297f32270960cba Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 21 Apr 2023 17:34:39 +0900 Subject: [PATCH 06/67] inherit OptimizationAlgorithm --- .../algorithms/qrao/magic_rounding.py | 4 +- .../qrao/quantum_random_access_optimizer.py | 225 +++++++++++------- .../qrao/semideterministic_rounding.py | 5 + 3 files changed, 151 insertions(+), 83 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index fb9003741..d4ed8cd73 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -426,8 +426,8 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: # weighted sampling if expectation_values is None: raise NotImplementedError( - "Magic rounding with weighted sampling requires the trace values " - "to be available, but they are not." + "Magic rounding with weighted sampling requires the expectation values of the " + "``RoundingContext`` to be available, but they are not." ) bases, basis_shots = self._sample_bases_weighted( q2vars, expectation_values, vars_per_qubit diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index f84f962ef..453aefcbc 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -13,18 +13,24 @@ """Quantum Random Access Optimizer class.""" import time -from typing import List, Optional, Tuple, Union +from typing import List, Optional, Tuple, Union, cast import numpy as np from qiskit import QuantumCircuit -from qiskit.algorithms.minimum_eigensolvers import (MinimumEigensolver, - MinimumEigensolverResult, - NumPyMinimumEigensolver) - -from qiskit_optimization.algorithms import (OptimizationResult, - OptimizationResultStatus, - SolutionSample) -from qiskit_optimization.problems import Variable +from qiskit.algorithms.minimum_eigensolvers import ( + MinimumEigensolver, + MinimumEigensolverResult, + NumPyMinimumEigensolver, +) + +from qiskit_optimization.algorithms import ( + OptimizationAlgorithm, + OptimizationResult, + OptimizationResultStatus, + SolutionSample, +) +from qiskit_optimization.converters import QuadraticProgramToQubo +from qiskit_optimization.problems import QuadraticProgram, Variable from .quantum_random_access_encoding import QuantumRandomAccessEncoding from .rounding_common import RoundingContext, RoundingResult, RoundingScheme @@ -42,9 +48,10 @@ def __init__( variables: List[Variable], status: OptimizationResultStatus, samples: Optional[List[SolutionSample]], + encoding: QuantumRandomAccessEncoding, relaxed_fval: float, - relaxed_results: MinimumEigensolverResult, - rounding_results: RoundingResult, + relaxed_result: MinimumEigensolverResult, + rounding_result: RoundingResult, ) -> None: """ Args: @@ -53,8 +60,10 @@ def __init__( variables: The list of variables of the optimization problem. status: The termination status of the optimization algorithm. samples: The list of ``SolutionSample`` obtained from the optimization algorithm. - relaxed_results: The result obtained from the underlying minimum eigensolver. - rounding_results: The rounding results. + encoding: The encoding used for the optimization. + relaxed_fval: The optimal function value of the relaxed problem. + relaxed_result: The result obtained from the underlying minimum eigensolver. + rounding_result: The rounding result. """ super().__init__( x=x, @@ -64,52 +73,58 @@ def __init__( raw_results=None, samples=samples, ) + self._encoding = encoding self._relaxed_fval = relaxed_fval - self._relaxed_results = relaxed_results - self._rounding_results = rounding_results + self._relaxed_result = relaxed_result + self._rounding_result = rounding_result @property - def relaxed_results( - self, - ) -> MinimumEigensolverResult: - """The result obtained from the underlying minimum eigensolver.""" - return self._relaxed_results + def encoding(self) -> QuantumRandomAccessEncoding: + """The encoding used for the optimization.""" + return self._encoding @property - def rounding_results(self) -> RoundingResult: - """The rounding results.""" - return self._rounding_results + def relaxed_fval(self) -> float: + """The optimal function value of the relaxed problem.""" + return self._relaxed_fval @property - def expectation_values(self): - """List of expectation values, one corresponding to each decision variable""" - expectation_values = [v[0] for v in self._relaxed_results.aux_operators_evaluated] - return expectation_values + def relaxed_result( + self, + ) -> MinimumEigensolverResult: + """The result obtained from the underlying minimum eigensolver.""" + return self._relaxed_result @property - def relaxed_fval(self) -> float: - """Relaxed function value, in the conventions of the original ``QuadraticProgram``.""" - return self._relaxed_fval - + def rounding_result(self) -> RoundingResult: + """The rounding result.""" + return self._rounding_result -class QuantumRandomAccessOptimizer: +class QuantumRandomAccessOptimizer(OptimizationAlgorithm): """Quantum Random Access Optimizer class.""" def __init__( self, min_eigen_solver: MinimumEigensolver, + penalty: Optional[float] = None, + max_vars_per_qubit: int = 3, rounding_scheme: Optional[RoundingScheme] = None, ): """ Args: min_eigen_solver: The minimum eigensolver to use for solving the relaxed problem. + penalty: The factor that is used to scale the penalty terms corresponding to linear + equality constraints. If ``None`` is provided, the penalty will be automatically + determined. rounding_scheme: The rounding scheme. If ``None`` is provided, ``SemideterministicRounding()`` will be used. """ self.min_eigen_solver = min_eigen_solver - if rounding_scheme is None: - rounding_scheme = SemideterministicRounding() + self.penalty = penalty + # Use ``QuadraticProgramToQubo`` to convert the problem to a QUBO. + self._converters = [QuadraticProgramToQubo(penalty=penalty)] + self._max_vars_per_qubit = max_vars_per_qubit self.rounding_scheme = rounding_scheme @property @@ -127,6 +142,42 @@ def min_eigen_solver(self, min_eigen_solver: MinimumEigensolver) -> None: ) self._min_eigen_solver = min_eigen_solver + @property + def max_vars_per_qubit(self) -> int: + """Return the maximum number of variables per qubit.""" + return self._max_vars_per_qubit + + @max_vars_per_qubit.setter + def max_vars_per_qubit(self, max_vars_per_qubit: int) -> None: + """Set the maximum number of variables per qubit.""" + self._max_vars_per_qubit = max_vars_per_qubit + + @property + def rounding_scheme(self) -> RoundingScheme: + """Return the rounding scheme.""" + return self._rounding_scheme + + @rounding_scheme.setter + def rounding_scheme(self, rounding_scheme: RoundingScheme) -> None: + """Set the rounding scheme.""" + if rounding_scheme is None: + rounding_scheme = SemideterministicRounding() + self._rounding_scheme = rounding_scheme + + def get_compatibility_msg(self, problem: QuadraticProgram) -> str: + """Checks whether a given problem can be solved with this optimizer. + + Checks whether the given problem is compatible, i.e., whether the problem can be converted + to a QUBO, and otherwise, returns a message explaining the incompatibility. + + Args: + problem: The optimization problem to check compatibility. + + Returns: + A message describing the incompatibility. + """ + return QuadraticProgramToQubo.get_compatibility_msg(problem) + def solve_relaxed( self, encoding: QuantumRandomAccessEncoding, @@ -154,19 +205,22 @@ def solve_relaxed( # Solve the relaxed problem start_time_relaxed = time.time() - relaxed_results = self.min_eigen_solver.compute_minimum_eigenvalue( + relaxed_result = self.min_eigen_solver.compute_minimum_eigenvalue( encoding.qubit_op, aux_operators=variable_ops ) - relaxed_results.time_taken = time.time() - start_time_relaxed + relaxed_result.time_taken = time.time() - start_time_relaxed - # Get auxiliary trace values for rounding. - expectation_values = [v[0] for v in relaxed_results.aux_operators_evaluated] + # Get auxiliary expectaion values for rounding. + if relaxed_result.aux_operators_evaluated is not None: + expectation_values = [v[0] for v in relaxed_result.aux_operators_evaluated] + else: + expectation_values = None # Get the circuit corresponding to the relaxed solution. if hasattr(self.min_eigen_solver, "ansatz"): - circuit = self.min_eigen_solver.ansatz.bind_parameters(relaxed_results.optimal_point) + circuit = self.min_eigen_solver.ansatz.bind_parameters(relaxed_result.optimal_point) elif isinstance(self.min_eigen_solver, NumPyMinimumEigensolver): - statevector = relaxed_results.eigenstate + statevector = relaxed_result.eigenstate circuit = QuantumCircuit(encoding.num_qubits) circuit.initialize(statevector) else: @@ -178,64 +232,73 @@ def solve_relaxed( circuit=circuit, ) - return relaxed_results, rounding_context + return relaxed_result, rounding_context - def solve(self, encoding: QuantumRandomAccessEncoding) -> QuantumRandomAccessOptimizationResult: + def solve(self, problem: QuadraticProgram) -> QuantumRandomAccessOptimizationResult: """Solve the relaxed Hamiltonian given by the encoding and round the solution by the given rounding scheme. Args: - encoding: The ``QuantumRandomAccessEncoding``, which must have already been encoded - with a ``QuadraticProgram``. + problem: The ``QuadraticProgram`` to be solved. + Returns: The result of the quantum random access optimization. Raises: ValueError: If the encoding has not been encoded with a ``QuadraticProgram``. """ - if not encoding.frozen: - raise ValueError( - "The encoding must call ``encode()`` with a ``QuadraticProgram`` before being passed" - "to the QuantumRandomAccessOptimizer." - ) + # Convert the problem to a QUBO + self._verify_compatibility(problem) + qubo = self._convert(problem, self._converters) + # Encode the QUBO into a quantum random access encoding + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=self.max_vars_per_qubit) + encoding.encode(qubo) # Solve the relaxed problem - (relaxed_results, rounding_context) = self.solve_relaxed(encoding) + (relaxed_result, rounding_context) = self.solve_relaxed(encoding) # Round the solution - rounding_results = self.rounding_scheme.round(rounding_context) - - # Process rounding results - samples: List[SolutionSample] = [] - for sample in rounding_results.samples: - if encoding.problem.is_feasible(sample.x): - status = OptimizationResultStatus.SUCCESS - else: - status = OptimizationResultStatus.INFEASIBLE - samples.append( - SolutionSample( - x=sample.x, - fval=encoding.problem.objective.evaluate(sample.x), - probability=sample.probability, - status=status, - ) - ) + rounding_result = self.rounding_scheme.round(rounding_context) - # Get the best sample - fsense = {"MINIMIZE": min, "MAXIMIZE": max}[encoding.problem.objective.sense.name] - best_sample = fsense(samples, key=lambda x: x.fval) + return self.process_result(problem, encoding, relaxed_result, rounding_result) - relaxed_fval = encoding.problem.objective.sense.value * ( - encoding.offset + relaxed_results.eigenvalue.real + def process_result( + self, + problem: QuadraticProgram, + encoding: QuantumRandomAccessEncoding, + relaxed_result: MinimumEigensolverResult, + rounding_result: RoundingResult, + ) -> QuantumRandomAccessOptimizationResult: + """Process the relaxed result of the minimum eigensolver and rounding scheme. + + Args: + problem: The ``QuadraticProgram`` to be solved. + encoding: The ``QuantumRandomAccessEncoding``, which must have already been ``encode()``ed + with the corresponding problem. + relaxed_result: The relaxed result of the minimum eigensolver. + rounding_result: The result of the rounding scheme. + + Returns: + The result of the quantum random access optimization. + """ + samples, best_sol = self._interpret_samples( + problem=problem, raw_samples=rounding_result.samples, converters=self._converters ) - return QuantumRandomAccessOptimizationResult( - x=best_sample.x, - fval=best_sample.fval, - variables=encoding.problem.variables, - status=OptimizationResultStatus.SUCCESS, - samples=samples, - relaxed_fval=relaxed_fval, - relaxed_results=relaxed_results, - rounding_results=rounding_results, + relaxed_fval = encoding.problem.objective.sense.value * ( + encoding.offset + relaxed_result.eigenvalue.real + ) + return cast( + QuantumRandomAccessOptimizationResult, + self._interpret( + x=best_sol.x, + converters=self._converters, + problem=problem, + result_class=QuantumRandomAccessOptimizationResult, + samples=samples, + encoding=encoding, + relaxed_fval=relaxed_fval, + relaxed_result=relaxed_result, + rounding_result=rounding_result, + ), ) diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 6977e915a..67948de9f 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -59,6 +59,11 @@ def round(self, ctx: RoundingContext) -> SemideterministicRoundingResult: def sign(val) -> int: return 0 if (val > 0) else 1 + if ctx.expectation_values is None: + raise NotImplementedError( + "Semideterministric rounding with weighted sampling requires the expectation " + "values of the ``RoundingContext`` to be available, but they are not." + ) rounded_vars = [ sign(e) if not np.isclose(0, e) else self.rng.randint(2) for e in ctx.expectation_values ] From 6a679434c50dea706fd25464ef8f20d689d16341 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 8 May 2023 23:15:47 +0900 Subject: [PATCH 07/67] add unittests for encoding --- .../qrao/encoding_commutation_verifier.py | 2 +- .../algorithms/qrao/magic_rounding.py | 6 +- .../qrao/quantum_random_access_encoding.py | 71 +++---- test/algorithms/qrao/__init__.py | 11 ++ .../test_quantum_random_access_encoding.py | 177 ++++++++++++++++++ 5 files changed, 229 insertions(+), 38 deletions(-) create mode 100644 test/algorithms/qrao/__init__.py create mode 100644 test/algorithms/qrao/test_quantum_random_access_encoding.py diff --git a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py index 6a6fbe94d..80f05495a 100644 --- a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py +++ b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py @@ -49,7 +49,7 @@ def __getitem__(self, i: int) -> Tuple[str, float, float]: encoding = self._encoding str_dvars = f"{i:0{encoding.num_vars}b}" dvars = [int(b) for b in str_dvars] - encoded_bitstr_qc = encoding.state_prep(dvars) + encoded_bitstr_qc = encoding.state_preparation_circuit(dvars) # Evaluate the original objective function problem = encoding.problem diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index d4ed8cd73..6953e0785 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -22,7 +22,7 @@ from qiskit.primitives import Sampler from qiskit.quantum_info import SparsePauliOp -from .quantum_random_access_encoding import z_to_21p_qrac_basis_circuit, z_to_31p_qrac_basis_circuit +from .quantum_random_access_encoding import _z_to_21p_qrac_basis_circuit, _z_to_31p_qrac_basis_circuit from .rounding_common import RoundingContext, RoundingResult, RoundingScheme, RoundingSolutionSample @@ -157,9 +157,9 @@ def _make_circuits( circuits = [] for basis in bases: if vars_per_qubit == 3: - qc = circ.compose(z_to_31p_qrac_basis_circuit(basis).inverse(), inplace=False) + qc = circ.compose(_z_to_31p_qrac_basis_circuit(basis).inverse(), inplace=False) elif vars_per_qubit == 2: - qc = circ.compose(z_to_21p_qrac_basis_circuit(basis).inverse(), inplace=False) + qc = circ.compose(_z_to_21p_qrac_basis_circuit(basis).inverse(), inplace=False) elif vars_per_qubit == 1: qc = circ.copy() qc.measure_all() diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 655105769..a209d1da4 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -23,9 +23,9 @@ from qiskit_optimization.exceptions import QiskitOptimizationError from qiskit_optimization.problems.quadratic_program import QuadraticProgram +from qiskit.opflow import PauliSumOp - -def z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumCircuit: +def _z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (3,1,p)-QRAC. Args: @@ -41,11 +41,12 @@ def z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumC circ = QuantumCircuit(len(bases)) BETA = np.arccos(1 / np.sqrt(3)) # pylint: disable=invalid-name - if bit_flip: - # if bit_flip == 1: then flip the state of the first qubit to |1> - circ.x(0) for i, base in enumerate(reversed(bases)): + if bit_flip: + # if bit_flip == 1: then flip the state of the qubit to |1> + circ.x(i) + if base == 0: circ.r(-BETA, -np.pi / 4, i) elif base == 1: @@ -59,7 +60,7 @@ def z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumC return circ -def z_to_21p_qrac_basis_circuit(bases: int, bit_flip: int = 0) -> QuantumCircuit: +def _z_to_21p_qrac_basis_circuit(bases: int, bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (2,1,p)-QRAC. Args: @@ -74,11 +75,12 @@ def z_to_21p_qrac_basis_circuit(bases: int, bit_flip: int = 0) -> QuantumCircuit """ circ = QuantumCircuit(1) - if bit_flip: - # if bit_flip == 1: then flip the state of the first qubit to |1> - circ.x(0) - for i, base in enumerate(reversed(bases)): + if bit_flip: + # if bit_flip == 1: then flip the state of the qubit to |1> + circ.x(i) + + if base == 0: circ.r(-1 * np.pi / 4, -np.pi / 2, i) elif base == 1: @@ -88,7 +90,7 @@ def z_to_21p_qrac_basis_circuit(bases: int, bit_flip: int = 0) -> QuantumCircuit return circ -def qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: +def _qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: """ Return the circuit that prepares the state for a (1,1,p), (2,1,p), or (3,1,p)-QRAC. @@ -126,8 +128,8 @@ def qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| - base = 2 * base_index0 + base_index1 - circ = z_to_31p_qrac_basis_circuit(base, bit_flip) + base = [2 * base_index0 + base_index1] + circ = _z_to_31p_qrac_basis_circuit(base, bit_flip) elif len(bit_list) == 2: # Prepare (2,1,p)-qrac @@ -138,8 +140,8 @@ def qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf # # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| - base = base_index0 - circ = z_to_21p_qrac_basis_circuit(base, bit_flip) + base = [base_index0] + circ = _z_to_21p_qrac_basis_circuit(base, bit_flip) else: bit_flip = bit_list[0] @@ -150,7 +152,7 @@ def qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: return circ -def qrac_state_prep_multiqubit( +def _qrac_state_prep_multiqubit( dvars: List[int], q2vars: List[List[int]], max_vars_per_qubit: int, @@ -212,28 +214,28 @@ def qrac_state_prep_multiqubit( raise ValueError(f"Not all dvars were included in q2vars: {remaining_dvars}") # Prepare the individual qrac circuit and combine them into a multiqubit circuit - qracs = [qrac_state_prep_1q(qi_bits) for qi_bits in variable_mappings] + qracs = [_qrac_state_prep_1q(qi_bits) for qi_bits in variable_mappings] qrac_circ = reduce(lambda x, y: x.tensor(y), qracs) return qrac_circ -def q2vars_from_var2op(var2op: Dict[int, Tuple[int, SparsePauliOp]]) -> List[List[int]]: - """ - Converts a dictionary mapping decision variables to qubits and Pauli operators to a list of - lists of decision variables. +# def q2vars_from_var2op(var2op: Dict[int, Tuple[int, SparsePauliOp]]) -> List[List[int]]: +# """ +# Converts a dictionary mapping decision variables to qubits and Pauli operators to a list of +# lists of decision variables. - Args: - var2op: A dictionary mapping decision variables to qubits and Pauli operators. +# Args: +# var2op: A dictionary mapping decision variables to qubits and Pauli operators. - Returns: - A list of lists of decision variables. Each inner list contains the indices of decision - variables mapped to a specific qubit. - """ - num_qubits = max(qubit_index for qubit_index, _ in var2op.values()) + 1 - q2vars: List[List[int]] = [[] for i in range(num_qubits)] - for var, (q, _) in var2op.items(): - q2vars[q].append(var) - return q2vars +# Returns: +# A list of lists of decision variables. Each inner list contains the indices of decision +# variables mapped to a specific qubit. +# """ +# num_qubits = max(qubit_index for qubit_index, _ in var2op.values()) + 1 +# q2vars: List[List[int]] = [[] for i in range(num_qubits)] +# for var, (q, _) in var2op.items(): +# q2vars[q].append(var) +# return q2vars class QuantumRandomAccessEncoding: @@ -348,6 +350,7 @@ def freeze(self): """ if self._frozen is False: self._qubit_op = self._qubit_op.simplify() + self._qubit_op = PauliSumOp(self._qubit_op) self._frozen = True @property @@ -571,7 +574,7 @@ def encode(self, problem: QuadraticProgram) -> None: self.freeze() - def state_prep(self, dvars: List[int]) -> QuantumCircuit: + def state_preparation_circuit(self, dvars: List[int]) -> QuantumCircuit: """ Generate a circuit that prepares the state corresponding to the given binary string. @@ -581,4 +584,4 @@ def state_prep(self, dvars: List[int]) -> QuantumCircuit: Returns: A QuantumCircuit that prepares the state corresponding to the given binary string. """ - return qrac_state_prep_multiqubit(dvars, self.q2vars, self.max_vars_per_qubit) + return _qrac_state_prep_multiqubit(dvars, self.q2vars, self.max_vars_per_qubit) diff --git a/test/algorithms/qrao/__init__.py b/test/algorithms/qrao/__init__.py new file mode 100644 index 000000000..26f7536d3 --- /dev/null +++ b/test/algorithms/qrao/__init__.py @@ -0,0 +1,11 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py new file mode 100644 index 000000000..9f02f501c --- /dev/null +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -0,0 +1,177 @@ +"""Tests for qrao""" +import unittest +from test.optimization_test_case import QiskitOptimizationTestCase + +import numpy as np +from qiskit.circuit import QuantumCircuit +from qiskit.opflow import PauliSumOp +from qiskit.quantum_info import SparsePauliOp + +from qiskit_optimization.algorithms.qrao import ( + EncodingCommutationVerifier, + QuantumRandomAccessEncoding, +) +from qiskit_optimization.problems import QuadraticProgram + + +class TestQuantumRandomAccessEncoding(QiskitOptimizationTestCase): + """QuantumRandomAccessEncoding tests.""" + + def setUp(self): + super().setUp() + self.problem = QuadraticProgram() + self.problem.binary_var("x") + self.problem.binary_var("y") + self.problem.binary_var("z") + self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + + def test_31p_qrac_encoding(self): + """Test (3,1,p) QRAC""" + encoding = QuantumRandomAccessEncoding(3) + self.assertFalse(encoding.frozen) # frozen is False + encoding.encode(self.problem) + expected_op = PauliSumOp( + SparsePauliOp( + ["X", "Y", "Z"], coeffs=[-np.sqrt(3) / 2, 2 * -np.sqrt(3) / 2, 3 * -np.sqrt(3) / 2] + ), + coeff=1.0, + ) + + self.assertTrue(encoding.frozen) # frozen is True + self.assertEqual(encoding.qubit_op, expected_op) + self.assertEqual(encoding.num_vars, 3) + self.assertEqual(encoding.num_qubits, 1) + self.assertEqual(encoding.offset, 3) + self.assertEqual(encoding.max_vars_per_qubit, 3) + self.assertEqual(encoding.q2vars, [[0, 1, 2]]) + self.assertEqual( + encoding.var2op, + { + 0: (0, SparsePauliOp(["X"], coeffs=[1.0])), + 1: (0, SparsePauliOp(["Y"], coeffs=[1.0])), + 2: (0, SparsePauliOp(["Z"], coeffs=[1.0])), + }, + ) + self.assertEqual(encoding.compression_ratio, 3) + self.assertEqual(encoding.minimum_recovery_probability, (1 + 1 / np.sqrt(3)) / 2) + self.assertEqual(encoding.problem, self.problem) + + def test_21p_qrac_encoding(self): + """Test (2,1,p) QRAC""" + encoding = QuantumRandomAccessEncoding(2) + self.assertFalse(encoding.frozen) # frozen is False + encoding.encode(self.problem) + expected_op = PauliSumOp( + SparsePauliOp( + ["XI", "ZI", "IX"], + coeffs=[-np.sqrt(2) / 2, 2 * -np.sqrt(2) / 2, 3 * -np.sqrt(2) / 2], + ), + coeff=1.0, + ) + + self.assertTrue(encoding.frozen) # frozen is True + self.assertEqual(encoding.qubit_op, expected_op) + self.assertEqual(encoding.num_vars, 3) + self.assertEqual(encoding.num_qubits, 2) + self.assertEqual(encoding.offset, 3) + self.assertEqual(encoding.max_vars_per_qubit, 2) + self.assertEqual(encoding.q2vars, [[0, 1], [2]]) + self.assertEqual( + encoding.var2op, + { + 0: (0, SparsePauliOp(["X"], coeffs=[1.0])), + 1: (0, SparsePauliOp(["Z"], coeffs=[1.0])), + 2: (1, SparsePauliOp(["X"], coeffs=[1.0])), + }, + ) + self.assertEqual(encoding.compression_ratio, 1.5) + self.assertEqual(encoding.minimum_recovery_probability, (1 + 1 / np.sqrt(2)) / 2) + self.assertEqual(encoding.problem, self.problem) + + def test_11p_qrac_encoding(self): + """Test (1,1,p) QRAC""" + encoding = QuantumRandomAccessEncoding(1) + self.assertFalse(encoding.frozen) # frozen is False + encoding.encode(self.problem) + expected_op = PauliSumOp( + SparsePauliOp(["ZII", "IZI", "IIZ"], coeffs=[-0.5, -1.0, -1.5]), + coeff=1.0, + ) + + self.assertTrue(encoding.frozen) # frozen is True + self.assertEqual(encoding.qubit_op, expected_op) + self.assertEqual(encoding.num_vars, 3) + self.assertEqual(encoding.num_qubits, 3) + self.assertEqual(encoding.offset, 3) + self.assertEqual(encoding.max_vars_per_qubit, 1) + self.assertEqual(encoding.q2vars, [[0], [1], [2]]) + self.assertEqual( + encoding.var2op, + { + 0: (0, SparsePauliOp(["Z"], coeffs=[1.0])), + 1: (1, SparsePauliOp(["Z"], coeffs=[1.0])), + 2: (2, SparsePauliOp(["Z"], coeffs=[1.0])), + }, + ) + self.assertEqual(encoding.compression_ratio, 1) + self.assertEqual(encoding.minimum_recovery_probability, 1) + self.assertEqual(encoding.problem, self.problem) + + def test_qrac_state_prep(self): + """Test that state preparation circuit is correct""" + dvars = [0, 1, 1] + with self.subTest(msg="(3,1,p) QRAC"): + encoding = QuantumRandomAccessEncoding(3) + encoding.encode(self.problem) + state_prep_circ = encoding.state_preparation_circuit(dvars=dvars) + circ = QuantumCircuit(1) + BETA = np.arccos(1 / np.sqrt(3)) + circ.r(np.pi - BETA, np.pi / 4, 0) + self.assertEqual(state_prep_circ, circ) + + with self.subTest(msg="(2,1,p) QRAC"): + encoding = QuantumRandomAccessEncoding(2) + encoding.encode(self.problem) + state_prep_circ = encoding.state_preparation_circuit(dvars=dvars) + circ = QuantumCircuit(2) + circ.x(0) + circ.r(-3 * np.pi / 4, -np.pi / 2, 0) + circ.r(-3 * np.pi / 4, -np.pi / 2, 1) + self.assertEqual(state_prep_circ, circ) + + with self.subTest(msg="(1,1,p) QRAC"): + encoding = QuantumRandomAccessEncoding(1) + encoding.encode(self.problem) + state_prep_circ = encoding.state_preparation_circuit(dvars=dvars) + circ = QuantumCircuit(3) + circ.x(0) + circ.x(1) + self.assertEqual(state_prep_circ, circ) + + def test_qrac_unsupported_encoding(self): + """Test that exception is raised if ``max_vars_per_qubit`` is invalid""" + with self.assertRaises(ValueError): + QuantumRandomAccessEncoding(4) + with self.assertRaises(ValueError): + QuantumRandomAccessEncoding(0) + + +class TestEncodingCommutationVerifier(QiskitOptimizationTestCase): + """Tests for EncodingCommutationVerifier.""" + + def test_encoding_commutation_verifier(self): + """Test EncodingCommutationVerifier""" + problem = QuadraticProgram() + problem.binary_var("x") + problem.binary_var("y") + problem.binary_var("z") + problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) + encoding.encode(problem) + verifier = EncodingCommutationVerifier(encoding) + for _, obj_val, encoded_obj_val in verifier: + self.assertAlmostEqual(obj_val, encoded_obj_val) + +if __name__ == "__main__": + unittest.main() From 41f86ebeae66d23f0637df938c2c3a5ce9165094 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Tue, 9 May 2023 20:58:32 +0900 Subject: [PATCH 08/67] add unittests for optimizer --- test/algorithms/qrao/test_magic_rounding.py | 76 +++++++ .../test_quantum_random_access_encoding.py | 15 +- .../test_quantum_random_access_optimizer.py | 185 ++++++++++++++++++ .../qrao/test_semideterministic_rounding.py | 57 ++++++ 4 files changed, 332 insertions(+), 1 deletion(-) create mode 100644 test/algorithms/qrao/test_magic_rounding.py create mode 100644 test/algorithms/qrao/test_quantum_random_access_optimizer.py create mode 100644 test/algorithms/qrao/test_semideterministic_rounding.py diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py new file mode 100644 index 000000000..96971d1ea --- /dev/null +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -0,0 +1,76 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for MagicRounding""" +import unittest +from test.optimization_test_case import QiskitOptimizationTestCase + +import numpy as np + +from qiskit_optimization.algorithms.qrao import ( + QuantumRandomAccessEncoding, + SemideterministicRounding, + SemideterministicRoundingResult, + RoundingContext, + MagicRounding, + MagicRoundingResult, +) +from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample + +from qiskit_optimization.problems import QuadraticProgram + +from qiskit.primitives import Sampler + +class TestMagicRounding(QiskitOptimizationTestCase): + """MagicRounding tests.""" + + def setUp(self): + super().setUp() + self.problem = QuadraticProgram() + self.problem.binary_var("x") + self.problem.binary_var("y") + self.problem.binary_var("z") + self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + + def test_magic_rounding(self): + """Test MagicRounding""" + encoding = QuantumRandomAccessEncoding() + rounding_scheme = MagicRounding(Sampler(), seed=123) + expectation_values = [1, -1, 0, 0.7, -0.3] + result = rounding_scheme.round( + RoundingContext(expectation_values=expectation_values, encoding=encoding) + ) + self.assertIsInstance(result, SemideterministicRoundingResult) + self.assertIsInstance(result.samples[0], RoundingSolutionSample) + self.assertEqual(result.expectation_values, [1, -1, 0, 0.7, -0.3]) + np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 0, 0, 1]) + self.assertEqual(result.samples[0].probability, 1.0) + + + + def test_semideterministic_rounding(self): + """Test SemideterministicRounding""" + encoding = QuantumRandomAccessEncoding() + rounding_scheme = SemideterministicRounding(seed=123) + expectation_values = [1, -1, 0, 0.7, -0.3] + result = rounding_scheme.round( + RoundingContext(expectation_values=expectation_values, encoding=encoding) + ) + self.assertIsInstance(result, SemideterministicRoundingResult) + self.assertIsInstance(result.samples[0], RoundingSolutionSample) + self.assertEqual(result.expectation_values, [1, -1, 0, 0.7, -0.3]) + np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 0, 0, 1]) + self.assertEqual(result.samples[0].probability, 1.0) + + +if __name__ == "__main__": + unittest.main() diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index 9f02f501c..602415dab 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -1,4 +1,16 @@ -"""Tests for qrao""" +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for QuantumRandomAccessEncoding""" import unittest from test.optimization_test_case import QiskitOptimizationTestCase @@ -170,6 +182,7 @@ def test_encoding_commutation_verifier(self): encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) encoding.encode(problem) verifier = EncodingCommutationVerifier(encoding) + self.assertEqual(len(verifier), 2**encoding.num_vars) for _, obj_val, encoded_obj_val in verifier: self.assertAlmostEqual(obj_val, encoded_obj_val) diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py new file mode 100644 index 000000000..3cf14245f --- /dev/null +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -0,0 +1,185 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for QuantumRandomAccessOptimizer""" +import unittest +from test.optimization_test_case import QiskitOptimizationTestCase + +import numpy as np +from qiskit.algorithms.minimum_eigensolvers import ( + NumPyMinimumEigensolver, + NumPyMinimumEigensolverResult, + VQE, + VQEResult, +) +from qiskit.algorithms.optimizers import COBYLA +from qiskit.circuit.library import QAOAAnsatz, RealAmplitudes +from qiskit.primitives import Estimator +from qiskit.utils import algorithm_globals + +from qiskit_optimization.algorithms.optimization_algorithm import OptimizationResultStatus +from qiskit_optimization.algorithms.qrao import ( + QuantumRandomAccessEncoding, + QuantumRandomAccessOptimizationResult, + QuantumRandomAccessOptimizer, + RoundingContext, + SemideterministicRoundingResult, +) +from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample +from qiskit_optimization.problems import QuadraticProgram + + +class TestQuantumRandomAccessOptimizer(QiskitOptimizationTestCase): + """QuantumRandomAccessOptimizer tests.""" + + def setUp(self): + super().setUp() + self.problem = QuadraticProgram() + self.problem.binary_var("x") + self.problem.binary_var("y") + self.problem.binary_var("z") + self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + self.encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) + self.encoding.encode(self.problem) + self.ansatz = RealAmplitudes(self.encoding.num_qubits) # for VQE + algorithm_globals.random_seed = 50 + + def test_solve_relaxed_numpy(self): + """Test QuantumRandomAccessOptimizer with NumPyMinimumEigensolver.""" + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + relaxed_results, rounding_context = qrao.solve_relaxed(encoding=self.encoding) + self.assertIsInstance(relaxed_results, NumPyMinimumEigensolverResult) + self.assertAlmostEqual(relaxed_results.eigenvalue, -3.24037, places=5) + self.assertEqual(len(relaxed_results.aux_operators_evaluated), 3) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[0][0], 0.26726, places=5) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[1][0], 0.53452, places=5) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[2][0], 0.80178, places=5) + self.assertIsInstance(rounding_context, RoundingContext) + self.assertEqual(rounding_context.circuit.num_qubits, self.ansatz.num_qubits) + self.assertEqual(rounding_context.encoding, self.encoding) + self.assertAlmostEqual(rounding_context.expectation_values[0], 0.26726, places=5) + self.assertAlmostEqual(rounding_context.expectation_values[1], 0.53452, places=5) + self.assertAlmostEqual(rounding_context.expectation_values[2], 0.80178, places=5) + + def test_solve_relaxed_vqe(self): + """Test QuantumRandomAccessOptimizer with VQE.""" + vqe = VQE( + ansatz=self.ansatz, + optimizer=COBYLA(), + estimator=Estimator(), + ) + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe) + relaxed_results, rounding_context = qrao.solve_relaxed(encoding=self.encoding) + self.assertIsInstance(relaxed_results, VQEResult) + self.assertAlmostEqual(relaxed_results.eigenvalue, -2.73861, places=5) + self.assertEqual(len(relaxed_results.aux_operators_evaluated), 3) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[0][0], 0.31632, places=4) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[1][0], 0, places=5) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[2][0], 0.94865, places=5) + self.assertIsInstance(rounding_context, RoundingContext) + self.assertEqual(rounding_context.circuit.num_qubits, self.ansatz.num_qubits) + self.assertEqual(rounding_context.encoding, self.encoding) + self.assertAlmostEqual(rounding_context.expectation_values[0], 0.31632, places=4) + self.assertAlmostEqual(rounding_context.expectation_values[1], 0, places=5) + self.assertAlmostEqual(rounding_context.expectation_values[2], 0.94865, places=5) + + def test_solve_relaxed_qaoa(self): + """Test QuantumRandomAccessOptimizer with QAOA.""" + qaoa_ansatz = QAOAAnsatz( + cost_operator=self.encoding.qubit_op, + ) + qaoa = VQE( + ansatz=qaoa_ansatz, + optimizer=COBYLA(), + estimator=Estimator(), + ) + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=qaoa) + relaxed_results, rounding_context = qrao.solve_relaxed(encoding=self.encoding) + self.assertIsInstance(relaxed_results, VQEResult) + self.assertAlmostEqual(relaxed_results.eigenvalue, -3.24036, places=4) + self.assertEqual(len(relaxed_results.aux_operators_evaluated), 3) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[0][0], 0.26777, places=4) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[1][0], 0.53456, places=4) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[2][0], 0.80158, places=5) + self.assertIsInstance(rounding_context, RoundingContext) + self.assertEqual(rounding_context.circuit.num_qubits, self.ansatz.num_qubits) + self.assertEqual(rounding_context.encoding, self.encoding) + self.assertAlmostEqual(rounding_context.expectation_values[0], 0.26777, places=4) + self.assertAlmostEqual(rounding_context.expectation_values[1], 0.53456, places=4) + self.assertAlmostEqual(rounding_context.expectation_values[2], 0.80158, places=5) + + def test_require_aux_operator_support(self): + """Test whether the eigensolver supports auxiliary operator. + If auxiliary operators are not supported, a TypeError should be raised. + """ + + class ModifiedVQE(VQE): + """Modified VQE method without auxiliary operator support. + Since no existing eigensolver seems to lack auxiliary operator support, + we have created one that claims to lack it. + """ + + @classmethod + def supports_aux_operators(cls) -> bool: + return False + + vqe = ModifiedVQE( + ansatz=self.ansatz, + optimizer=COBYLA(), + estimator=Estimator(), + ) + with self.assertRaises(TypeError): + QuantumRandomAccessOptimizer(min_eigen_solver=vqe) + + def test_solve_numpy(self): + """Test QuantumRandomAccessOptimizer with NumPyMinimumEigensolver.""" + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + results = qrao.solve(problem=self.problem) + self.assertIsInstance(results, QuantumRandomAccessOptimizationResult) + self.assertEqual(results.fval, 0) + self.assertEqual(len(results.samples), 1) + np.testing.assert_array_almost_equal(results.samples[0].x, [0, 0, 0]) + self.assertAlmostEqual(results.samples[0].fval, 0) + self.assertAlmostEqual(results.samples[0].probability, 1.0) + self.assertEqual(results.samples[0].status, OptimizationResultStatus.SUCCESS) + self.assertAlmostEqual(results.relaxed_fval, -0.24037, places=5) + self.assertIsInstance(results.relaxed_result, NumPyMinimumEigensolverResult) + self.assertAlmostEqual(results.relaxed_result.eigenvalue, -3.24037, places=5) + self.assertEqual(len(results.relaxed_result.aux_operators_evaluated), 3) + self.assertAlmostEqual( + results.relaxed_result.aux_operators_evaluated[0][0], 0.26726, places=5 + ) + self.assertAlmostEqual( + results.relaxed_result.aux_operators_evaluated[1][0], 0.53452, places=5 + ) + self.assertAlmostEqual( + results.relaxed_result.aux_operators_evaluated[2][0], 0.80178, places=5 + ) + self.assertIsInstance(results.rounding_result, SemideterministicRoundingResult) + self.assertAlmostEqual(results.rounding_result.expectation_values[0], 0.26726, places=5) + self.assertAlmostEqual(results.rounding_result.expectation_values[1], 0.53452, places=5) + self.assertAlmostEqual(results.rounding_result.expectation_values[2], 0.80178, places=5) + self.assertIsInstance(results.rounding_result.samples[0], RoundingSolutionSample) + + def test_empty_encoding(self): + """Test the encoding is empty.""" + np_solver = NumPyMinimumEigensolver() + encoding = QuantumRandomAccessEncoding(3) + with self.assertRaises(ValueError): + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + qrao.solve_relaxed(encoding=encoding) + + +if __name__ == "__main__": + unittest.main() diff --git a/test/algorithms/qrao/test_semideterministic_rounding.py b/test/algorithms/qrao/test_semideterministic_rounding.py new file mode 100644 index 000000000..94c3185a5 --- /dev/null +++ b/test/algorithms/qrao/test_semideterministic_rounding.py @@ -0,0 +1,57 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Tests for SemideterministicRounding""" +import unittest +from test.optimization_test_case import QiskitOptimizationTestCase + +import numpy as np + +from qiskit_optimization.algorithms.qrao import ( + QuantumRandomAccessEncoding, + SemideterministicRounding, + SemideterministicRoundingResult, + RoundingContext, +) +from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample + +from qiskit_optimization.problems import QuadraticProgram + + +class TestSemideterministicRounding(QiskitOptimizationTestCase): + """SemideterministicRounding tests.""" + + def setUp(self): + super().setUp() + self.problem = QuadraticProgram() + self.problem.binary_var("x") + self.problem.binary_var("y") + self.problem.binary_var("z") + self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + + def test_semideterministic_rounding(self): + """Test SemideterministicRounding""" + encoding = QuantumRandomAccessEncoding() + rounding_scheme = SemideterministicRounding(seed=123) + expectation_values = [1, -1, 0, 0.7, -0.3] + result = rounding_scheme.round( + RoundingContext(expectation_values=expectation_values, encoding=encoding) + ) + self.assertIsInstance(result, SemideterministicRoundingResult) + self.assertIsInstance(result.samples[0], RoundingSolutionSample) + self.assertEqual(result.expectation_values, [1, -1, 0, 0.7, -0.3]) + np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 0, 0, 1]) + self.assertEqual(result.samples[0].probability, 1.0) + + +if __name__ == "__main__": + unittest.main() From b4277adec343dd474a86ab3731c1fffa8ab70f00 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Tue, 9 May 2023 21:04:33 +0900 Subject: [PATCH 09/67] add unittests for optimizer Co-authored-by: Jim Garrison Co-authored-by: Bryce Fuller Co-authored-by: Jennifer Glick Co-authored-by: Caleb Johnson Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com> Co-authored-by: Toshinari Itoko Co-authored-by: Areeq Hasan --- qiskit_optimization/algorithms/qrao/magic_rounding.py | 11 ++++++++--- .../algorithms/qrao/semideterministic_rounding.py | 9 ++++++--- test/algorithms/qrao/test_magic_rounding.py | 3 +++ 3 files changed, 17 insertions(+), 6 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 6953e0785..3b51b6d4b 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -441,17 +441,22 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: # values will be total number of observations. soln_counts = self._compute_dv_counts(basis_counts, bases, var2op, vars_per_qubit) + if self.shots is None: + shots = 1024 + else: + shots = self.shots + soln_samples = [ RoundingSolutionSample( x=np.asarray([int(bit) for bit in soln]), - probability=count / self.shots, + probability=count / shots, ) for soln, count in soln_counts.items() ] assert np.isclose( - sum(soln_counts.values()), self.shots - ), f"{sum(soln_counts.values())} != {self.shots}" + sum(soln_counts.values()), shots + ), f"{sum(soln_counts.values())} != {shots}" assert len(bases) == len(basis_shots) == len(basis_counts) stop_time = time.time() diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 67948de9f..844dec5f5 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -54,15 +54,18 @@ def round(self, ctx: RoundingContext) -> SemideterministicRoundingResult: Returns: Result containing the rounded solution. + + Raises: + NotImplementedError: If the expectation values are not available in the context. """ def sign(val) -> int: return 0 if (val > 0) else 1 if ctx.expectation_values is None: - raise NotImplementedError( - "Semideterministric rounding with weighted sampling requires the expectation " - "values of the ``RoundingContext`` to be available, but they are not." + raise NotImplementedError( + "Semideterministric rounding with weighted sampling requires the expectation " + "values of the ``RoundingContext`` to be available, but they are not." ) rounded_vars = [ sign(e) if not np.isclose(0, e) else self.rng.randint(2) for e in ctx.expectation_values diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 96971d1ea..9214f0c3a 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -41,6 +41,9 @@ def setUp(self): self.problem.binary_var("z") self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + + + def test_magic_rounding(self): """Test MagicRounding""" encoding = QuantumRandomAccessEncoding() From 4408846d2b1e98eb510d0513020faa56f97d2ad8 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 10 May 2023 19:09:29 +0900 Subject: [PATCH 10/67] add reno and unittests for magic rounding --- .../algorithms/qrao/magic_rounding.py | 48 +++--- releasenotes/notes/qrao-89d5ff1d2927de64.yaml | 54 +++++++ test/algorithms/qrao/test_magic_rounding.py | 153 ++++++++++++++---- .../test_quantum_random_access_encoding.py | 70 +++++++- 4 files changed, 269 insertions(+), 56 deletions(-) create mode 100644 releasenotes/notes/qrao-89d5ff1d2927de64.yaml diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 3b51b6d4b..e05fa793e 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -22,7 +22,10 @@ from qiskit.primitives import Sampler from qiskit.quantum_info import SparsePauliOp -from .quantum_random_access_encoding import _z_to_21p_qrac_basis_circuit, _z_to_31p_qrac_basis_circuit +from .quantum_random_access_encoding import ( + _z_to_21p_qrac_basis_circuit, + _z_to_31p_qrac_basis_circuit, +) from .rounding_common import RoundingContext, RoundingResult, RoundingScheme, RoundingSolutionSample @@ -123,6 +126,7 @@ def __init__( self._sampler = sampler self.rng = np.random.RandomState(seed) self._basis_sampling = basis_sampling + self._shots = None super().__init__() @property @@ -130,11 +134,6 @@ def sampler(self) -> Sampler: """Returns the ``Sampler`` used to sample the magic bases.""" return self._sampler - @property - def shots(self) -> int: - """Returns the number of samples to collect from each magic basis.""" - return self._sampler.options.get("shots") - @property def basis_sampling(self): """Basis sampling method (either ``"uniform"`` or ``"weighted"``).""" @@ -293,8 +292,7 @@ def _sample_bases_uniform( self, q2vars: List[List[int]], vars_per_qubit: int ) -> Tuple[np.ndarray, np.ndarray]: """ - Sample measurement bases for each qubit uniformly at random. If the number of shots - is not specified, we default to 1024. + Sample measurement bases for each qubit uniformly at random. Args: q2vars: A list of lists of integers. Each inner list contains the indices of decision @@ -313,14 +311,9 @@ def _sample_bases_uniform( corresponds to the number of shots to use for the corresponding basis in the bases array. """ - # If the number of shots is not specified, we default to 1024. - if self.shots is None: - shots = 1024 - else: - shots = self.shots bases = [ self.rng.choice(2 ** (vars_per_qubit - 1), size=len(q2vars)).tolist() - for _ in range(shots) + for _ in range(self._shots) ] bases, basis_shots = np.unique(bases, axis=0, return_counts=True) return bases, basis_shots @@ -387,8 +380,11 @@ def _sample_bases_weighted( elif vars_per_qubit == 1: basis_probs.append([1.0]) bases = [ - [self.rng.choice(2 ** (vars_per_qubit - 1), p=probs) for probs in basis_probs] - for _ in range(self.shots) + [ + self.rng.choice(2 ** (vars_per_qubit - 1), p=[p.real for p in probs]) + for probs in basis_probs + ] + for _ in range(self._shots) ] bases, basis_shots = np.unique(bases, axis=0, return_counts=True) return bases, basis_shots @@ -404,7 +400,7 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: Raises: NotImplementedError: If the circuit is not available for magic rounding. - + ValueError: If the sampler is not configured with a number of shots. """ start_time = time.time() expectation_values = ctx.expectation_values @@ -419,6 +415,13 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: "semideterministic rounding instead." ) + if self._sampler.options.get("shots") is None: + raise ValueError( + "Magic rounding requires the sampler to be configured with a number of shots." + ) + else: + self._shots = self._sampler.options.shots + if self.basis_sampling == "uniform": # uniform sampling bases, basis_shots = self._sample_bases_uniform(q2vars, vars_per_qubit) @@ -441,22 +444,17 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: # values will be total number of observations. soln_counts = self._compute_dv_counts(basis_counts, bases, var2op, vars_per_qubit) - if self.shots is None: - shots = 1024 - else: - shots = self.shots - soln_samples = [ RoundingSolutionSample( x=np.asarray([int(bit) for bit in soln]), - probability=count / shots, + probability=count / self._shots, ) for soln, count in soln_counts.items() ] assert np.isclose( - sum(soln_counts.values()), shots - ), f"{sum(soln_counts.values())} != {shots}" + sum(soln_counts.values()), self._shots + ), f"{sum(soln_counts.values())} != {self._shots}" assert len(bases) == len(basis_shots) == len(basis_counts) stop_time = time.time() diff --git a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml new file mode 100644 index 000000000..d15621e6b --- /dev/null +++ b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml @@ -0,0 +1,54 @@ +--- +features: + - | + Added a new optimization algorithm, :class:`~.QuantumRandomAccessOptimizer`. This approach + incorporates Quantum Random Access Codes (QRACs) as a tool to encode multiple classical binary + variables into a single qubit, thereby saving quantum resources and enabling exploration of + larger problem instances on a quantum computer. The encodings produce a local quantum + Hamiltonian whose ground state can be approximated with standard algorithms such as VQE and + QAOA, and then rounded to yield approximation solutions of the original problem. + + For example: + + .. code-block:: python + + from qiskit.algorithms.optimizers import COBYLA + from qiskit.algorithms.minimum_eigensolvers import VQE + from qiskit.circuit.library import RealAmplitudes + from qiskit.primitives import Estimator + + from qiskit_optimization.algorithms.qrao import ( + QuantumRandomAccessOptimizer, + QuantumRandomAccessEncoding, + SemideterministicRounding, + MagicRounding, + QuantumRandomAccessOptimizationResult, + ) + from qiskit_optimization.problems import QuadraticProgram + + problem = QuadraticProgram() + problem.binary_var("x") + problem.binary_var("y") + problem.binary_var("z") + problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + + ansatz = RealAmplitudes(1) + vqe = VQE( + ansatz=ansatz, + optimizer=COBYLA(), + estimator=Estimator(), + ) + # solve() automatically performs the encoding, optimization, and rounding + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe) + result = qrao.solve(problem) + + # solve_relazed() only performs the optimization. The encoding and rounding must be done manually. + # encoding + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) + encoding.encode(problem) + # optimization + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe) + relaxed_results, rounding_context = qrao.solve_relaxed(encoding=encoding) + # rounding + rounding = SemideterministicRounding() + result = rounding.round(rounding_context) diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 9214f0c3a..3422f2749 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -15,6 +15,7 @@ from test.optimization_test_case import QiskitOptimizationTestCase import numpy as np +import ddt from qiskit_optimization.algorithms.qrao import ( QuantumRandomAccessEncoding, @@ -30,49 +31,141 @@ from qiskit.primitives import Sampler + +import numpy as np +from qiskit.algorithms.minimum_eigensolvers import ( + NumPyMinimumEigensolver, + NumPyMinimumEigensolverResult, + VQE, + VQEResult, +) +from qiskit.algorithms.optimizers import COBYLA +from qiskit.circuit.library import QAOAAnsatz, RealAmplitudes +from qiskit.primitives import Estimator +from qiskit.utils import algorithm_globals + +from qiskit_optimization.algorithms.optimization_algorithm import OptimizationResultStatus +from qiskit_optimization.algorithms.qrao import ( + QuantumRandomAccessEncoding, + QuantumRandomAccessOptimizationResult, + QuantumRandomAccessOptimizer, + RoundingContext, + SemideterministicRoundingResult, +) +from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample +from qiskit_optimization.problems import QuadraticProgram + + class TestMagicRounding(QiskitOptimizationTestCase): """MagicRounding tests.""" def setUp(self): + """Set up for all tests.""" super().setUp() self.problem = QuadraticProgram() self.problem.binary_var("x") self.problem.binary_var("y") self.problem.binary_var("z") self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) - - - - - def test_magic_rounding(self): - """Test MagicRounding""" - encoding = QuantumRandomAccessEncoding() - rounding_scheme = MagicRounding(Sampler(), seed=123) - expectation_values = [1, -1, 0, 0.7, -0.3] - result = rounding_scheme.round( - RoundingContext(expectation_values=expectation_values, encoding=encoding) + self.sampler = Sampler(options={"shots": 10000, "seed": 42}) + + def test_magic_rounding_constructor(self): + """Test constructor""" + # test default + magic_rounding = MagicRounding(self.sampler) + self.assertEqual(magic_rounding.sampler, self.sampler) + self.assertEqual(magic_rounding.basis_sampling, "uniform") + # test weighted basis sampling + magic_rounding = MagicRounding(self.sampler, basis_sampling="weighted") + self.assertEqual(magic_rounding.sampler, self.sampler) + self.assertEqual(magic_rounding.basis_sampling, "weighted") + # test uniform basis sampling + magic_rounding = MagicRounding(self.sampler, basis_sampling="uniform") + self.assertEqual(magic_rounding.sampler, self.sampler) + self.assertEqual(magic_rounding.basis_sampling, "uniform") + # test invalid basis sampling + with self.assertRaises(ValueError): + MagicRounding(self.sampler, basis_sampling="invalid") + + def test_magic_rounding_round_uniform(self): + """Test round method with uniform basis sampling""" + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) + encoding.encode(self.problem) + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + _, rounding_context = qrao.solve_relaxed(encoding=encoding) + magic_rounding = MagicRounding(self.sampler, seed=42) + rounding_result = magic_rounding.round(rounding_context) + self.assertIsInstance(rounding_result, MagicRoundingResult) + np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) + np.testing.assert_allclose(rounding_result.basis_shots, [2536, 2486, 2477, 2501]) + expected_basis_counts = [ + {"0": 2436.0, "1": 100.0}, + {"0": 461.0, "1": 2025.0}, + {"0": 831.0, "1": 1646.0}, + {"0": 1259.0, "1": 1242.0}, + ] + for i, basis_counts in enumerate(rounding_result.basis_counts): + self.assertEqual(basis_counts, expected_basis_counts[i]) + samples = rounding_result.samples + samples.sort(key=lambda sample: np.array2string(sample.x)) + expected_samples = [ + RoundingSolutionSample(x=np.array([0, 0, 0]), probability=0.2436), + RoundingSolutionSample(x=np.array([0, 0, 1]), probability=0.1242), + RoundingSolutionSample(x=np.array([0, 1, 0]), probability=0.1646), + RoundingSolutionSample(x=np.array([0, 1, 1]), probability=0.0461), + RoundingSolutionSample(x=np.array([1, 0, 0]), probability=0.2025), + RoundingSolutionSample(x=np.array([1, 0, 1]), probability=0.0831), + RoundingSolutionSample(x=np.array([1, 1, 0]), probability=0.1259), + RoundingSolutionSample(x=np.array([1, 1, 1]), probability=0.01), + ] + for i, sample in enumerate(samples): + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + np.testing.assert_allclose( + rounding_result.expectation_values, + [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], ) - self.assertIsInstance(result, SemideterministicRoundingResult) - self.assertIsInstance(result.samples[0], RoundingSolutionSample) - self.assertEqual(result.expectation_values, [1, -1, 0, 0.7, -0.3]) - np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 0, 0, 1]) - self.assertEqual(result.samples[0].probability, 1.0) - - - def test_semideterministic_rounding(self): - """Test SemideterministicRounding""" - encoding = QuantumRandomAccessEncoding() - rounding_scheme = SemideterministicRounding(seed=123) - expectation_values = [1, -1, 0, 0.7, -0.3] - result = rounding_scheme.round( - RoundingContext(expectation_values=expectation_values, encoding=encoding) + def test_magic_rounding_round_weighted(self): + """Test round method with weighted basis sampling""" + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) + encoding.encode(self.problem) + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + _, rounding_context = qrao.solve_relaxed(encoding=encoding) + magic_rounding = MagicRounding(self.sampler, basis_sampling="weighted", seed=42) + rounding_result = magic_rounding.round(rounding_context) + self.assertIsInstance(rounding_result, MagicRoundingResult) + np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) + np.testing.assert_allclose(rounding_result.basis_shots, [4542, 2703, 1559, 1196]) + expected_basis_counts = [ + {"0": 4393.0, "1": 149.0}, + {"0": 501.0, "1": 2202.0}, + {"0": 523.0, "1": 1036.0}, + {"0": 583.0, "1": 613.0}, + ] + for i, basis_counts in enumerate(rounding_result.basis_counts): + self.assertEqual(basis_counts, expected_basis_counts[i]) + samples = rounding_result.samples + samples.sort(key=lambda sample: np.array2string(sample.x)) + expected_samples = [ + RoundingSolutionSample(x=np.array([0, 0, 0]), probability=0.4393), + RoundingSolutionSample(x=np.array([0, 0, 1]), probability=0.0613), + RoundingSolutionSample(x=np.array([0, 1, 0]), probability=0.1036), + RoundingSolutionSample(x=np.array([0, 1, 1]), probability=0.0501), + RoundingSolutionSample(x=np.array([1, 0, 0]), probability=0.2202), + RoundingSolutionSample(x=np.array([1, 0, 1]), probability=0.0523), + RoundingSolutionSample(x=np.array([1, 1, 0]), probability=0.0583), + RoundingSolutionSample(x=np.array([1, 1, 1]), probability=0.0149), + ] + for i, sample in enumerate(samples): + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + np.testing.assert_allclose( + rounding_result.expectation_values, + [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], ) - self.assertIsInstance(result, SemideterministicRoundingResult) - self.assertIsInstance(result.samples[0], RoundingSolutionSample) - self.assertEqual(result.expectation_values, [1, -1, 0, 0.7, -0.3]) - np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 0, 0, 1]) - self.assertEqual(result.samples[0].probability, 1.0) if __name__ == "__main__": diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index 602415dab..9d27ac30e 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -11,10 +11,14 @@ # that they have been altered from the originals. """Tests for QuantumRandomAccessEncoding""" +import itertools import unittest from test.optimization_test_case import QiskitOptimizationTestCase +from ddt import ddt, data, unpack import numpy as np +import networkx as nx + from qiskit.circuit import QuantumCircuit from qiskit.opflow import PauliSumOp from qiskit.quantum_info import SparsePauliOp @@ -23,7 +27,8 @@ EncodingCommutationVerifier, QuantumRandomAccessEncoding, ) -from qiskit_optimization.problems import QuadraticProgram +from qiskit_optimization.problems import QuadraticProgram, QuadraticObjective +from qiskit_optimization.applications import Maxcut class TestQuantumRandomAccessEncoding(QiskitOptimizationTestCase): @@ -168,6 +173,7 @@ def test_qrac_unsupported_encoding(self): QuantumRandomAccessEncoding(0) +@ddt class TestEncodingCommutationVerifier(QiskitOptimizationTestCase): """Tests for EncodingCommutationVerifier.""" @@ -186,5 +192,67 @@ def test_encoding_commutation_verifier(self): for _, obj_val, encoded_obj_val in verifier: self.assertAlmostEqual(obj_val, encoded_obj_val) + @data(*itertools.product([1, 2, 3], ["minimize", "maximize"])) + @unpack + def test_one_qubit_qrac(self, max_vars_per_qubit, task): + """Test commutation of single qubit QRAC with non-uniform weights, degree 1 terms""" + + problem = QuadraticProgram() + nodes = list(range(max_vars_per_qubit)) + _ = [problem.binary_var(name=f"x{i}") for i in nodes] + obj = {f"x{i}": 2 * (i + 1) for i in nodes} + if task == "minimize": + problem.minimize(linear=obj) + else: + problem.maximize(linear=obj) + check_problem_commutation(problem, max_vars_per_qubit) + + @data( + *itertools.product( + [1, 2, 3], [QuadraticObjective.Sense.MINIMIZE, QuadraticObjective.Sense.MAXIMIZE] + ) + ) + @unpack + def test_uniform_weights_degree_2(self, max_vars_per_qubit, task): + """Test problem commutation with degree 2 terms""" + # Note that the variable embedding has some qubits with 1, 2, and 3 qubits + elist = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 0), (0, 3), (1, 4), (2, 4)] + graph = nx.from_edgelist(elist) + for u, v in elist: + graph[u][v]["weight"] = (u + 1) * (v + 2) + + maxcut = Maxcut(graph) + problem = maxcut.to_quadratic_program() + problem.objective.sense = task + check_problem_commutation(problem, max_vars_per_qubit) + + @data(1, 2, 3) + def test_random_unweighted_maxcut(self, max_vars_per_qubit): + """Test problem commutation with random unweighted MaxCut""" + graph = nx.random_regular_graph(3, 8) + maxcut = Maxcut(graph) + problem = maxcut.to_quadratic_program() + check_problem_commutation(problem, max_vars_per_qubit) + + @data(1, 2, 3) + def test_random_weighted_maxcut(self, max_vars_per_qubit): + """Test problem commutation with random weighted MaxCut""" + graph = nx.random_regular_graph(3, 8) + for u, v in graph.edges: + graph[u][v]["weight"] = np.random.randint(1, 10) + maxcut = Maxcut(graph) + problem = maxcut.to_quadratic_program() + check_problem_commutation(problem, max_vars_per_qubit) + + +def check_problem_commutation(problem: QuadraticProgram, max_vars_per_qubit: int): + """Utility function to check that the problem commutes with its encoding""" + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=max_vars_per_qubit) + encoding.encode(problem) + verifier = EncodingCommutationVerifier(encoding) + assert len(verifier) == 2**encoding.num_vars + assert all(np.isclose(obj_val, encoded_obj_val) for _, obj_val, encoded_obj_val in verifier) + + if __name__ == "__main__": unittest.main() From efcb66d56a4d220762b2f834e38958d262b4abc4 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 10 May 2023 20:08:40 +0900 Subject: [PATCH 11/67] clean up --- .../algorithms/optimization_algorithm.py | 2 +- .../algorithms/qrao/magic_rounding.py | 49 ++++++++++--------- .../qrao/prototype-qrao.code-workspace | 23 --------- .../qrao/quantum_random_access_encoding.py | 36 ++++---------- .../qrao/quantum_random_access_optimizer.py | 5 +- .../algorithms/qrao/rounding_common.py | 1 + .../qrao/semideterministic_rounding.py | 2 +- qiskit_optimization/algorithms/qrao/utils.py | 8 +-- releasenotes/notes/qrao-89d5ff1d2927de64.yaml | 2 - test/algorithms/qrao/test_magic_rounding.py | 32 +----------- .../test_quantum_random_access_encoding.py | 12 ++--- 11 files changed, 51 insertions(+), 121 deletions(-) delete mode 100644 qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace diff --git a/qiskit_optimization/algorithms/optimization_algorithm.py b/qiskit_optimization/algorithms/optimization_algorithm.py index 68ee6c244..2d63a11bb 100644 --- a/qiskit_optimization/algorithms/optimization_algorithm.py +++ b/qiskit_optimization/algorithms/optimization_algorithm.py @@ -491,7 +491,7 @@ def _interpret_samples( cls, problem: QuadraticProgram, raw_samples: List[SolutionSample], - converters: List[QuadraticProgramConverter], + converters: Union[QuadraticProgramConverter, List[QuadraticProgramConverter]], ) -> Tuple[List[SolutionSample], SolutionSample]: """Interpret and sort all samples and return the raw sample corresponding to the best one""" converters = cls._check_converters(converters) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index e05fa793e..eadd64866 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -14,7 +14,7 @@ import time from collections import defaultdict -from typing import Dict, List, Optional, Tuple +from typing import Any, Dict, List, Optional, Tuple import numpy as np from qiskit import QuantumCircuit @@ -37,8 +37,8 @@ def __init__( samples: List[RoundingSolutionSample], expectation_values: List[float], bases: np.ndarray, - basis_shots: int, - basis_counts: Dict[str, Dict[str, int]], + basis_shots: np.ndarray, + basis_counts: List[Dict[str, int]], time_taken: Optional[float] = None, ): """ @@ -141,7 +141,7 @@ def basis_sampling(self): @staticmethod def _make_circuits( - circ: QuantumCircuit, bases: List[List[int]], vars_per_qubit: int + circ: QuantumCircuit, bases: np.ndarray[Any, Any], vars_per_qubit: int ) -> List[QuantumCircuit]: """Make a list of circuits to measure in the given magic bases. @@ -166,7 +166,11 @@ def _make_circuits( return circuits def _evaluate_magic_bases( - self, circuit: QuantumCircuit, bases: np.array, basis_shots: np.array, vars_per_qubit: int + self, + circuit: QuantumCircuit, + bases: np.ndarray, + basis_shots: np.ndarray, + vars_per_qubit: int, ) -> List[Dict[str, int]]: """ Given a quantum circuit to measure, a list of magic bases to measure, and a list of the @@ -259,8 +263,8 @@ def _unpack_measurement_outcome( def _compute_dv_counts( self, - basis_counts: Dict[str, Dict[str, int]], - bases: List[List[int]], + basis_counts: List[Dict[str, int]], + bases: np.ndarray[Any, Any], var2op: Dict[int, Tuple[int, SparsePauliOp]], vars_per_qubit: int, ): @@ -278,14 +282,14 @@ def _compute_dv_counts( Returns: A dictionary of counts for each decision variable configuration. """ - dv_counts = defaultdict(int) + dv_counts: Dict[str, int] = defaultdict(int) for base, counts in zip(bases, basis_counts): # For each measurement outcome... for bitstr, count in counts.items(): - # For each bit in the observed bitstring... + # For each bit in the observed bit string... soln = self._unpack_measurement_outcome(bitstr, base, var2op, vars_per_qubit) - soln = "".join([str(bit) for bit in soln]) - dv_counts[soln] += count + soln_str = "".join([str(bit) for bit in soln]) + dv_counts[soln_str] += count return dv_counts def _sample_bases_uniform( @@ -311,11 +315,11 @@ def _sample_bases_uniform( corresponds to the number of shots to use for the corresponding basis in the bases array. """ - bases = [ + bases_ = [ self.rng.choice(2 ** (vars_per_qubit - 1), size=len(q2vars)).tolist() for _ in range(self._shots) ] - bases, basis_shots = np.unique(bases, axis=0, return_counts=True) + bases, basis_shots = np.unique(bases_, axis=0, return_counts=True) return bases, basis_shots def _sample_bases_weighted( @@ -346,16 +350,16 @@ def _sample_bases_weighted( # First, we make sure all Pauli expectation values have absolute value # at most 1. Otherwise, some of the probabilities computed below might # be negative. - tv = np.clip(expectation_values, -1, 1) + clipped_expectation_values = np.clip(expectation_values, -1, 1) # basis_probs will have num_qubits number of elements. # Each element will be a list of length 4 specifying the # probability of picking the corresponding magic basis on that qubit. basis_probs = [] for dvars in q2vars: if vars_per_qubit == 3: - x = 0.5 * (1 - tv[dvars[0]]) - y = 0.5 * (1 - tv[dvars[1]]) if (len(dvars) > 1) else 0 - z = 0.5 * (1 - tv[dvars[2]]) if (len(dvars) > 2) else 0 + x = 0.5 * (1 - clipped_expectation_values[dvars[0]]) + y = 0.5 * (1 - clipped_expectation_values[dvars[1]]) if (len(dvars) > 1) else 0 + z = 0.5 * (1 - clipped_expectation_values[dvars[2]]) if (len(dvars) > 2) else 0 # ppp: mu± = .5(I ± 1/sqrt(3)( X + Y + Z)) # pmm: X mu± X = .5(I ± 1/sqrt(3)( X - Y - Z)) # mpm: Y mu± Y = .5(I ± 1/sqrt(3)(-X + Y - Z)) @@ -368,8 +372,8 @@ def _sample_bases_weighted( # fmt: on basis_probs.append([ppp_mmm, pmm_mpp, mpm_pmp, ppm_mmp]) elif vars_per_qubit == 2: - x = 0.5 * (1 - tv[dvars[0]]) - z = 0.5 * (1 - tv[dvars[1]]) if (len(dvars) > 1) else 0 + x = 0.5 * (1 - clipped_expectation_values[dvars[0]]) + z = 0.5 * (1 - clipped_expectation_values[dvars[1]]) if (len(dvars) > 1) else 0 # pp: xi± = .5(I ± 1/sqrt(2)( X + Z )) # pm: X xi± X = .5(I ± 1/sqrt(2)( X - Z )) # fmt: off @@ -379,14 +383,14 @@ def _sample_bases_weighted( basis_probs.append([pp_mm, pm_mp]) elif vars_per_qubit == 1: basis_probs.append([1.0]) - bases = [ + bases_ = [ [ self.rng.choice(2 ** (vars_per_qubit - 1), p=[p.real for p in probs]) for probs in basis_probs ] for _ in range(self._shots) ] - bases, basis_shots = np.unique(bases, axis=0, return_counts=True) + bases, basis_shots = np.unique(bases_, axis=0, return_counts=True) return bases, basis_shots def round(self, ctx: RoundingContext) -> MagicRoundingResult: @@ -419,8 +423,7 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: raise ValueError( "Magic rounding requires the sampler to be configured with a number of shots." ) - else: - self._shots = self._sampler.options.shots + self._shots = self._sampler.options.shots if self.basis_sampling == "uniform": # uniform sampling diff --git a/qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace b/qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace deleted file mode 100644 index d2de79c12..000000000 --- a/qiskit_optimization/algorithms/qrao/prototype-qrao.code-workspace +++ /dev/null @@ -1,23 +0,0 @@ -{ - "folders": [ - { - "path": "../../../../prototype-qrao" - }, - { - "path": "../../.." - }, - { - "path": "../../../../terra" - } - ], - "settings": { - "cSpell.words": [ - "ndarray", - "QRAC", - "qrao", - "qubits", - "QUBO" - ], - "esbonio.sphinx.confDir": "" - } -} \ No newline at end of file diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index a209d1da4..d3920ca4b 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -18,12 +18,14 @@ import numpy as np import rustworkx as rx + from qiskit import QuantumCircuit +from qiskit.opflow import PauliSumOp from qiskit.quantum_info import SparsePauliOp from qiskit_optimization.exceptions import QiskitOptimizationError from qiskit_optimization.problems.quadratic_program import QuadraticProgram -from qiskit.opflow import PauliSumOp + def _z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (3,1,p)-QRAC. @@ -41,7 +43,6 @@ def _z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> Quantum circ = QuantumCircuit(len(bases)) BETA = np.arccos(1 / np.sqrt(3)) # pylint: disable=invalid-name - for i, base in enumerate(reversed(bases)): if bit_flip: # if bit_flip == 1: then flip the state of the qubit to |1> @@ -60,7 +61,7 @@ def _z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> Quantum return circ -def _z_to_21p_qrac_basis_circuit(bases: int, bit_flip: int = 0) -> QuantumCircuit: +def _z_to_21p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (2,1,p)-QRAC. Args: @@ -80,7 +81,6 @@ def _z_to_21p_qrac_basis_circuit(bases: int, bit_flip: int = 0) -> QuantumCircui # if bit_flip == 1: then flip the state of the qubit to |1> circ.x(i) - if base == 0: circ.r(-1 * np.pi / 4, -np.pi / 2, i) elif base == 1: @@ -191,13 +191,13 @@ def _qrac_state_prep_multiqubit( # Map each decision variable associated with the current qubit to a binary value and add it # to the qubit bits - for dv in qi_vars: + for dvar in qi_vars: try: - qi_bits.append(dvars[dv]) + qi_bits.append(dvars[dvar]) except IndexError: - raise ValueError(f"Decision variable not included in dvars: {dv}") from None + raise ValueError(f"Decision variable not included in dvars: {dvar}") from None try: - remaining_dvars.remove(dv) + remaining_dvars.remove(dvar) except KeyError: raise ValueError( f"Unused decision variable(s) in dvars: {remaining_dvars}" @@ -219,25 +219,6 @@ def _qrac_state_prep_multiqubit( return qrac_circ -# def q2vars_from_var2op(var2op: Dict[int, Tuple[int, SparsePauliOp]]) -> List[List[int]]: -# """ -# Converts a dictionary mapping decision variables to qubits and Pauli operators to a list of -# lists of decision variables. - -# Args: -# var2op: A dictionary mapping decision variables to qubits and Pauli operators. - -# Returns: -# A list of lists of decision variables. Each inner list contains the indices of decision -# variables mapped to a specific qubit. -# """ -# num_qubits = max(qubit_index for qubit_index, _ in var2op.values()) + 1 -# q2vars: List[List[int]] = [[] for i in range(num_qubits)] -# for var, (q, _) in var2op.items(): -# q2vars[q].append(var) -# return q2vars - - class QuantumRandomAccessEncoding: """This class specifies a Quantum Random Access Code that can be used to encode the binary variables of a QUBO (quadratic unconstrained binary optimization @@ -494,6 +475,7 @@ def _find_variable_partition(quad: np.ndarray) -> Dict[int, List[int]]: Returns: Dict: a dictionary of the variable partition of the quad based on the node coloring. """ + # pylint: disable=E1101 color2node: Dict[int, List[int]] = defaultdict(list) num_nodes = quad.shape[0] graph = rx.PyGraph() diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 453aefcbc..158d4525c 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -29,7 +29,7 @@ OptimizationResultStatus, SolutionSample, ) -from qiskit_optimization.converters import QuadraticProgramToQubo +from qiskit_optimization.converters import QuadraticProgramConverter, QuadraticProgramToQubo from qiskit_optimization.problems import QuadraticProgram, Variable from .quantum_random_access_encoding import QuantumRandomAccessEncoding @@ -100,6 +100,7 @@ def rounding_result(self) -> RoundingResult: """The rounding result.""" return self._rounding_result + class QuantumRandomAccessOptimizer(OptimizationAlgorithm): """Quantum Random Access Optimizer class.""" @@ -123,7 +124,7 @@ def __init__( self.min_eigen_solver = min_eigen_solver self.penalty = penalty # Use ``QuadraticProgramToQubo`` to convert the problem to a QUBO. - self._converters = [QuadraticProgramToQubo(penalty=penalty)] + self._converters: QuadraticProgramConverter = QuadraticProgramToQubo(penalty=penalty) self._max_vars_per_qubit = max_vars_per_qubit self.rounding_scheme = rounding_scheme diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index 0e5ccefe7..84c7f26f7 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -20,6 +20,7 @@ from qiskit.circuit import QuantumCircuit +from qiskit_optimization.algorithms import SolutionSample from .quantum_random_access_encoding import QuantumRandomAccessEncoding diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 844dec5f5..972622aaa 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -1,6 +1,6 @@ # This code is part of Qiskit. # -# (C) Copyright IBM 2022. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory diff --git a/qiskit_optimization/algorithms/qrao/utils.py b/qiskit_optimization/algorithms/qrao/utils.py index b679f61a0..502acee04 100644 --- a/qiskit_optimization/algorithms/qrao/utils.py +++ b/qiskit_optimization/algorithms/qrao/utils.py @@ -1,6 +1,6 @@ # This code is part of Qiskit. # -# (C) Copyright IBM 2021, 2022. +# (C) Copyright IBM 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory @@ -65,11 +65,7 @@ def get_random_maxcut_docplex_model( nodes = list(range(num_nodes)) var = [mod.binary_var(name="x" + str(i)) for i in nodes] mod.maximize( - mod.sum( - edges[i, j] * (var[i] + var[j] - 2 * var[i] * var[j]) - for i in nodes - for j in nodes - ) + mod.sum(edges[i, j] * (var[i] + var[j] - 2 * var[i] * var[j]) for i in nodes for j in nodes) ) if draw: # pragma: no cover (tested by treon) diff --git a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml index d15621e6b..a64dffe16 100644 --- a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml +++ b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml @@ -21,8 +21,6 @@ features: QuantumRandomAccessOptimizer, QuantumRandomAccessEncoding, SemideterministicRounding, - MagicRounding, - QuantumRandomAccessOptimizationResult, ) from qiskit_optimization.problems import QuadraticProgram diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 3422f2749..680a305fd 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -15,42 +15,14 @@ from test.optimization_test_case import QiskitOptimizationTestCase import numpy as np -import ddt +from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver +from qiskit.primitives import Sampler from qiskit_optimization.algorithms.qrao import ( - QuantumRandomAccessEncoding, - SemideterministicRounding, - SemideterministicRoundingResult, - RoundingContext, MagicRounding, MagicRoundingResult, -) -from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample - -from qiskit_optimization.problems import QuadraticProgram - -from qiskit.primitives import Sampler - - -import numpy as np -from qiskit.algorithms.minimum_eigensolvers import ( - NumPyMinimumEigensolver, - NumPyMinimumEigensolverResult, - VQE, - VQEResult, -) -from qiskit.algorithms.optimizers import COBYLA -from qiskit.circuit.library import QAOAAnsatz, RealAmplitudes -from qiskit.primitives import Estimator -from qiskit.utils import algorithm_globals - -from qiskit_optimization.algorithms.optimization_algorithm import OptimizationResultStatus -from qiskit_optimization.algorithms.qrao import ( QuantumRandomAccessEncoding, - QuantumRandomAccessOptimizationResult, QuantumRandomAccessOptimizer, - RoundingContext, - SemideterministicRoundingResult, ) from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample from qiskit_optimization.problems import QuadraticProgram diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index 9d27ac30e..1fb6274eb 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -142,8 +142,8 @@ def test_qrac_state_prep(self): encoding.encode(self.problem) state_prep_circ = encoding.state_preparation_circuit(dvars=dvars) circ = QuantumCircuit(1) - BETA = np.arccos(1 / np.sqrt(3)) - circ.r(np.pi - BETA, np.pi / 4, 0) + beta = np.arccos(1 / np.sqrt(3)) + circ.r(np.pi - beta, np.pi / 4, 0) self.assertEqual(state_prep_circ, circ) with self.subTest(msg="(2,1,p) QRAC"): @@ -218,8 +218,8 @@ def test_uniform_weights_degree_2(self, max_vars_per_qubit, task): # Note that the variable embedding has some qubits with 1, 2, and 3 qubits elist = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 0), (0, 3), (1, 4), (2, 4)] graph = nx.from_edgelist(elist) - for u, v in elist: - graph[u][v]["weight"] = (u + 1) * (v + 2) + for w, v in elist: + graph[w][v]["weight"] = (w + 1) * (v + 2) maxcut = Maxcut(graph) problem = maxcut.to_quadratic_program() @@ -238,8 +238,8 @@ def test_random_unweighted_maxcut(self, max_vars_per_qubit): def test_random_weighted_maxcut(self, max_vars_per_qubit): """Test problem commutation with random weighted MaxCut""" graph = nx.random_regular_graph(3, 8) - for u, v in graph.edges: - graph[u][v]["weight"] = np.random.randint(1, 10) + for w, v in graph.edges: + graph[w][v]["weight"] = np.random.randint(1, 10) maxcut = Maxcut(graph) problem = maxcut.to_quadratic_program() check_problem_commutation(problem, max_vars_per_qubit) From 2ae38b07e4a420d6ae884cd7c91d8a17a90249e8 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 11 May 2023 18:08:40 +0900 Subject: [PATCH 12/67] remove a unnecessary file --- qiskit_optimization/algorithms/qrao/utils.py | 83 -------------------- 1 file changed, 83 deletions(-) delete mode 100644 qiskit_optimization/algorithms/qrao/utils.py diff --git a/qiskit_optimization/algorithms/qrao/utils.py b/qiskit_optimization/algorithms/qrao/utils.py deleted file mode 100644 index 502acee04..000000000 --- a/qiskit_optimization/algorithms/qrao/utils.py +++ /dev/null @@ -1,83 +0,0 @@ -# This code is part of Qiskit. -# -# (C) Copyright IBM 2023. -# -# This code is licensed under the Apache License, Version 2.0. You may -# obtain a copy of this license in the LICENSE.txt file in the root directory -# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. -# -# Any modifications or derivative works of this code must retain this -# copyright notice, and modified files need to carry a notice indicating -# that they have been altered from the originals. - -"""Utility functions related to Quantum Random Access Optimization""" - -from typing import Optional - -import numpy as np -import networkx as nx -from docplex.mp.model import Model - -from qiskit_optimization import QuadraticProgram -from qiskit_optimization.translators import from_docplex_mp - - -def get_random_maxcut_docplex_model( - *, - num_nodes: int = 6, - degree: int = 3, - seed: Optional[int] = None, - weight: int = 1, - draw: bool = False, -) -> Model: - """Prepare a random DOcplex max-cut model - - Args: - - num_nodes: The number of vertices in the graph - - degree: The degree of each node in the graph - - seed: The seed to use for randomness - - weight: If `-1`, each edge will randomly have weight `-1` or `1`. - Otherwise, each graph edge will have a random integer weight - between `1` and `weight`, inclusive. (It follows that if `weight - == 1`, all edge weights are `1`). - - draw: If `True`, will call `nx.draw()` on the generated graph before - returning. - - """ - rng = np.random.RandomState(seed) - graph = nx.random_regular_graph(d=degree, n=num_nodes, seed=rng) - edges = np.zeros((num_nodes, num_nodes)) - for i, j in graph.edges(): - if weight == 1: - w = 1 - elif weight == -1: - w = rng.choice((-1, 1)) - else: - w = rng.randint(1, weight + 1) - edges[i, j] = edges[j, i] = w - - mod = Model("maxcut") - nodes = list(range(num_nodes)) - var = [mod.binary_var(name="x" + str(i)) for i in nodes] - mod.maximize( - mod.sum(edges[i, j] * (var[i] + var[j] - 2 * var[i] * var[j]) for i in nodes for j in nodes) - ) - - if draw: # pragma: no cover (tested by treon) - nx.draw(graph, with_labels=True, font_color="whitesmoke") - - return mod - - -def get_random_maxcut_qp(*args, **kwargs) -> QuadraticProgram: - """Prepare a random max-cut `QuadraticProgram`, using the same arguments as - :func:`get_random_maxcut_docplex_model`. - - """ - mod = get_random_maxcut_docplex_model(*args, **kwargs) - return from_docplex_mp(mod) From fc4d3792d2833d77e0958a3d1ea6baff5dc3a918 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 11 May 2023 20:38:38 +0900 Subject: [PATCH 13/67] update the code --- .../algorithms/optimization_algorithm.py | 4 +- .../algorithms/qrao/magic_rounding.py | 63 ++++++------------- .../qrao/quantum_random_access_optimizer.py | 3 +- .../algorithms/qrao/rounding_common.py | 49 +++------------ .../qrao/semideterministic_rounding.py | 28 ++++++--- test/algorithms/qrao/test_magic_rounding.py | 48 +++++++++----- .../test_quantum_random_access_optimizer.py | 4 +- .../qrao/test_semideterministic_rounding.py | 12 ++-- 8 files changed, 86 insertions(+), 125 deletions(-) diff --git a/qiskit_optimization/algorithms/optimization_algorithm.py b/qiskit_optimization/algorithms/optimization_algorithm.py index 2d63a11bb..daf383204 100644 --- a/qiskit_optimization/algorithms/optimization_algorithm.py +++ b/qiskit_optimization/algorithms/optimization_algorithm.py @@ -491,7 +491,9 @@ def _interpret_samples( cls, problem: QuadraticProgram, raw_samples: List[SolutionSample], - converters: Union[QuadraticProgramConverter, List[QuadraticProgramConverter]], + converters: Optional[ + Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] + ] = None, ) -> Tuple[List[SolutionSample], SolutionSample]: """Interpret and sort all samples and return the raw sample corresponding to the best one""" converters = cls._check_converters(converters) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index eadd64866..721d49d33 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -11,8 +11,8 @@ # that they have been altered from the originals. """Magic basis rounding module""" +from dataclasses import dataclass -import time from collections import defaultdict from typing import Any, Dict, List, Optional, Tuple @@ -22,53 +22,25 @@ from qiskit.primitives import Sampler from qiskit.quantum_info import SparsePauliOp +from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from .quantum_random_access_encoding import ( _z_to_21p_qrac_basis_circuit, _z_to_31p_qrac_basis_circuit, ) -from .rounding_common import RoundingContext, RoundingResult, RoundingScheme, RoundingSolutionSample +from .rounding_common import RoundingContext, RoundingResult, RoundingScheme +@dataclass class MagicRoundingResult(RoundingResult): - """Result of magic rounding""" + """Result of magic rounding.""" - def __init__( - self, - samples: List[RoundingSolutionSample], - expectation_values: List[float], - bases: np.ndarray, - basis_shots: np.ndarray, - basis_counts: List[Dict[str, int]], - time_taken: Optional[float] = None, - ): - """ - Args: - samples: List of samples of the rounding. - expectation_values: Expectation values of the encoding. - bases: The bases used for the magic rounding. - basis_shots: The number of shots used for each basis. - basis_counts: The counts for each basis. - time_taken: Time taken for the rounding. - """ - self._bases = bases - self._basis_shots = basis_shots - self._basis_counts = basis_counts - super().__init__(samples, expectation_values, time_taken=time_taken) - - @property - def bases(self): - """Return the bases used for the magic rounding.""" - return self._bases - - @property - def basis_shots(self): - """Return the number of shots used for each basis.""" - return self._basis_shots - - @property - def basis_counts(self): - """Return the counts for each basis.""" - return self._basis_counts + bases: np.ndarray + """The bases used for the magic rounding""" + basis_shots: np.ndarray + """The number of shots used for each basis""" + basis_counts: List[Dict[str, int]] + """The basis_counts represents the resulting counts obtained by measuring with the bases + corresponding to the number of shots specified in basis_shots.""" class MagicRounding(RoundingScheme): @@ -406,7 +378,6 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: NotImplementedError: If the circuit is not available for magic rounding. ValueError: If the sampler is not configured with a number of shots. """ - start_time = time.time() expectation_values = ctx.expectation_values circuit = ctx.circuit q2vars = ctx.encoding.q2vars @@ -448,9 +419,13 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: soln_counts = self._compute_dv_counts(basis_counts, bases, var2op, vars_per_qubit) soln_samples = [ - RoundingSolutionSample( + SolutionSample( x=np.asarray([int(bit) for bit in soln]), + fval=ctx.encoding.problem.objective.evaluate([int(bit) for bit in soln]), probability=count / self._shots, + status=OptimizationResultStatus.SUCCESS + if ctx.encoding.problem.is_feasible([int(bit) for bit in soln]) + else OptimizationResultStatus.INFEASIBLE, ) for soln, count in soln_counts.items() ] @@ -459,14 +434,12 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: sum(soln_counts.values()), self._shots ), f"{sum(soln_counts.values())} != {self._shots}" assert len(bases) == len(basis_shots) == len(basis_counts) - stop_time = time.time() # Create a MagicRoundingResult object to return return MagicRoundingResult( - samples=soln_samples, expectation_values=expectation_values, + samples=soln_samples, bases=bases, basis_shots=basis_shots, basis_counts=basis_counts, - time_taken=stop_time - start_time, ) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 158d4525c..b2dee9515 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -283,7 +283,7 @@ def process_result( The result of the quantum random access optimization. """ samples, best_sol = self._interpret_samples( - problem=problem, raw_samples=rounding_result.samples, converters=self._converters + problem=problem, raw_samples=rounding_result.samples ) relaxed_fval = encoding.problem.objective.sense.value * ( @@ -293,7 +293,6 @@ def process_result( QuantumRandomAccessOptimizationResult, self._interpret( x=best_sol.x, - converters=self._converters, problem=problem, result_class=QuantumRandomAccessOptimizationResult, samples=samples, diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index 84c7f26f7..db1565a79 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -9,30 +9,27 @@ # Any modifications or derivative works of this code must retain this # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. - """Common classes for rounding schemes""" -from typing import List, Optional from abc import ABC, abstractmethod from dataclasses import dataclass - -import numpy as np +from typing import List, Optional from qiskit.circuit import QuantumCircuit from qiskit_optimization.algorithms import SolutionSample -from .quantum_random_access_encoding import QuantumRandomAccessEncoding - -# pylint: disable=too-few-public-methods +from .quantum_random_access_encoding import QuantumRandomAccessEncoding @dataclass -class RoundingSolutionSample: - """Partial SolutionSample for use in rounding results""" +class RoundingResult: + """Base class for a rounding result""" - x: np.ndarray - probability: float + expectation_values: List[float] + """Expectation values""" + samples: List[SolutionSample] + """List of samples after rounding""" class RoundingContext: @@ -55,36 +52,6 @@ def __init__( self.circuit = circuit -class RoundingResult: - """Base class for a rounding result""" - - def __init__( - self, - samples: List[RoundingSolutionSample], - expectation_values: List[float], - time_taken: Optional[float] = None, - ): - """ - Args: - samples: List of samples of the rounding. - expectation_values: Expectation values of the encoding. - time_taken: Time taken for rounding. - """ - self._samples = samples - self._expectation_values = expectation_values - self.time_taken = time_taken - - @property - def samples(self) -> List[RoundingSolutionSample]: - """List of samples for the rounding""" - return self._samples - - @property - def expectation_values(self): - """Expectation values""" - return self._expectation_values - - class RoundingScheme(ABC): """Base class for a rounding scheme""" diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 972622aaa..d67c12d8c 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -11,21 +11,22 @@ # that they have been altered from the originals. """Semideterministic rounding module""" +from dataclasses import dataclass from typing import Optional import numpy as np +from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample + from .rounding_common import ( - RoundingSolutionSample, RoundingScheme, RoundingContext, RoundingResult, ) -# pylint: disable=too-few-public-methods - +@dataclass class SemideterministicRoundingResult(RoundingResult): """Result of semideterministic rounding""" @@ -64,21 +65,28 @@ def sign(val) -> int: if ctx.expectation_values is None: raise NotImplementedError( - "Semideterministric rounding with weighted sampling requires the expectation " - "values of the ``RoundingContext`` to be available, but they are not." + "Semideterministric rounding requires the expectation values of the ", + "``RoundingContext`` to be available, but they are not.", ) - rounded_vars = [ - sign(e) if not np.isclose(0, e) else self.rng.randint(2) for e in ctx.expectation_values - ] + rounded_vars = np.array( + [ + sign(e) if not np.isclose(0, e) else self.rng.randint(2) + for e in ctx.expectation_values + ] + ) soln_samples = [ - RoundingSolutionSample( + SolutionSample( x=np.asarray(rounded_vars), + fval=ctx.encoding.problem.objective.evaluate(rounded_vars), probability=1.0, + status=OptimizationResultStatus.SUCCESS + if ctx.encoding.problem.is_feasible(rounded_vars) + else OptimizationResultStatus.INFEASIBLE, ) ] result = SemideterministicRoundingResult( - samples=soln_samples, expectation_values=ctx.expectation_values + expectation_values=ctx.expectation_values, samples=soln_samples ) return result diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 680a305fd..0628d984f 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -24,7 +24,7 @@ QuantumRandomAccessEncoding, QuantumRandomAccessOptimizer, ) -from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample +from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.problems import QuadraticProgram @@ -82,14 +82,14 @@ def test_magic_rounding_round_uniform(self): samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ - RoundingSolutionSample(x=np.array([0, 0, 0]), probability=0.2436), - RoundingSolutionSample(x=np.array([0, 0, 1]), probability=0.1242), - RoundingSolutionSample(x=np.array([0, 1, 0]), probability=0.1646), - RoundingSolutionSample(x=np.array([0, 1, 1]), probability=0.0461), - RoundingSolutionSample(x=np.array([1, 0, 0]), probability=0.2025), - RoundingSolutionSample(x=np.array([1, 0, 1]), probability=0.0831), - RoundingSolutionSample(x=np.array([1, 1, 0]), probability=0.1259), - RoundingSolutionSample(x=np.array([1, 1, 1]), probability=0.01), + make_solution_sample(x=np.array([0, 0, 0]), probability=0.2436, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.1242, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1646, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0461, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.2025, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0831, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.1259, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) @@ -122,14 +122,14 @@ def test_magic_rounding_round_weighted(self): samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ - RoundingSolutionSample(x=np.array([0, 0, 0]), probability=0.4393), - RoundingSolutionSample(x=np.array([0, 0, 1]), probability=0.0613), - RoundingSolutionSample(x=np.array([0, 1, 0]), probability=0.1036), - RoundingSolutionSample(x=np.array([0, 1, 1]), probability=0.0501), - RoundingSolutionSample(x=np.array([1, 0, 0]), probability=0.2202), - RoundingSolutionSample(x=np.array([1, 0, 1]), probability=0.0523), - RoundingSolutionSample(x=np.array([1, 1, 0]), probability=0.0583), - RoundingSolutionSample(x=np.array([1, 1, 1]), probability=0.0149), + make_solution_sample(x=np.array([0, 0, 0]), probability=0.4393, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.0613, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1036, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0501, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.2202, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0523, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.0583, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.0149, problem=self.problem), ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) @@ -140,5 +140,19 @@ def test_magic_rounding_round_weighted(self): ) +def make_solution_sample( + x: np.ndarray, probability: float, problem: QuadraticProgram +) -> SolutionSample: + """Make a solution sample.""" + return SolutionSample( + x=x, + fval=problem.objective.evaluate(x), + probability=probability, + status=OptimizationResultStatus.SUCCESS + if problem.is_feasible(x) + else OptimizationResultStatus.INFEASIBLE, + ) + + if __name__ == "__main__": unittest.main() diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py index 3cf14245f..d97116189 100644 --- a/test/algorithms/qrao/test_quantum_random_access_optimizer.py +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -26,6 +26,7 @@ from qiskit.primitives import Estimator from qiskit.utils import algorithm_globals +from qiskit_optimization.algorithms import SolutionSample from qiskit_optimization.algorithms.optimization_algorithm import OptimizationResultStatus from qiskit_optimization.algorithms.qrao import ( QuantumRandomAccessEncoding, @@ -34,7 +35,6 @@ RoundingContext, SemideterministicRoundingResult, ) -from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample from qiskit_optimization.problems import QuadraticProgram @@ -170,7 +170,7 @@ def test_solve_numpy(self): self.assertAlmostEqual(results.rounding_result.expectation_values[0], 0.26726, places=5) self.assertAlmostEqual(results.rounding_result.expectation_values[1], 0.53452, places=5) self.assertAlmostEqual(results.rounding_result.expectation_values[2], 0.80178, places=5) - self.assertIsInstance(results.rounding_result.samples[0], RoundingSolutionSample) + self.assertIsInstance(results.rounding_result.samples[0], SolutionSample) def test_empty_encoding(self): """Test the encoding is empty.""" diff --git a/test/algorithms/qrao/test_semideterministic_rounding.py b/test/algorithms/qrao/test_semideterministic_rounding.py index 94c3185a5..7c5967274 100644 --- a/test/algorithms/qrao/test_semideterministic_rounding.py +++ b/test/algorithms/qrao/test_semideterministic_rounding.py @@ -22,8 +22,7 @@ SemideterministicRoundingResult, RoundingContext, ) -from qiskit_optimization.algorithms.qrao.rounding_common import RoundingSolutionSample - +from qiskit_optimization.algorithms import SolutionSample from qiskit_optimization.problems import QuadraticProgram @@ -33,21 +32,20 @@ class TestSemideterministicRounding(QiskitOptimizationTestCase): def setUp(self): super().setUp() self.problem = QuadraticProgram() - self.problem.binary_var("x") - self.problem.binary_var("y") - self.problem.binary_var("z") - self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + var_dict = self.problem.binary_var_dict(5) + self.problem.minimize(linear={name: 1 for name in var_dict}) def test_semideterministic_rounding(self): """Test SemideterministicRounding""" encoding = QuantumRandomAccessEncoding() + encoding.encode(self.problem) rounding_scheme = SemideterministicRounding(seed=123) expectation_values = [1, -1, 0, 0.7, -0.3] result = rounding_scheme.round( RoundingContext(expectation_values=expectation_values, encoding=encoding) ) self.assertIsInstance(result, SemideterministicRoundingResult) - self.assertIsInstance(result.samples[0], RoundingSolutionSample) + self.assertIsInstance(result.samples[0], SolutionSample) self.assertEqual(result.expectation_values, [1, -1, 0, 0.7, -0.3]) np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 0, 0, 1]) self.assertEqual(result.samples[0].probability, 1.0) From 27ca8f1c4a021349a570024ed8fb5d231259f5fd Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 12 May 2023 17:15:23 +0900 Subject: [PATCH 14/67] add tutorial and update the code --- .../13_quantum_random_access_optimizer.ipynb | 736 ++++++++++++++++++ .../algorithms/qrao/magic_rounding.py | 29 +- .../qrao/quantum_random_access_encoding.py | 32 +- .../qrao/quantum_random_access_optimizer.py | 2 +- .../algorithms/qrao/rounding_common.py | 2 +- .../qrao/semideterministic_rounding.py | 14 +- .../test_quantum_random_access_encoding.py | 6 +- 7 files changed, 779 insertions(+), 42 deletions(-) create mode 100644 docs/tutorials/13_quantum_random_access_optimizer.ipynb diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb new file mode 100644 index 000000000..8942080c9 --- /dev/null +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -0,0 +1,736 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Quantum Random Access Optimization" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Quantum Random Access Optimization (QRAO) module is designed to enable users to leverage a new quantum method for combinatorial optimization problems [1]. This approach incorporates Quantum Random Access Codes (QRACs) as a tool to encode multiple classical binary variables into a single qubit, thereby saving quantum resources and enabling exploration of larger problem instances on a quantum computer. The encodings produce a local quantum Hamiltonian whose ground state can be approximated with standard algorithms such as VQE and QAOA, and then rounded to yield approximation solutions of the original problem.\n", + "\n", + "QRAO through a series of 3 classes:\n", + "1. The encoding class (`QuantumRandomAccessEncoding`): This class encodes the original problem into a relaxed problem that requires fewer resources to solve.\n", + "2. The rounding schemes (`SemideterministicRounding` and `MagicRounding`): This scheme is used to round the solution obtained from the relaxed problem back to a solution of the original problem.\n", + "3. The optimizer class (`QuantumRandomAccessOptimizer`): This class performs the high-level optimization algorithm, utilizing the capabilities of the encoding class and the rounding scheme.\n", + "\n", + "\n", + "### References\n", + "\n", + "[1] Bryce Fuller, Charles Hadfield, Jennifer R. Glick, Takashi Imamichi, Toshinari Itoko, Richard J. Thompson, Yang Jiao, Marna M. Kagele, Adriana W. Blom-Schieber, Rudy Raymond, Antonio Mezzacapo, *Approximate Solutions of Combinatorial Problems via Quantum Relaxations,* [arXiv:2111.03167](https://arxiv.org/abs/2111.03167)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_optimization.algorithms.qrao import (\n", + " QuantumRandomAccessEncoding,\n", + " SemideterministicRounding,\n", + " QuantumRandomAccessOptimizer,\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set up a combinatorial optimization problem\n", + "\n", + "In this tutorial, we will consider a random max-cut problem instance and use QRAO to try to find a maximum cut; in other words, a partition of the graph's vertices (nodes) into two sets that maximizes the number of edges between the sets.\n", + "\n", + "To begin, we utilize the `Maxcut` class from Qiskit Optimization's application module. It allows us to generate a `QuadraticProgram` representation of the given graph.\n", + "\n", + "Note that once our problem is represented as a `QuadraticProgram`, it needs to be converted into the appropriate format for QRAO, which is a [quadratic unconstrained binary optimization (QUBO)](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization) problem. While a `QuadraticProgram` generated by `Maxcut` is already in QUBO form, if you define your own problem, make sure to convert it into a QUBO before proceeding. You can refer to this [tutorial](https://qiskit.org/documentation/optimization/tutorials/02_converters_for_quadratic_programs.html) for guidance on converting QuadraticPrograms.\n", + "\n", + "Note that once our problem has been represented as a `QuadraticProgram`, it will need to be converted to the correct type, a [quadratic unconstrained binary optimization (QUBO)](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization) problem, so that it is compatible with QRAO.\n", + "A `QuadraticProgram` generated by `Maxcut`is already a QUBO, but if you define your own problem be sure you convert it to a QUBO before proceeding. Here is [a tutorial](https://qiskit.org/documentation/optimization/tutorials/02_converters_for_quadratic_programs.html) on converting `QuadraticPrograms`." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\\ This file has been generated by DOcplex\n", + "\\ ENCODING=ISO-8859-1\n", + "\\Problem name: Max-cut\n", + "\n", + "Maximize\n", + " obj: 3 x_0 + 3 x_1 + 3 x_2 + 3 x_3 + 3 x_4 + 3 x_5 + [ - 4 x_0*x_1 - 4 x_0*x_3\n", + " - 4 x_0*x_4 - 4 x_1*x_2 - 4 x_1*x_5 - 4 x_2*x_3 - 4 x_2*x_4 - 4 x_3*x_5\n", + " - 4 x_4*x_5 ]/2\n", + "Subject To\n", + "\n", + "Bounds\n", + " 0 <= x_0 <= 1\n", + " 0 <= x_1 <= 1\n", + " 0 <= x_2 <= 1\n", + " 0 <= x_3 <= 1\n", + " 0 <= x_4 <= 1\n", + " 0 <= x_5 <= 1\n", + "\n", + "Binaries\n", + " x_0 x_1 x_2 x_3 x_4 x_5\n", + "End\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import networkx as nx\n", + "\n", + "from qiskit_optimization.applications import Maxcut\n", + "\n", + "seed = 1\n", + "num_nodes = 6\n", + "graph = nx.random_regular_graph(d=3, n=num_nodes, seed=seed)\n", + "nx.draw(graph, with_labels=True, pos=nx.spring_layout(graph, seed=seed))\n", + "\n", + "maxcut = Maxcut(graph)\n", + "problem = maxcut.to_quadratic_program()\n", + "print(problem.export_as_lp_string())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Encode the problem into a quantum Hamiltonian\n", + "\n", + "Once we have appropriately configured our problem, we proceed to encode it using the `QuantumRandomAccessEncoding` class from the `qrao` module. This encoding step allows us to generate a quantum Hamiltonian operator that represents our problem. In particular, we employ a Quantum Random Access Code (QRAC) to encode multiple classical binary variables (corresponding to the nodes of our max-cut graph) into each qubit.\n", + "\n", + "It's important to note that the resulting \"relaxed\" Hamiltonian, produced by this encoding, will not be diagonal. This differs from the standard workflow in `qiskit-optimization`, which typically generates a diagonal (Ising) Hamiltonian suitable for optimization using a [`MinimumEigenOptimizer`](https://qiskit.org/documentation/optimization/tutorials/03_minimum_eigen_optimizer.html).\n", + "\n", + "In our encoding process, we employ a $(3,1,p)-$QRAC, where each qubit can accommodate a maximum of 3 classical binary variables. The parameter $p$ represents the bit recovery probability achieved through measurement. Depending on the nature of the problem, some qubits may have fewer than 3 classical variables assigned to them. To evaluate the compression achieved, we can examine the `compression_ratio` attribute of the encoding, which provides the ratio between the number of original binary variables and the number of qubits used (at best, a factor of 3)." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Our encoded Hamiltonian is:\n", + "( 1.4999999999999998 * XX\n", + "+ 1.4999999999999998 * XY\n", + "+ 1.4999999999999998 * XZ\n", + "+ 1.4999999999999998 * YX\n", + "+ 1.4999999999999998 * ZX\n", + "+ 1.4999999999999998 * YY\n", + "+ 1.4999999999999998 * YZ\n", + "+ 1.4999999999999998 * ZY\n", + "+ 1.4999999999999998 * ZZ ).\n", + "\n", + "We achieve a compression ratio of (6 binary variables : 2 qubits) ≈ 3.0.\n", + "\n" + ] + } + ], + "source": [ + "from qiskit_optimization.algorithms.qrao import QuantumRandomAccessEncoding\n", + "\n", + "\n", + "# Create an encoding object with a maximum of 3 variables per qubit, aka a (3,1,p)-QRAC\n", + "encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3)\n", + "\n", + "# Encode the QUBO problem into an encoded Hamiltonian\n", + "encoding.encode(problem)\n", + "\n", + "# This is our encoded Hamiltonian\n", + "print(f\"Our encoded Hamiltonian is:\\n( {encoding.qubit_op} ).\\n\")\n", + "print(\n", + " \"We achieve a compression ratio of \"\n", + " f\"({encoding.num_vars} binary variables : {encoding.num_qubits} qubits) \"\n", + " f\"≈ {encoding.compression_ratio}.\\n\"\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solve the problem using the `QuantumRandomAccessOptimizer`\n", + "\n", + "Having successfully encoded our input problem as a relaxed Hamiltonian, we proceed to solve it using the `QuantumRandomAccessOptimizer`. This optimizer allows us to find an approximate solution to the relaxed problem by leveraging quantum computing techniques.\n", + "\n", + "To set up the optimizer, we need to specify two crucial components:\n", + "\n", + "1. **Minimum Eigensolver**: We specify a minimum eigensolver to heuristically search for the ground state of the relaxed problem Hamiltonian. As an example, we can use the Variational Quantum Eigensolver (VQE). Alternatively, the Quantum Approximate Optimization Algorithm (QAOA) can be utilized. For simulation purposes, we'll employ an Aer simulator, but you can choose a quantum device as the backend if desired.\n", + "2. **Rounding Scheme**: To map the ground state results back to a solution for the original problem, we specify a rounding scheme. By default, the `SemideterministicRounding` is used, but alternative scheme, `MagicRounding`, is also available." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.algorithms.optimizers import COBYLA\n", + "from qiskit.algorithms.minimum_eigensolvers import VQE\n", + "from qiskit.circuit.library import RealAmplitudes\n", + "from qiskit.primitives import Estimator\n", + "\n", + "from qiskit_optimization.algorithms.qrao import (\n", + " QuantumRandomAccessOptimizer,\n", + " SemideterministicRounding,\n", + ")\n", + "\n", + "\n", + "# Prepare the VQE algorithm\n", + "ansatz = RealAmplitudes(2)\n", + "vqe = VQE(\n", + " ansatz=ansatz,\n", + " optimizer=COBYLA(),\n", + " estimator=Estimator(),\n", + ")\n", + "\n", + "# Use semideterministic rounding, known as \"Pauli rounding\"\n", + "# in https://arxiv.org/pdf/2111.03167v2.pdf\n", + "# (This is the default if no rounding scheme is specified.)\n", + "semidterministic_rounding = SemideterministicRounding()\n", + "\n", + "# Construct the optimizer\n", + "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=semidterministic_rounding)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we move forward with solving the problem by invoking the `solve()` method. It's important to note that when calling `solve()`, we pass the `problem` itself as an argument. Although we previously used `encode()` in `QuantumRandomAccessEncoding` to provide a clear understanding of the flow, `solve(problem)` automatically encodes the problem internally using `QuantumRandomAccessEncoding`. This provides a streamlined and simplified workflow that eliminates the need for explicit encoding steps.\n", + "\n", + "The result is provides us as a `QuantumRandomAccessOptimizationResult`.\n", + "The `x` contains the binary values representing the best solution found, while the `fval` contains the corresponding objective value.\n", + "\n", + "The `relaxed_fval` provides the expectation value of the relaxed Hamiltonian, adjusted to be in the units of the original optimization problem. For maximization problems, the best possible relaxed function value will always be greater than or equal to the best possible function value of the original problem. In practice, this often holds true for the best found value and best found function value as well." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The objective function value: 5.0\n", + "x: [0 1 1 0 1 0]\n", + "relaxed function value: 8.999999950367048\n", + "\n" + ] + } + ], + "source": [ + "# Solve the optimization problem\n", + "results = qrao.solve(problem)\n", + "\n", + "print(\n", + " f\"The objective function value: {results.fval}\\n\"\n", + " f\"x: {results.x}\\n\"\n", + " f\"relaxed function value: {-1 * results.relaxed_fval}\\n\"\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interpret the solution" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the context of [max-cut](https://en.wikipedia.org/wiki/Maximum_cut), the result's \"optimal value\" tells us which subset each node belongs to given the partition found by the optimizer." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The obtained solution places a partition between nodes [0 2 4] and nodes [1 3 5].\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "print(\n", + " f\"The obtained solution places a partition between nodes {np.where(results.x == 0)[0]} \"\n", + " f\"and nodes {np.where(results.x == 1)[0]}.\"\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Inspect the results of subroutines" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The [`MinimumEigensolverResult`](https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html) that results from performing VQE (or, QAOA) on the relaxed Hamiltonian is available:" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results.relaxed_result" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The result of the rounding scheme is also worth considering. In this example, we used the `SemideterministricRounding`. It's important to note that with semideterministic rounding, a single sample is generated as the result, making it the optimal solution candidate.\n", + "\n", + "However, if we use the `MagicRounding` instead, multiple samples would be generated, each with a probability associated with it. These probabilities sum up to one, providing a distribution of potential optimal solutions." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[SolutionSample(x=array([0, 1, 1, 0, 1, 0]), fval=5.0, probability=1.0, status=)]" + ] + }, + "execution_count": 46, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "results.samples" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exact Problem Solution with the `NumpyMinimumEigensolver`\n", + "\n", + "To assess the performance of QRAO in approximating the optimal solution, we can utilize the `NumpyMinimumEigensolver`, an exact classical optimizer. We can obtain the exact optimal solution to the problem as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "objective function value: 9.0\n", + "variable values: x_0=0.0, x_1=1.0, x_2=0.0, x_3=1.0, x_4=1.0, x_5=0.0\n", + "status: SUCCESS\n" + ] + } + ], + "source": [ + "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n", + "\n", + "from qiskit_optimization.algorithms import MinimumEigenOptimizer\n", + "\n", + "exact_mes = NumPyMinimumEigensolver()\n", + "exact = MinimumEigenOptimizer(exact_mes)\n", + "exact_result = exact.solve(problem)\n", + "print(exact_result.prettyprint())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The approximation ratio (QRAO's approximate optimal function value divided by the exact optimal function value) tells us how closely QRAO approximated the optimal solution to the problem." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "QRAO Approximate Optimal Function Value: 5.0\n", + "Exact Optimal Function Value: 9.0\n", + "Approximation Ratio: 0.56\n" + ] + } + ], + "source": [ + "print(\"QRAO Approximate Optimal Function Value:\", results.fval)\n", + "print(\"Exact Optimal Function Value:\", exact_result.fval)\n", + "print(f\"Approximation Ratio: {results.fval / exact_result.fval :.2f}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solve the problem using the `QuantumRandomAccessOptimizer` with `MagicRounding`\n", + "\n", + "Magic rounding is a quantum technique employed to map the ground state results of our encoded Hamiltonian back to a solution of the original problem. Unlike semideterministic rounding, magic rounding requires a quantum backend, which can be either hardware or a simulator. The backend is passed to the MagicRounding class through a `Sampler`, which also determines the total number of shots (samples) that magic rounding will utilize. Consequently, we need to specify `Estimator` and `Sampler` for the optimizer and the rounding scheme, respectively.\n", + "\n", + "In practice, users may choose to set a significantly higher number of magic rounding shots compared to the shots used by the minimum eigensolver for the relaxed problem. This difference arises because the minimum eigensolver estimates expectation values, while the magic rounding scheme returns the sample corresponding to the maximum function value found. When estimating an expectation value, increasing the number of shots enhances the convergence to the true value. However, when aiming to identify the largest possible function value, we often sample from the tail of a distribution of outcomes. As a result, until we observe the highest value outcome in our distribution, each additional shot increases the expected return value.\n", + "\n", + "\n", + "In this tutorial, we use the `Estimator` and `Sampler` for solving the relaxed Hamiltonian and for performing magic rounding, respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.primitives import Sampler\n", + "\n", + "from qiskit_optimization.algorithms.qrao import MagicRounding\n", + "\n", + "\n", + "estimator = Estimator(options={\"shots\": 1000, \"seed\": seed})\n", + "sampler = Sampler(options={\"shots\": 10000, \"seed\": seed})\n", + "\n", + "# Prepare the VQE algorithm\n", + "ansatz = RealAmplitudes(2)\n", + "vqe = VQE(\n", + " ansatz=ansatz,\n", + " optimizer=COBYLA(),\n", + " estimator=estimator,\n", + ")\n", + "\n", + "\n", + "# Use magic rounding\n", + "magic_rounding = MagicRounding(sampler=sampler)\n", + "\n", + "# Construct the optimizer\n", + "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=magic_rounding)\n", + "\n", + "results = qrao.solve(problem)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The objective function value: 9.0\n", + "x: [1 0 1 0 0 1]\n", + "relaxed function value: 8.999994845360565\n", + "\n" + ] + } + ], + "source": [ + "print(\n", + " f\"The objective function value: {results.fval}\\n\"\n", + " f\"x: {results.x}\\n\"\n", + " f\"relaxed function value: {-1 * results.relaxed_fval}\\n\"\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since magic rounding relies on nondeterministic measurements, the method collects a number of samples based on the shots count provided to the `Sampler` mentioned earlier. These samples are then consolidated, taking into account duplicates and calculating the empirical probability for each `SolutionSample`. Each sample in the consolidation process includes a corresponding function value (`fval`).\n", + "\n", + "From the consolidated samples, we select the sample with the \"optimal\" function value. In the case of a max-cut problem, this means choosing the sample with the largest function value as our solution." + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The number of distinct samples is 56.\n", + "Top 10 samples with the largest fval:\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0095, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0112, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0204, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0213, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0197, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0207, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0203, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0214, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.021, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0223, status=)\n" + ] + } + ], + "source": [ + "print(f\"The number of distinct samples is {len(results.samples)}.\")\n", + "print(\"Top 10 samples with the largest fval:\")\n", + "for sample in results.samples[:10]:\n", + " print(sample)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Alternative: Solve the Problem in Two Explicit Steps\n", + "\n", + "In the previous part of this tutorial, we utilized the `qrao.solve()` method, which solved the encoded problem (the ground state of the relaxed Hamiltonian) and performed rounding to map the ground state results back to a solution of the original problem. However, it is also possible to explicitly break down the calculation into these two distinct steps. This can be beneficial, especially when comparing solutions obtained across multiple rounding schemes applied to a candidate ground state.\n", + "\n", + "In this section, we will explore how to perform each of these steps explicitly.\n", + "\n", + "## Manually solve the relaxed problem.\n", + "\n", + "Let's start by invoking the `qrao.solve_relaxed()` method to directly solve the relaxed problem encoded by `QuantumRandomAccessEncoding`.\n", + "This method allows us to focus solely on solving the relaxed problem without performing rounding.\n", + "\n", + "By invoking `qrao.solve_relaxed()`, we obtain two essential outputs:\n", + "\n", + "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the ground state, eigenvalues, and other relevant details. You can refer to the Qiskit Terra [documentation]((https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html)) for a comprehensive explanation of the entries within this object.\n", + "- `RoundingContext`: This object encapsulates essential information about the encoding and the solution of the relaxed problem in a form that is ready for consumption by the rounding chemes." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [], + "source": [ + "# Encode the QUBO problem into a relaxed Hamiltonian\n", + "encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3)\n", + "encoding.encode(problem)\n", + "\n", + "# Solve the relaxed problem\n", + "relaxed_results, rounding_context = qrao.solve_relaxed(encoding)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Manually perform rounding on the relaxed problem results\n", + "\n", + "Next, we proceed with rounding the results obtained from solving the relaxed problem. To achieve this, we call the `round()` method on an instance of the desired rounding scheme and pass it the `RoundingContext` object. Below, we provide an example for both rounding schemes, utilizing the relaxed solution obtained in the previous step.\n", + "\n", + "By manually performing the rounding step, we have more flexibility and control over the rounding scheme applied to the relaxed problem results. This allows for greater exploration and comparison of different rounding strategies." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SemideterministicRoundingResult(expectation_values=[0.010963479306130598, 0.025946706266548325, 0.01044933784106082, -0.04120945001189341, 0.028550195543948588, 0.014195270980882519], samples=[SolutionSample(x=array([0, 0, 0, 1, 0, 0]), fval=3.0, probability=1.0, status=)])" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sdr_results" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The objective function value: 3.0\n", + "x: [0 0 0 1 0 0]\n", + "relaxed function value: -8.999995535781801\n", + "The number of distinct samples is 1.\n" + ] + } + ], + "source": [ + "# Round the relaxed solution using semideterministic rounding\n", + "semidterministic_rounding = SemideterministicRounding()\n", + "sdr_results = semidterministic_rounding.round(rounding_context)\n", + "qrao_results_sdr = qrao.process_result(\n", + " problem=problem, encoding=encoding, relaxed_result=relaxed_results, rounding_result=sdr_results\n", + ")\n", + "\n", + "print(\n", + " f\"The objective function value: {qrao_results_sdr.fval}\\n\"\n", + " f\"x: {qrao_results_sdr.x}\\n\"\n", + " f\"relaxed function value: {-1 * qrao_results_sdr.relaxed_fval}\\n\"\n", + " f\"The number of distinct samples is {len(qrao_results_sdr.samples)}.\"\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The objective function value: 9.0\n", + "x: [1 0 1 0 0 1]\n", + "relaxed function value: -8.999995535781801\n", + "The number of distinct samples is 56.\n" + ] + } + ], + "source": [ + "magic_rounding = MagicRounding(sampler=sampler)\n", + "mr_results = magic_rounding.round(rounding_context)\n", + "qrao_results_mr = qrao.process_result(\n", + " problem=problem, encoding=encoding, relaxed_result=relaxed_results, rounding_result=mr_results\n", + ")\n", + "\n", + "print(\n", + " f\"The objective function value: {qrao_results_mr.fval}\\n\"\n", + " f\"x: {qrao_results_mr.x}\\n\"\n", + " f\"relaxed function value: {-1 * qrao_results_mr.relaxed_fval}\\n\"\n", + " f\"The number of distinct samples is {len(qrao_results_mr.samples)}.\"\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Fri May 12 16:53:28 2023 JST
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "

This code is a part of Qiskit

© Copyright IBM 2017, 2023.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.

" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import qiskit.tools.jupyter\n", + "\n", + "%qiskit_version_table\n", + "%qiskit_copyright" + ] + } + ], + "metadata": { + "interpreter": { + "hash": "091032f753fd8b52e996fc03d6323ff523db19d64607db6acd8c3783811ef968" + }, + "kernelspec": { + "display_name": "Python 3.9.12 ('prototype-qrao')", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 721d49d33..d26580d21 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -113,12 +113,12 @@ def basis_sampling(self): @staticmethod def _make_circuits( - circ: QuantumCircuit, bases: np.ndarray[Any, Any], vars_per_qubit: int + circuit: QuantumCircuit, bases: np.ndarray[Any, Any], vars_per_qubit: int ) -> List[QuantumCircuit]: """Make a list of circuits to measure in the given magic bases. Args: - circ: Quantum circuit to measure. + circuit: Quantum circuit to measure. bases: List of magic bases to measure in. vars_per_qubit: Number of variables per qubit. @@ -128,11 +128,11 @@ def _make_circuits( circuits = [] for basis in bases: if vars_per_qubit == 3: - qc = circ.compose(_z_to_31p_qrac_basis_circuit(basis).inverse(), inplace=False) + qc = circuit.compose(_z_to_31p_qrac_basis_circuit(basis).inverse(), inplace=False) elif vars_per_qubit == 2: - qc = circ.compose(_z_to_21p_qrac_basis_circuit(basis).inverse(), inplace=False) + qc = circuit.compose(_z_to_21p_qrac_basis_circuit(basis).inverse(), inplace=False) elif vars_per_qubit == 1: - qc = circ.copy() + qc = circuit.copy() qc.measure_all() circuits.append(qc) return circuits @@ -319,6 +319,7 @@ def _sample_bases_weighted( corresponds to the number of shots to use for the corresponding basis in the bases array. """ + # pylint: disable=C0401 # First, we make sure all Pauli expectation values have absolute value # at most 1. Otherwise, some of the probabilities computed below might # be negative. @@ -365,11 +366,11 @@ def _sample_bases_weighted( bases, basis_shots = np.unique(bases_, axis=0, return_counts=True) return bases, basis_shots - def round(self, ctx: RoundingContext) -> MagicRoundingResult: + def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: """Perform magic rounding using the given RoundingContext. Args: - ctx: The context containing the information needed for the rounding. + rounding_context: The context containing the information needed for the rounding. Returns: MagicRoundingResult: The results of the magic rounding process. @@ -378,11 +379,11 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: NotImplementedError: If the circuit is not available for magic rounding. ValueError: If the sampler is not configured with a number of shots. """ - expectation_values = ctx.expectation_values - circuit = ctx.circuit - q2vars = ctx.encoding.q2vars - var2op = ctx.encoding.var2op - vars_per_qubit = ctx.encoding.max_vars_per_qubit + expectation_values = rounding_context.expectation_values + circuit = rounding_context.circuit + q2vars = rounding_context.encoding.q2vars + var2op = rounding_context.encoding.var2op + vars_per_qubit = rounding_context.encoding.max_vars_per_qubit if circuit is None: raise NotImplementedError( @@ -421,10 +422,10 @@ def round(self, ctx: RoundingContext) -> MagicRoundingResult: soln_samples = [ SolutionSample( x=np.asarray([int(bit) for bit in soln]), - fval=ctx.encoding.problem.objective.evaluate([int(bit) for bit in soln]), + fval=rounding_context.encoding.problem.objective.evaluate([int(bit) for bit in soln]), probability=count / self._shots, status=OptimizationResultStatus.SUCCESS - if ctx.encoding.problem.is_feasible([int(bit) for bit in soln]) + if rounding_context.encoding.problem.is_feasible([int(bit) for bit in soln]) else OptimizationResultStatus.INFEASIBLE, ) for soln, count in soln_counts.items() diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index d3920ca4b..874e8e384 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -113,11 +113,11 @@ def _qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: if len(bit_list) == 3: # Prepare (3,1,p)-qrac - # In the following lines, the input bits are XOR'd to match the + # In the following lines, the input bits are XORed to match the # conventions used in the paper. # To understand why this transformation happens, # observe that the two states that define each magic basis - # correspond to the same bitstrings but with a global bitflip. + # correspond to the same bitstrings but with a global bit flip. # Thus the three bits of information we use to construct these states are: # base_index0,base_index1 : two bits to pick one of four magic bases # bit_flip: one bit to indicate which magic basis projector we are interested in. @@ -152,15 +152,15 @@ def _qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: return circ -def _qrac_state_prep_multiqubit( - dvars: List[int], +def _qrac_state_prep_multi_qubit( + x: List[int], q2vars: List[List[int]], max_vars_per_qubit: int, ) -> QuantumCircuit: - """Prepares a multiqubit QRAC state. + """Prepares a multi qubit QRAC state. Args: - dvars: The state of each decision variable (0 or 1). + x: The state of each decision variable (0 or 1). q2vars: A list of lists of integers. Each inner list contains the indices of decision variables mapped to a specific qubit. max_vars_per_qubit: The maximum number of decision variables that can be mapped to a @@ -170,12 +170,12 @@ def _qrac_state_prep_multiqubit( A QuantumCircuit object representing the prepared state. Raises: - ValueError: If any qubit is associated with more than ``max_vars_per_qubit`` variables. - ValueError: If a decision variable in ``q2vars`` is not included in ``dvars``. - ValueError: If there are unused decision variables in `dvars` after mapping to qubits. + ValueError: If any qubit is associated with more than `max_vars_per_qubit` variables. + ValueError: If a decision variable in ``q2vars`` is not included in `x`. + ValueError: If there are unused decision variables in `x` after mapping to qubits. """ # Create a set of all remaining decision variables - remaining_dvars = set(range(len(dvars))) + remaining_dvars = set(range(len(x))) # Create a list to store the binary mappings of each qubit to its corresponding decision variables variable_mappings: List[List[int]] = [] # Check that each qubit is associated with at most max_vars_per_qubit variables @@ -193,7 +193,7 @@ def _qrac_state_prep_multiqubit( # to the qubit bits for dvar in qi_vars: try: - qi_bits.append(dvars[dvar]) + qi_bits.append(x[dvar]) except IndexError: raise ValueError(f"Decision variable not included in dvars: {dvar}") from None try: @@ -213,7 +213,7 @@ def _qrac_state_prep_multiqubit( if remaining_dvars: raise ValueError(f"Not all dvars were included in q2vars: {remaining_dvars}") - # Prepare the individual qrac circuit and combine them into a multiqubit circuit + # Prepare the individual qrac circuit and combine them into a multi qubit circuit qracs = [_qrac_state_prep_1q(qi_bits) for qi_bits in variable_mappings] qrac_circ = reduce(lambda x, y: x.tensor(y), qracs) return qrac_circ @@ -272,7 +272,7 @@ def var2op(self) -> Dict[int, Tuple[int, SparsePauliOp]]: @property def q2vars(self) -> List[List[int]]: - """Each element contains the list of decision variable indice(s) encoded on that qubit""" + """Each element contains the list of decision variable indices encoded on that qubit""" return self._q2vars @property @@ -556,14 +556,14 @@ def encode(self, problem: QuadraticProgram) -> None: self.freeze() - def state_preparation_circuit(self, dvars: List[int]) -> QuantumCircuit: + def state_preparation_circuit(self, x: List[int]) -> QuantumCircuit: """ Generate a circuit that prepares the state corresponding to the given binary string. Args: - dvars: A list of binary values to be encoded into the state. + x: A list of binary values to be encoded into the state. Returns: A QuantumCircuit that prepares the state corresponding to the given binary string. """ - return _qrac_state_prep_multiqubit(dvars, self.q2vars, self.max_vars_per_qubit) + return _qrac_state_prep_multi_qubit(x, self.q2vars, self.max_vars_per_qubit) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index b2dee9515..b638288a4 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -211,7 +211,7 @@ def solve_relaxed( ) relaxed_result.time_taken = time.time() - start_time_relaxed - # Get auxiliary expectaion values for rounding. + # Get auxiliary expectation values for rounding. if relaxed_result.aux_operators_evaluated is not None: expectation_values = [v[0] for v in relaxed_result.aux_operators_evaluated] else: diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index db1565a79..fd812f0c3 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -56,7 +56,7 @@ class RoundingScheme(ABC): """Base class for a rounding scheme""" @abstractmethod - def round(self, ctx: RoundingContext) -> RoundingResult: + def round(self, rounding_context: RoundingContext) -> RoundingResult: """Perform rounding Returns: an instance of RoundingResult diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index d67c12d8c..3db048f66 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -47,11 +47,11 @@ def __init__(self, *, seed: Optional[int] = None): super().__init__() self.rng = np.random.RandomState(seed) - def round(self, ctx: RoundingContext) -> SemideterministicRoundingResult: + def round(self, rounding_context: RoundingContext) -> SemideterministicRoundingResult: """Perform semideterministic rounding Args: - ctx: Rounding context containing information about the problem and solution. + rounding_context: Rounding context containing information about the problem and solution. Returns: Result containing the rounded solution. @@ -63,7 +63,7 @@ def round(self, ctx: RoundingContext) -> SemideterministicRoundingResult: def sign(val) -> int: return 0 if (val > 0) else 1 - if ctx.expectation_values is None: + if rounding_context.expectation_values is None: raise NotImplementedError( "Semideterministric rounding requires the expectation values of the ", "``RoundingContext`` to be available, but they are not.", @@ -71,22 +71,22 @@ def sign(val) -> int: rounded_vars = np.array( [ sign(e) if not np.isclose(0, e) else self.rng.randint(2) - for e in ctx.expectation_values + for e in rounding_context.expectation_values ] ) soln_samples = [ SolutionSample( x=np.asarray(rounded_vars), - fval=ctx.encoding.problem.objective.evaluate(rounded_vars), + fval=rounding_context.encoding.problem.objective.evaluate(rounded_vars), probability=1.0, status=OptimizationResultStatus.SUCCESS - if ctx.encoding.problem.is_feasible(rounded_vars) + if rounding_context.encoding.problem.is_feasible(rounded_vars) else OptimizationResultStatus.INFEASIBLE, ) ] result = SemideterministicRoundingResult( - expectation_values=ctx.expectation_values, samples=soln_samples + expectation_values=rounding_context.expectation_values, samples=soln_samples ) return result diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index 1fb6274eb..86acc6c3b 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -140,7 +140,7 @@ def test_qrac_state_prep(self): with self.subTest(msg="(3,1,p) QRAC"): encoding = QuantumRandomAccessEncoding(3) encoding.encode(self.problem) - state_prep_circ = encoding.state_preparation_circuit(dvars=dvars) + state_prep_circ = encoding.state_preparation_circuit(x=dvars) circ = QuantumCircuit(1) beta = np.arccos(1 / np.sqrt(3)) circ.r(np.pi - beta, np.pi / 4, 0) @@ -149,7 +149,7 @@ def test_qrac_state_prep(self): with self.subTest(msg="(2,1,p) QRAC"): encoding = QuantumRandomAccessEncoding(2) encoding.encode(self.problem) - state_prep_circ = encoding.state_preparation_circuit(dvars=dvars) + state_prep_circ = encoding.state_preparation_circuit(x=dvars) circ = QuantumCircuit(2) circ.x(0) circ.r(-3 * np.pi / 4, -np.pi / 2, 0) @@ -159,7 +159,7 @@ def test_qrac_state_prep(self): with self.subTest(msg="(1,1,p) QRAC"): encoding = QuantumRandomAccessEncoding(1) encoding.encode(self.problem) - state_prep_circ = encoding.state_preparation_circuit(dvars=dvars) + state_prep_circ = encoding.state_preparation_circuit(x=dvars) circ = QuantumCircuit(3) circ.x(0) circ.x(1) From 668add2b8b3920836b1059f5e494f796c22e1ea8 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 12 May 2023 17:16:39 +0900 Subject: [PATCH 15/67] update pylintdict --- .pylintdict | 3 +++ 1 file changed, 3 insertions(+) diff --git a/.pylintdict b/.pylintdict index 07a9e754b..f8c0f43cc 100644 --- a/.pylintdict +++ b/.pylintdict @@ -160,6 +160,8 @@ qiskit qiskit's qn qp +qrac +qrao quadratically quadraticconstraint quadraticobjective @@ -185,6 +187,7 @@ rz sahar scipy sdp +semideterministic sherrington simonetto slsqp From 9c3ac42e87859485606712115f136fcfdd787176 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 12 May 2023 17:30:11 +0900 Subject: [PATCH 16/67] fix lint --- qiskit_optimization/algorithms/qrao/magic_rounding.py | 4 +++- .../algorithms/qrao/quantum_random_access_encoding.py | 1 + 2 files changed, 4 insertions(+), 1 deletion(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index d26580d21..91b411b79 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -422,7 +422,9 @@ def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: soln_samples = [ SolutionSample( x=np.asarray([int(bit) for bit in soln]), - fval=rounding_context.encoding.problem.objective.evaluate([int(bit) for bit in soln]), + fval=rounding_context.encoding.problem.objective.evaluate( + [int(bit) for bit in soln] + ), probability=count / self._shots, status=OptimizationResultStatus.SUCCESS if rounding_context.encoding.problem.is_feasible([int(bit) for bit in soln]) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 874e8e384..943ac649a 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -106,6 +106,7 @@ def _qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: TypeError: if the number of arguments is not 1, 2, or 3 ValueError: if any of the arguments are not 0 or 1 """ + # pylint: disable=C0401 if len(bit_list) not in (1, 2, 3): raise TypeError(f"qrac_state_prep_1q requires 1, 2, or 3 arguments, not {len(bit_list)}.") if not all(bit in (0, 1) for bit in bit_list): From 872927d4093d71752d58ae4f954b67a8a4c002ba Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Wed, 17 May 2023 12:47:59 +0900 Subject: [PATCH 17/67] Update docs/tutorials/13_quantum_random_access_optimizer.ipynb Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com> --- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 8942080c9..be66a5d97 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -23,7 +23,7 @@ "\n", "### References\n", "\n", - "[1] Bryce Fuller, Charles Hadfield, Jennifer R. Glick, Takashi Imamichi, Toshinari Itoko, Richard J. Thompson, Yang Jiao, Marna M. Kagele, Adriana W. Blom-Schieber, Rudy Raymond, Antonio Mezzacapo, *Approximate Solutions of Combinatorial Problems via Quantum Relaxations,* [arXiv:2111.03167](https://arxiv.org/abs/2111.03167)" + "[1] Bryce Fuller et al., *Approximate Solutions of Combinatorial Problems via Quantum Relaxations,* [arXiv:2111.03167](https://arxiv.org/abs/2111.03167)" ] }, { From 59ecdd663cea15429005d12e66fa3d0b701714bb Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Wed, 17 May 2023 12:48:20 +0900 Subject: [PATCH 18/67] Update qiskit_optimization/algorithms/qrao/magic_rounding.py Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com> --- qiskit_optimization/algorithms/qrao/magic_rounding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 91b411b79..85431b96b 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -113,7 +113,7 @@ def basis_sampling(self): @staticmethod def _make_circuits( - circuit: QuantumCircuit, bases: np.ndarray[Any, Any], vars_per_qubit: int + circuit: QuantumCircuit, bases: np.ndarray, vars_per_qubit: int ) -> List[QuantumCircuit]: """Make a list of circuits to measure in the given magic bases. From 40ae2772cec1dcc15ab9803ea08fbbad4e5b941a Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Wed, 17 May 2023 12:50:57 +0900 Subject: [PATCH 19/67] Update releasenotes/notes/qrao-89d5ff1d2927de64.yaml Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- releasenotes/notes/qrao-89d5ff1d2927de64.yaml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml index a64dffe16..2fd45f841 100644 --- a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml +++ b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml @@ -40,7 +40,7 @@ features: qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe) result = qrao.solve(problem) - # solve_relazed() only performs the optimization. The encoding and rounding must be done manually. + # solve_relaxed() only performs the optimization. The encoding and rounding must be done manually. # encoding encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) encoding.encode(problem) From 7fb0f40dd6f18a5312deb352ec16eca81452cd00 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 17 May 2023 19:41:37 +0900 Subject: [PATCH 20/67] update the code --- .pylintdict | 1 - .../13_quantum_random_access_optimizer.ipynb | 265 +++++++++++++----- .../algorithms/qrao/__init__.py | 4 +- .../qrao/encoding_commutation_verifier.py | 12 +- .../algorithms/qrao/magic_rounding.py | 82 ++++-- .../qrao/quantum_random_access_encoding.py | 73 ++--- .../qrao/quantum_random_access_optimizer.py | 34 +-- .../algorithms/qrao/rounding_common.py | 28 +- .../qrao/semideterministic_rounding.py | 45 ++- releasenotes/notes/qrao-89d5ff1d2927de64.yaml | 10 + .../test_quantum_random_access_encoding.py | 31 +- .../test_quantum_random_access_optimizer.py | 4 +- .../qrao/test_semideterministic_rounding.py | 6 +- 13 files changed, 375 insertions(+), 220 deletions(-) diff --git a/.pylintdict b/.pylintdict index e9930e63c..7b3e4cfa8 100644 --- a/.pylintdict +++ b/.pylintdict @@ -188,7 +188,6 @@ rz sahar scipy sdp -semideterministic sherrington simonetto slsqp diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index be66a5d97..848f16c67 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -13,7 +13,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The Quantum Random Access Optimization (QRAO) module is designed to enable users to leverage a new quantum method for combinatorial optimization problems [1]. This approach incorporates Quantum Random Access Codes (QRACs) as a tool to encode multiple classical binary variables into a single qubit, thereby saving quantum resources and enabling exploration of larger problem instances on a quantum computer. The encodings produce a local quantum Hamiltonian whose ground state can be approximated with standard algorithms such as VQE and QAOA, and then rounded to yield approximation solutions of the original problem.\n", + "The Quantum Random Access Optimization (QRAO) module is designed to enable users to leverage a new quantum method for combinatorial optimization problems [1]. This approach incorporates Quantum Random Access Codes (QRACs) as a tool to encode multiple classical binary variables into a single qubit, thereby saving quantum resources and enabling exploration of larger problem instances on a quantum computer. The encodings produce a local quantum Hamiltonian whose ground state can be approximated with standard algorithms such as VQE, and then rounded to yield approximation solutions of the original problem.\n", "\n", "QRAO through a series of 3 classes:\n", "1. The encoding class (`QuantumRandomAccessEncoding`): This class encodes the original problem into a relaxed problem that requires fewer resources to solve.\n", @@ -28,7 +28,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -58,7 +58,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -131,7 +131,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -184,13 +184,13 @@ "\n", "To set up the optimizer, we need to specify two crucial components:\n", "\n", - "1. **Minimum Eigensolver**: We specify a minimum eigensolver to heuristically search for the ground state of the relaxed problem Hamiltonian. As an example, we can use the Variational Quantum Eigensolver (VQE). Alternatively, the Quantum Approximate Optimization Algorithm (QAOA) can be utilized. For simulation purposes, we'll employ an Aer simulator, but you can choose a quantum device as the backend if desired.\n", + "1. **Minimum Eigensolver**: We specify a minimum eigensolver to heuristically search for the ground state of the relaxed problem Hamiltonian. As an example, we can use the Variational Quantum Eigensolver (VQE). For simulation purposes, we'll employ an simulator, but you can choose a quantum device as the backend if desired.\n", "2. **Rounding Scheme**: To map the ground state results back to a solution for the original problem, we specify a rounding scheme. By default, the `SemideterministicRounding` is used, but alternative scheme, `MagicRounding`, is also available." ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -237,16 +237,16 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The objective function value: 5.0\n", - "x: [0 1 1 0 1 0]\n", - "relaxed function value: 8.999999950367048\n", + "The objective function value: 4.0\n", + "x: [1 0 0 0 1 0]\n", + "relaxed function value: 8.999999982036968\n", "\n" ] } @@ -278,14 +278,14 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [0 2 4] and nodes [1 3 5].\n" + "The obtained solution places a partition between nodes [1 2 3 5] and nodes [0 4].\n" ] } ], @@ -306,24 +306,25 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "The [`MinimumEigensolverResult`](https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html) that results from performing VQE (or, QAOA) on the relaxed Hamiltonian is available:" + "The [`MinimumEigensolverResult`](https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html) that results from performing VQE on the relaxed Hamiltonian is available:" ] }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 35, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -344,16 +345,16 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[SolutionSample(x=array([0, 1, 1, 0, 1, 0]), fval=5.0, probability=1.0, status=)]" + "[SolutionSample(x=array([1, 0, 0, 0, 1, 0]), fval=4.0, probability=1.0, status=)]" ] }, - "execution_count": 46, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -374,7 +375,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -407,16 +408,16 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "QRAO Approximate Optimal Function Value: 5.0\n", + "QRAO Approximate Optimal Function Value: 4.0\n", "Exact Optimal Function Value: 9.0\n", - "Approximation Ratio: 0.56\n" + "Approximation Ratio: 0.44\n" ] } ], @@ -433,7 +434,8 @@ "source": [ "## Solve the problem using the `QuantumRandomAccessOptimizer` with `MagicRounding`\n", "\n", - "Magic rounding is a quantum technique employed to map the ground state results of our encoded Hamiltonian back to a solution of the original problem. Unlike semideterministic rounding, magic rounding requires a quantum backend, which can be either hardware or a simulator. The backend is passed to the MagicRounding class through a `Sampler`, which also determines the total number of shots (samples) that magic rounding will utilize. Consequently, we need to specify `Estimator` and `Sampler` for the optimizer and the rounding scheme, respectively.\n", + "Magic rounding is a quantum technique employed to map the ground state results of our encoded Hamiltonian back to a solution of the original problem. Unlike semideterministic rounding, magic rounding requires a quantum backend, which can be either hardware or a simulator. \n", + "The backend is passed to the MagicRounding class through a `Sampler`, which also determines the total number of shots (samples) that magic rounding will utilize. Note that to specify the backend, you need to choose a `Sampler` from providers such as Aer or IBM Runtime. Consequently, we need to specify `Estimator` and `Sampler` for the optimizer and the rounding scheme, respectively.\n", "\n", "In practice, users may choose to set a significantly higher number of magic rounding shots compared to the shots used by the minimum eigensolver for the relaxed problem. This difference arises because the minimum eigensolver estimates expectation values, while the magic rounding scheme returns the sample corresponding to the maximum function value found. When estimating an expectation value, increasing the number of shots enhances the convergence to the true value. However, when aiming to identify the largest possible function value, we often sample from the tail of a distribution of outcomes. As a result, until we observe the highest value outcome in our distribution, each additional shot increases the expected return value.\n", "\n", @@ -443,7 +445,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -475,7 +477,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -484,7 +486,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999994845360565\n", + "relaxed function value: 8.9999905487688\n", "\n" ] } @@ -509,7 +511,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -518,16 +520,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0095, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0112, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0204, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0213, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0197, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0085, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0102, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0207, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0217, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0225, status=)\n", "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0207, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0203, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0214, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.021, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0223, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0201, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0211, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0202, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0212, status=)\n" ] } ], @@ -556,13 +558,13 @@ "\n", "By invoking `qrao.solve_relaxed()`, we obtain two essential outputs:\n", "\n", - "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the ground state, eigenvalues, and other relevant details. You can refer to the Qiskit Terra [documentation]((https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html)) for a comprehensive explanation of the entries within this object.\n", + "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the ground state, eigenvalues, and other relevant details. You can refer to the Qiskit Terra [documentation](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.EigensolverResult.html#qiskit.algorithms.eigensolvers.EigensolverResult) for a comprehensive explanation of the entries within this object.\n", "- `RoundingContext`: This object encapsulates essential information about the encoding and the solution of the relaxed problem in a form that is ready for consumption by the rounding chemes." ] }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ @@ -588,27 +590,7 @@ }, { "cell_type": "code", - "execution_count": 67, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "SemideterministicRoundingResult(expectation_values=[0.010963479306130598, 0.025946706266548325, 0.01044933784106082, -0.04120945001189341, 0.028550195543948588, 0.014195270980882519], samples=[SolutionSample(x=array([0, 0, 0, 1, 0, 0]), fval=3.0, probability=1.0, status=)])" - ] - }, - "execution_count": 67, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "sdr_results" - ] - }, - { - "cell_type": "code", - "execution_count": 76, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -617,7 +599,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.999995535781801\n", + "relaxed function value: -8.99999314524776\n", "The number of distinct samples is 1.\n" ] } @@ -640,7 +622,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -649,7 +631,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.999995535781801\n", + "relaxed function value: -8.99999314524776\n", "The number of distinct samples is 56.\n" ] } @@ -669,9 +651,155 @@ ")" ] }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Apendix\n", + "### How to verify correctness of your encoding\n", + "We assume for sake of the QRAO method that **the relaxation commutes with the objective function.** This notebook demonstrates how one can verify this for any problem (a `QuadraticProgram` in the language of Qiskit Optimization). One might want to verify this for pedagogical purposes, or as a sanity check when investigating unexpected behavior with the QRAO. Any problem that does not commute should be considered a bug, and if such a problem is discovered, we encourage that you submit it as [an issue on GitHub](https://github.com/Qiskit/qiskit-optimization/issues).\n", + "\n", + "The `EncodingCommutationVerifier` class allows one to conveniently iterate over all decision variable states and compare each objective value with the corresponding encoded objective value, in order to identify any discrepancy." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\\ This file has been generated by DOcplex\n", + "\\ ENCODING=ISO-8859-1\n", + "\\Problem name: Max-cut\n", + "\n", + "Maximize\n", + " obj: 3 x_0 + 3 x_1 + 3 x_2 + 3 x_3 + 3 x_4 + 3 x_5 + [ - 4 x_0*x_1 - 4 x_0*x_3\n", + " - 4 x_0*x_4 - 4 x_1*x_2 - 4 x_1*x_5 - 4 x_2*x_3 - 4 x_2*x_4 - 4 x_3*x_5\n", + " - 4 x_4*x_5 ]/2\n", + "Subject To\n", + "\n", + "Bounds\n", + " 0 <= x_0 <= 1\n", + " 0 <= x_1 <= 1\n", + " 0 <= x_2 <= 1\n", + " 0 <= x_3 <= 1\n", + " 0 <= x_4 <= 1\n", + " 0 <= x_5 <= 1\n", + "\n", + "Binaries\n", + " x_0 x_1 x_2 x_3 x_4 x_5\n", + "End\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from qiskit_optimization.algorithms.qrao import EncodingCommutationVerifier\n", + "\n", + "seed = 1\n", + "num_nodes = 6\n", + "graph = nx.random_regular_graph(d=3, n=num_nodes, seed=seed)\n", + "nx.draw(graph, with_labels=True, pos=nx.spring_layout(graph, seed=seed))\n", + "\n", + "maxcut = Maxcut(graph)\n", + "problem = maxcut.to_quadratic_program()\n", + "print(problem.export_as_lp_string())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As before, we `encode()` the problem using the QuantumRandomAccessEncoding class:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Encoded Problem:\n", + "=================\n", + "1.4999999999999998 * XX\n", + "+ 1.4999999999999998 * XY\n", + "+ 1.4999999999999998 * XZ\n", + "+ 1.4999999999999998 * YX\n", + "+ 1.4999999999999998 * ZX\n", + "+ 1.4999999999999998 * YY\n", + "+ 1.4999999999999998 * YZ\n", + "+ 1.4999999999999998 * ZY\n", + "+ 1.4999999999999998 * ZZ\n", + "Offset = -4.5\n", + "Variables encoded on each qubit: [[0, 2, 5], [1, 3, 4]]\n" + ] + } + ], + "source": [ + "encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3)\n", + "encoding.encode(problem)\n", + "\n", + "print(\"Encoded Problem:\\n=================\")\n", + "print(encoding.qubit_op) # The Hamiltonian without the offset\n", + "print(\"Offset = \", encoding.offset)\n", + "print(\"Variables encoded on each qubit: \", encoding.q2vars)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we iterate over every decision variable state using `EncodingCommutationVerifier` and verify that, in each case, the problem objective value matches the encoded objective value:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "verifier = EncodingCommutationVerifier(encoding)\n", + "if not len(verifier) == 2**encoding.num_vars:\n", + " print(\"The number results of the encoded problem is not equal to 2 ** num_vars.\")\n", + "\n", + "for str_dvars, obj_val, encoded_obj_val in verifier:\n", + " if not np.isclose(obj_val, encoded_obj_val):\n", + " print(\n", + " f\"Violation identified: {str_dvars} evaluates to {obj_val} \"\n", + " f\"but the encoded problem evaluates to {encoded_obj_val}.\"\n", + " )" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are able to construct a problem that causes a violation, it is quite possible that you have discovered a bug in the `QuantumRandomAccessEncoding` logic. We would greatly appreciate it if you could share the problem with us by [submitting it as an issue](https://github.com/Qiskit/qiskit-optimization/issues) on GitHub." + ] + }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 21, "metadata": { "scrolled": false }, @@ -679,7 +807,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Fri May 12 16:53:28 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed May 17 19:39:55 2023 JST
" ], "text/plain": [ "" @@ -707,6 +835,13 @@ "%qiskit_version_table\n", "%qiskit_copyright" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index ccfe8c283..2fa09dbec 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -41,7 +41,6 @@ RoundingContext RoundingResult SemideterministicRounding - SemideterministicRoundingResult """ @@ -51,9 +50,9 @@ from .quantum_random_access_optimizer import ( QuantumRandomAccessOptimizationResult, QuantumRandomAccessOptimizer, + SemideterministicRounding, ) from .rounding_common import RoundingContext, RoundingResult, RoundingScheme -from .semideterministic_rounding import SemideterministicRounding, SemideterministicRoundingResult __all__ = [ "EncodingCommutationVerifier", @@ -62,7 +61,6 @@ "RoundingContext", "RoundingResult", "SemideterministicRounding", - "SemideterministicRoundingResult", "MagicRounding", "MagicRoundingResult", "QuantumRandomAccessOptimizer", diff --git a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py index 80f05495a..b9338ee2f 100644 --- a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py +++ b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py @@ -12,9 +12,9 @@ """The EncodingCommutationVerifier.""" -from typing import Tuple +from __future__ import annotations -from qiskit.primitives import Estimator +from qiskit.primitives import BaseEstimator, Estimator from qiskit_optimization.exceptions import QiskitOptimizationError @@ -24,10 +24,14 @@ class EncodingCommutationVerifier: """Class for verifying that the relaxation commutes with the objective function.""" - def __init__(self, encoding: QuantumRandomAccessEncoding, estimator: Estimator = None): + def __init__( + self, encoding: QuantumRandomAccessEncoding, estimator: BaseEstimator | None = None + ): """ Args: encoding: The encoding to verify. + estimator: The estimator to use for the verification. If None, qiskit.primitives + Estimator will be used by default. """ self._encoding = encoding if estimator is not None: @@ -42,7 +46,7 @@ def __iter__(self): for i in range(len(self)): yield self[i] - def __getitem__(self, i: int) -> Tuple[str, float, float]: + def __getitem__(self, i: int) -> tuple[str, float, float]: if i not in range(len(self)): raise IndexError(f"Index out of range: {i}") diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 85431b96b..06badd91d 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -11,10 +11,11 @@ # that they have been altered from the originals. """Magic basis rounding module""" +from __future__ import annotations + from dataclasses import dataclass from collections import defaultdict -from typing import Any, Dict, List, Optional, Tuple import numpy as np from qiskit import QuantumCircuit @@ -38,15 +39,17 @@ class MagicRoundingResult(RoundingResult): """The bases used for the magic rounding""" basis_shots: np.ndarray """The number of shots used for each basis""" - basis_counts: List[Dict[str, int]] + basis_counts: list[dict[str, int]] """The basis_counts represents the resulting counts obtained by measuring with the bases corresponding to the number of shots specified in basis_shots.""" class MagicRounding(RoundingScheme): - """Magic rounding scheme + """Magic rounding scheme that measures in magic bases, and then uses the measurement results + to round the solution. Since the magic rounding is based on the measurement results, it + requires a quantum backend, which can be either hardware or a simulator. - This scheme is described in https://arxiv.org/abs/2111.03167v2. + The details are described in https://arxiv.org/abs/2111.03167v2. """ _DECODING = { @@ -70,7 +73,7 @@ def __init__( self, sampler: Sampler, basis_sampling: str = "uniform", - seed: Optional[int] = None, + seed: int | None = None, ): """ Args: @@ -96,7 +99,7 @@ def __init__( "Please choose either 'uniform' or 'weighted'." ) self._sampler = sampler - self.rng = np.random.RandomState(seed) + self._rng = np.random.default_rng(seed) self._basis_sampling = basis_sampling self._shots = None super().__init__() @@ -114,7 +117,7 @@ def basis_sampling(self): @staticmethod def _make_circuits( circuit: QuantumCircuit, bases: np.ndarray, vars_per_qubit: int - ) -> List[QuantumCircuit]: + ) -> list[QuantumCircuit]: """Make a list of circuits to measure in the given magic bases. Args: @@ -124,7 +127,13 @@ def _make_circuits( Returns: List of quantum circuits to measure in the given magic bases. + + Raises: + ValueError: If ``vars_per_qubit`` is not 1, 2, or 3. """ + if vars_per_qubit not in (1, 2, 3): + raise ValueError("vars_per_qubit must be 1, 2, or 3.") + circuits = [] for basis in bases: if vars_per_qubit == 3: @@ -143,7 +152,7 @@ def _evaluate_magic_bases( bases: np.ndarray, basis_shots: np.ndarray, vars_per_qubit: int, - ) -> List[Dict[str, int]]: + ) -> list[dict[str, int]]: """ Given a quantum circuit to measure, a list of magic bases to measure, and a list of the shots to use for each magic basis configuration, measure the provided circuit in the magic @@ -156,7 +165,7 @@ def _evaluate_magic_bases( vars_per_qubit: The number of decision variables per qubit. Returns: - List[Dict[str, int]]: A list of counts dictionaries associated with each basis measurement. + A list of counts dictionaries associated with each basis measurement. Raises: AlgorithmError: If the primitive job failed. @@ -166,8 +175,8 @@ def _evaluate_magic_bases( # Batch the circuits into jobs where each group has the same number of # shots, so that you can wait for the queue as few times as possible if # using hardware. - circuit_indices_by_shots: Dict[int, List[int]] = defaultdict(list) - basis_counts: List[Optional[Dict[str, int]]] = [None] * len(circuits) + circuit_indices_by_shots: dict[int, list[int]] = defaultdict(list) + basis_counts: list[dict[str, int] | None] = [None] * len(circuits) assert len(circuits) == len(basis_shots) for i, shots in enumerate(basis_shots): circuit_indices_by_shots[shots].append(i) @@ -198,10 +207,10 @@ def _evaluate_magic_bases( def _unpack_measurement_outcome( self, bits: str, - basis: List[int], - var2op: Dict[int, Tuple[int, SparsePauliOp]], + basis: list[int], + var2op: dict[int, tuple[int, SparsePauliOp]], vars_per_qubit: int, - ) -> List[int]: + ) -> list[int]: """ Given a measurement outcome, a magic basis, and a mapping from decision variables to Pauli operators, return the values of the decision variables. @@ -213,7 +222,7 @@ def _unpack_measurement_outcome( vars_per_qubit: The number of decision variables per qubit. Returns: - List[int]: The values of the decision variables. + The values of the decision variables. """ output_bits = [] # iterate in order over decision variables @@ -235,9 +244,9 @@ def _unpack_measurement_outcome( def _compute_dv_counts( self, - basis_counts: List[Dict[str, int]], - bases: np.ndarray[Any, Any], - var2op: Dict[int, Tuple[int, SparsePauliOp]], + basis_counts: list[dict[str, int]], + bases: np.ndarray, + var2op: dict[int, tuple[int, SparsePauliOp]], vars_per_qubit: int, ): """ @@ -254,7 +263,7 @@ def _compute_dv_counts( Returns: A dictionary of counts for each decision variable configuration. """ - dv_counts: Dict[str, int] = defaultdict(int) + dv_counts: dict[str, int] = defaultdict(int) for base, counts in zip(bases, basis_counts): # For each measurement outcome... for bitstr, count in counts.items(): @@ -265,8 +274,8 @@ def _compute_dv_counts( return dv_counts def _sample_bases_uniform( - self, q2vars: List[List[int]], vars_per_qubit: int - ) -> Tuple[np.ndarray, np.ndarray]: + self, q2vars: list[list[int]], vars_per_qubit: int + ) -> tuple[np.ndarray, np.ndarray]: """ Sample measurement bases for each qubit uniformly at random. @@ -288,15 +297,15 @@ def _sample_bases_uniform( the bases array. """ bases_ = [ - self.rng.choice(2 ** (vars_per_qubit - 1), size=len(q2vars)).tolist() + self._rng.choice(2 ** (vars_per_qubit - 1), size=len(q2vars)).tolist() for _ in range(self._shots) ] bases, basis_shots = np.unique(bases_, axis=0, return_counts=True) return bases, basis_shots def _sample_bases_weighted( - self, q2vars: List[List[int]], expectation_values: List[float], vars_per_qubit: int - ) -> Tuple[np.ndarray, np.ndarray]: + self, q2vars: list[list[int]], expectation_values: list[float], vars_per_qubit: int + ) -> tuple[np.ndarray, np.ndarray]: """ Perform weighted sampling from the expectation values. The goal is to make smarter choices about which bases to measure in using the expectation values. @@ -319,7 +328,6 @@ def _sample_bases_weighted( corresponds to the number of shots to use for the corresponding basis in the bases array. """ - # pylint: disable=C0401 # First, we make sure all Pauli expectation values have absolute value # at most 1. Otherwise, some of the probabilities computed below might # be negative. @@ -333,6 +341,10 @@ def _sample_bases_weighted( x = 0.5 * (1 - clipped_expectation_values[dvars[0]]) y = 0.5 * (1 - clipped_expectation_values[dvars[1]]) if (len(dvars) > 1) else 0 z = 0.5 * (1 - clipped_expectation_values[dvars[2]]) if (len(dvars) > 2) else 0 + # In the coefficient of the Pauli operator within the magic bases, 'p' represents a + # positive sign, while 'm' signifies a negative sign. + # The four combinations of these signs are used to define the quantum system behavior + # in the context of magic bases. # ppp: mu± = .5(I ± 1/sqrt(3)( X + Y + Z)) # pmm: X mu± X = .5(I ± 1/sqrt(3)( X - Y - Z)) # mpm: Y mu± Y = .5(I ± 1/sqrt(3)(-X + Y - Z)) @@ -347,6 +359,10 @@ def _sample_bases_weighted( elif vars_per_qubit == 2: x = 0.5 * (1 - clipped_expectation_values[dvars[0]]) z = 0.5 * (1 - clipped_expectation_values[dvars[1]]) if (len(dvars) > 1) else 0 + # In the coefficient of the Pauli operator within the magic bases, 'p' represents a + # positive sign, while 'm' signifies a negative sign. + # The two combinations of these signs are used to define the quantum system behavior + # in the context of magic bases. # pp: xi± = .5(I ± 1/sqrt(2)( X + Z )) # pm: X xi± X = .5(I ± 1/sqrt(2)( X - Z )) # fmt: off @@ -358,7 +374,7 @@ def _sample_bases_weighted( basis_probs.append([1.0]) bases_ = [ [ - self.rng.choice(2 ** (vars_per_qubit - 1), p=[p.real for p in probs]) + self._rng.choice(2 ** (vars_per_qubit - 1), p=[p.real for p in probs]) for probs in basis_probs ] for _ in range(self._shots) @@ -376,8 +392,10 @@ def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: MagicRoundingResult: The results of the magic rounding process. Raises: - NotImplementedError: If the circuit is not available for magic rounding. + ValueError: If the circuit is not available for magic rounding. ValueError: If the sampler is not configured with a number of shots. + ValueError: If the expectation values are not available for magic rounding with the + weighted sampling. """ expectation_values = rounding_context.expectation_values circuit = rounding_context.circuit @@ -386,9 +404,9 @@ def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: vars_per_qubit = rounding_context.encoding.max_vars_per_qubit if circuit is None: - raise NotImplementedError( + raise ValueError( "Magic rounding requires a circuit to be available. Perhaps try " - "semideterministic rounding instead." + "Semideterministic rounding instead." ) if self._sampler.options.get("shots") is None: @@ -403,7 +421,7 @@ def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: else: # weighted sampling if expectation_values is None: - raise NotImplementedError( + raise ValueError( "Magic rounding with weighted sampling requires the expectation values of the " "``RoundingContext`` to be available, but they are not." ) @@ -436,7 +454,9 @@ def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: assert np.isclose( sum(soln_counts.values()), self._shots ), f"{sum(soln_counts.values())} != {self._shots}" - assert len(bases) == len(basis_shots) == len(basis_counts) + assert ( + len(bases) == len(basis_shots) == len(basis_counts) + ), f"{bases}, {basis_shots}, {basis_counts} are not the same length" # Create a MagicRoundingResult object to return return MagicRoundingResult( diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 943ac649a..0e126c68e 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -11,10 +11,10 @@ # that they have been altered from the originals. """The Quantum Random Access Encoding module.""" +from __future__ import annotations from collections import defaultdict from functools import reduce -from typing import Dict, List, Optional, Tuple import numpy as np import rustworkx as rx @@ -27,7 +27,7 @@ from qiskit_optimization.problems.quadratic_program import QuadraticProgram -def _z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumCircuit: +def _z_to_31p_qrac_basis_circuit(bases: list[int], bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (3,1,p)-QRAC. Args: @@ -61,7 +61,7 @@ def _z_to_31p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> Quantum return circ -def _z_to_21p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> QuantumCircuit: +def _z_to_21p_qrac_basis_circuit(bases: list[int], bit_flip: int = 0) -> QuantumCircuit: """Return the circuit that implements the rotation to the (2,1,p)-QRAC. Args: @@ -90,7 +90,7 @@ def _z_to_21p_qrac_basis_circuit(bases: List[int], bit_flip: int = 0) -> Quantum return circ -def _qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: +def _qrac_state_prep_1q(bit_list: list[int]) -> QuantumCircuit: """ Return the circuit that prepares the state for a (1,1,p), (2,1,p), or (3,1,p)-QRAC. @@ -154,8 +154,8 @@ def _qrac_state_prep_1q(bit_list: List[int]) -> QuantumCircuit: def _qrac_state_prep_multi_qubit( - x: List[int], - q2vars: List[List[int]], + x: list[int], + q2vars: list[list[int]], max_vars_per_qubit: int, ) -> QuantumCircuit: """Prepares a multi qubit QRAC state. @@ -178,7 +178,7 @@ def _qrac_state_prep_multi_qubit( # Create a set of all remaining decision variables remaining_dvars = set(range(len(x))) # Create a list to store the binary mappings of each qubit to its corresponding decision variables - variable_mappings: List[List[int]] = [] + variable_mappings: list[list[int]] = [] # Check that each qubit is associated with at most max_vars_per_qubit variables for qi_vars in q2vars: if len(qi_vars) > max_vars_per_qubit: @@ -188,7 +188,7 @@ def _qrac_state_prep_multi_qubit( f"not {len(qi_vars)} variables." ) # Create a list to store the binary mapping of the current qubit - qi_bits: List[int] = [] + qi_bits: list[int] = [] # Map each decision variable associated with the current qubit to a binary value and add it # to the qubit bits @@ -244,11 +244,11 @@ def __init__(self, max_vars_per_qubit: int = 3): raise ValueError("max_vars_per_qubit must be 1, 2, or 3") self._ops = self.OPERATORS[max_vars_per_qubit - 1] - self._qubit_op: Optional[SparsePauliOp] = None - self._offset: Optional[float] = None - self._problem: Optional[QuadraticProgram] = None - self._var2op: Dict[int, Tuple[int, SparsePauliOp]] = {} - self._q2vars: List[List[int]] = [] + self._qubit_op: SparsePauliOp | None = None + self._offset: float | None = None + self._problem: QuadraticProgram | None = None + self._var2op: dict[int, tuple[int, SparsePauliOp]] = {} + self._q2vars: list[list[int]] = [] self._frozen = False @property @@ -267,12 +267,12 @@ def max_vars_per_qubit(self) -> int: return len(self._ops) @property - def var2op(self) -> Dict[int, Tuple[int, SparsePauliOp]]: + def var2op(self) -> dict[int, tuple[int, SparsePauliOp]]: """Maps each decision variable to ``(qubit_index, operator)``""" return self._var2op @property - def q2vars(self) -> List[List[int]]: + def q2vars(self) -> list[list[int]]: """Each element contains the list of decision variable indices encoded on that qubit""" return self._q2vars @@ -292,23 +292,27 @@ def qubit_op(self) -> SparsePauliOp: """Relaxed Hamiltonian operator. Raises: - AttributeError: If no objective function has been provided yet, and - a qubit Hamiltonian cannot be constructed. Use the `encode` method - to manually compile this field. + RuntimeError: If the objective function has not been set yet. Use the ``encode`` method + to construct the Hamiltonian, or make sure that the objective function has been set. """ if self._qubit_op is None: - raise AttributeError( + raise RuntimeError( "Cannot return the relaxed Hamiltonian operator: no objective function has been " - "provided yet. Please use the ``encode`` method to construct the Hamiltonian, or make " + "provided yet. Use the ``encode`` method to construct the Hamiltonian, or make " "sure that the objective function has been set." ) return self._qubit_op @property def offset(self) -> float: - """Relaxed Hamiltonian offset""" + """Relaxed Hamiltonian offset + + Raises: + RuntimeError: If the offset has not been set yet. Use the ``encode`` method to construct + the Hamiltonian, or make sure that the objective function has been set. + """ if self._offset is None: - raise AttributeError( + raise RuntimeError( "Cannot return the relaxed Hamiltonian offset: The offset attribute cannot be " "accessed until the ``encode`` method has been called to generate the qubit " "Hamiltonian. Please call ``encode`` first." @@ -317,9 +321,14 @@ def offset(self) -> float: @property def problem(self) -> QuadraticProgram: - """The ``QuadraticProgram`` encoding a QUBO optimization problem""" + """The ``QuadraticProgram`` encoding a QUBO optimization problem + + Raises: + RuntimeError: If the ``QuadraticProgram`` has not been set yet. Use the ``encode`` + method to set the problem. + """ if self._problem is None: - raise AttributeError( + raise RuntimeError( "This object has not been associated with a ``QuadraticProgram``. " "Please use the ``encode`` method to set the problem." ) @@ -330,7 +339,7 @@ def freeze(self): Once an instance of this class is frozen, ``encode`` can no longer be called. """ - if self._frozen is False: + if not self._frozen: self._qubit_op = self._qubit_op.simplify() self._qubit_op = PauliSumOp(self._qubit_op) self._frozen = True @@ -340,7 +349,7 @@ def frozen(self) -> bool: """Whether the object is frozen or not.""" return self._frozen - def _add_variables(self, variables: List[int]) -> None: + def _add_variables(self, variables: list[int]) -> None: """Add variables to the Encoding object. Args: @@ -430,7 +439,7 @@ def _term2op(self, *variables: int) -> SparsePauliOp: @staticmethod def _generate_ising_coefficients( problem: QuadraticProgram, - ) -> Tuple[float, np.ndarray, np.ndarray]: + ) -> tuple[float, np.ndarray, np.ndarray]: """Generate coefficients of Hamiltonian from a given problem.""" num_vars = problem.get_num_vars() @@ -467,17 +476,17 @@ def _generate_ising_coefficients( return offset, linear, quad @staticmethod - def _find_variable_partition(quad: np.ndarray) -> Dict[int, List[int]]: + def _find_variable_partition(quad: np.ndarray) -> dict[int, list[int]]: """Find the variable partition of the quad based on the node coloring of the graph Args: - quad: coefficients of the quadratic part of the Hamiltonian. + coefficients of the quadratic part of the Hamiltonian. Returns: - Dict: a dictionary of the variable partition of the quad based on the node coloring. + A dictionary of the variable partition of the quad based on the node coloring. """ # pylint: disable=E1101 - color2node: Dict[int, List[int]] = defaultdict(list) + color2node: dict[int, list[int]] = defaultdict(list) num_nodes = quad.shape[0] graph = rx.PyGraph() graph.add_nodes_from(range(num_nodes)) @@ -557,7 +566,7 @@ def encode(self, problem: QuadraticProgram) -> None: self.freeze() - def state_preparation_circuit(self, x: List[int]) -> QuantumCircuit: + def state_preparation_circuit(self, x: list[int]) -> QuantumCircuit: """ Generate a circuit that prepares the state corresponding to the given binary string. diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index b638288a4..1490092a2 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -11,12 +11,14 @@ # that they have been altered from the originals. """Quantum Random Access Optimizer class.""" +from __future__ import annotations import time -from typing import List, Optional, Tuple, Union, cast +from typing import cast import numpy as np from qiskit import QuantumCircuit +from qiskit.algorithms import VariationalResult from qiskit.algorithms.minimum_eigensolvers import ( MinimumEigensolver, MinimumEigensolverResult, @@ -43,11 +45,11 @@ class QuantumRandomAccessOptimizationResult(OptimizationResult): def __init__( self, *, - x: Optional[Union[List[float], np.ndarray]], - fval: Optional[float], - variables: List[Variable], + x: list[float] | np.ndarray, + fval: float, + variables: list[Variable], status: OptimizationResultStatus, - samples: Optional[List[SolutionSample]], + samples: list[SolutionSample], encoding: QuantumRandomAccessEncoding, relaxed_fval: float, relaxed_result: MinimumEigensolverResult, @@ -107,24 +109,22 @@ class QuantumRandomAccessOptimizer(OptimizationAlgorithm): def __init__( self, min_eigen_solver: MinimumEigensolver, - penalty: Optional[float] = None, max_vars_per_qubit: int = 3, - rounding_scheme: Optional[RoundingScheme] = None, + rounding_scheme: RoundingScheme | None = None, + **kwargs, ): """ Args: min_eigen_solver: The minimum eigensolver to use for solving the relaxed problem. - penalty: The factor that is used to scale the penalty terms corresponding to linear - equality constraints. If ``None`` is provided, the penalty will be automatically - determined. + max_vars_per_qubit: The maximum number of decision variables per qubit. rounding_scheme: The rounding scheme. If ``None`` is provided, ``SemideterministicRounding()`` will be used. - """ self.min_eigen_solver = min_eigen_solver - self.penalty = penalty # Use ``QuadraticProgramToQubo`` to convert the problem to a QUBO. - self._converters: QuadraticProgramConverter = QuadraticProgramToQubo(penalty=penalty) + self._converters: QuadraticProgramConverter = QuadraticProgramToQubo( + penalty=kwargs.get("penalty") + ) self._max_vars_per_qubit = max_vars_per_qubit self.rounding_scheme = rounding_scheme @@ -159,7 +159,7 @@ def rounding_scheme(self) -> RoundingScheme: return self._rounding_scheme @rounding_scheme.setter - def rounding_scheme(self, rounding_scheme: RoundingScheme) -> None: + def rounding_scheme(self, rounding_scheme: RoundingScheme | None) -> None: """Set the rounding scheme.""" if rounding_scheme is None: rounding_scheme = SemideterministicRounding() @@ -182,7 +182,7 @@ def get_compatibility_msg(self, problem: QuadraticProgram) -> str: def solve_relaxed( self, encoding: QuantumRandomAccessEncoding, - ) -> Tuple[MinimumEigensolverResult, RoundingContext]: + ) -> tuple[MinimumEigensolverResult, RoundingContext]: """Solve the relaxed Hamiltonian given by the encoding. Args: @@ -218,8 +218,8 @@ def solve_relaxed( expectation_values = None # Get the circuit corresponding to the relaxed solution. - if hasattr(self.min_eigen_solver, "ansatz"): - circuit = self.min_eigen_solver.ansatz.bind_parameters(relaxed_result.optimal_point) + if isinstance(relaxed_result, VariationalResult): + circuit = relaxed_result.optimal_circuit.bind_parameters(relaxed_result.optimal_point) elif isinstance(self.min_eigen_solver, NumPyMinimumEigensolver): statevector = relaxed_result.eigenstate circuit = QuantumCircuit(encoding.num_qubits) diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index fd812f0c3..ec5e24c11 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -10,10 +10,10 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. """Common classes for rounding schemes""" +from __future__ import annotations from abc import ABC, abstractmethod from dataclasses import dataclass -from typing import List, Optional from qiskit.circuit import QuantumCircuit @@ -26,30 +26,22 @@ class RoundingResult: """Base class for a rounding result""" - expectation_values: List[float] + expectation_values: list[float] """Expectation values""" - samples: List[SolutionSample] + samples: list[SolutionSample] """List of samples after rounding""" +@dataclass class RoundingContext: """Information that is provided for rounding""" - def __init__( - self, - encoding: QuantumRandomAccessEncoding, - expectation_values: List[float], - circuit: Optional[QuantumCircuit] = None, - ): - """ - Args: - encoding: Encoding containing the problem information. - expectation_values: Expectation values of the encoding. - circuit: circuit corresponding to the encoding and expectation values. - """ - self.encoding = encoding - self.expectation_values = expectation_values - self.circuit = circuit + encoding: QuantumRandomAccessEncoding + """Encoding containing the problem information.""" + expectation_values: list[float] + """Expectation values for the relaxed Hamiltonian.""" + circuit: QuantumCircuit | None = None + """Circuit corresponding to the encoding and expectation values.""" class RoundingScheme(ABC): diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 3db048f66..901469b6c 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -10,15 +10,13 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -"""Semideterministic rounding module""" -from dataclasses import dataclass - -from typing import Optional +"""Semi-deterministic rounding module""" +from __future__ import annotations import numpy as np from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample - +from qiskit_optimization.exceptions import QiskitOptimizationError from .rounding_common import ( RoundingScheme, RoundingContext, @@ -26,29 +24,26 @@ ) -@dataclass -class SemideterministicRoundingResult(RoundingResult): - """Result of semideterministic rounding""" - - class SemideterministicRounding(RoundingScheme): - """Semideterministic rounding scheme + """Semi-deterministic rounding scheme This is referred to as "Pauli rounding" in https://arxiv.org/abs/2111.03167v2. """ - def __init__(self, *, seed: Optional[int] = None): + def __init__(self, *, atol: float = 1e-8, seed: int | None = None): """ Args: seed: Seed for random number generator, which is used to resolve expectation values near zero to either +1 or -1. + atol: Absolute tolerance for determining whether an expectation value is zero. """ super().__init__() - self.rng = np.random.RandomState(seed) + self._rng = np.random.default_rng(seed) + self._atol = atol - def round(self, rounding_context: RoundingContext) -> SemideterministicRoundingResult: - """Perform semideterministic rounding + def round(self, rounding_context: RoundingContext) -> RoundingResult: + """Perform semi-deterministic rounding Args: rounding_context: Rounding context containing information about the problem and solution. @@ -57,22 +52,18 @@ def round(self, rounding_context: RoundingContext) -> SemideterministicRoundingR Result containing the rounded solution. Raises: - NotImplementedError: If the expectation values are not available in the context. + QiskitOptimizationError: If the expectation values are not available in the context. """ - - def sign(val) -> int: - return 0 if (val > 0) else 1 - if rounding_context.expectation_values is None: - raise NotImplementedError( + raise QiskitOptimizationError( "Semideterministric rounding requires the expectation values of the ", "``RoundingContext`` to be available, but they are not.", ) - rounded_vars = np.array( - [ - sign(e) if not np.isclose(0, e) else self.rng.randint(2) - for e in rounding_context.expectation_values - ] + + rounded_vars = np.where( + np.isclose(rounding_context.expectation_values, 0, atol=self._atol), + self._rng.integers(2, size=len(rounding_context.expectation_values)), + np.less_equal(rounding_context.expectation_values, 0).astype(int), ) soln_samples = [ @@ -86,7 +77,7 @@ def sign(val) -> int: ) ] - result = SemideterministicRoundingResult( + result = RoundingResult( expectation_values=rounding_context.expectation_values, samples=soln_samples ) return result diff --git a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml index 2fd45f841..e1b297b84 100644 --- a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml +++ b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml @@ -8,6 +8,16 @@ features: Hamiltonian whose ground state can be approximated with standard algorithms such as VQE and QAOA, and then rounded to yield approximation solutions of the original problem. + :class:`~.QuantumRandomAccessOptimizer` has two methods for solving problems, + :meth:`~.QuantumRandomAccessOptimizer.solve` and + :meth:`~.QuantumRandomAccessOptimizer.solve_relaxed`. The solve method provides a seamless + workflow by automatically managing the encoding and rounding procedures, as demonstrated in the + example below. This allows for a simplified and streamlined user experience. + On the other hand, the solve_relaxed method offers the flexibility to break the computation + process into distinct steps. This feature can be advantageous when we need to compare solutions + obtained from different rounding schemes applied to a potential ground state. + + For example: .. code-block:: python diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index 86acc6c3b..a4eb06df2 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -177,6 +177,15 @@ def test_qrac_unsupported_encoding(self): class TestEncodingCommutationVerifier(QiskitOptimizationTestCase): """Tests for EncodingCommutationVerifier.""" + def check_problem_commutation(self, problem: QuadraticProgram, max_vars_per_qubit: int): + """Utility function to check that the problem commutes with its encoding""" + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=max_vars_per_qubit) + encoding.encode(problem) + verifier = EncodingCommutationVerifier(encoding) + self.assertEqual(len(verifier), 2**encoding.num_vars) + for _, obj_val, encoded_obj_val in verifier: + np.testing.assert_allclose(obj_val, encoded_obj_val) + def test_encoding_commutation_verifier(self): """Test EncodingCommutationVerifier""" problem = QuadraticProgram() @@ -187,10 +196,7 @@ def test_encoding_commutation_verifier(self): encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) encoding.encode(problem) - verifier = EncodingCommutationVerifier(encoding) - self.assertEqual(len(verifier), 2**encoding.num_vars) - for _, obj_val, encoded_obj_val in verifier: - self.assertAlmostEqual(obj_val, encoded_obj_val) + self.check_problem_commutation(problem, 3) @data(*itertools.product([1, 2, 3], ["minimize", "maximize"])) @unpack @@ -205,7 +211,7 @@ def test_one_qubit_qrac(self, max_vars_per_qubit, task): problem.minimize(linear=obj) else: problem.maximize(linear=obj) - check_problem_commutation(problem, max_vars_per_qubit) + self.check_problem_commutation(problem, max_vars_per_qubit) @data( *itertools.product( @@ -224,7 +230,7 @@ def test_uniform_weights_degree_2(self, max_vars_per_qubit, task): maxcut = Maxcut(graph) problem = maxcut.to_quadratic_program() problem.objective.sense = task - check_problem_commutation(problem, max_vars_per_qubit) + self.check_problem_commutation(problem, max_vars_per_qubit) @data(1, 2, 3) def test_random_unweighted_maxcut(self, max_vars_per_qubit): @@ -232,7 +238,7 @@ def test_random_unweighted_maxcut(self, max_vars_per_qubit): graph = nx.random_regular_graph(3, 8) maxcut = Maxcut(graph) problem = maxcut.to_quadratic_program() - check_problem_commutation(problem, max_vars_per_qubit) + self.check_problem_commutation(problem, max_vars_per_qubit) @data(1, 2, 3) def test_random_weighted_maxcut(self, max_vars_per_qubit): @@ -242,16 +248,7 @@ def test_random_weighted_maxcut(self, max_vars_per_qubit): graph[w][v]["weight"] = np.random.randint(1, 10) maxcut = Maxcut(graph) problem = maxcut.to_quadratic_program() - check_problem_commutation(problem, max_vars_per_qubit) - - -def check_problem_commutation(problem: QuadraticProgram, max_vars_per_qubit: int): - """Utility function to check that the problem commutes with its encoding""" - encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=max_vars_per_qubit) - encoding.encode(problem) - verifier = EncodingCommutationVerifier(encoding) - assert len(verifier) == 2**encoding.num_vars - assert all(np.isclose(obj_val, encoded_obj_val) for _, obj_val, encoded_obj_val in verifier) + self.check_problem_commutation(problem, max_vars_per_qubit) if __name__ == "__main__": diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py index d97116189..8bf8cc4d6 100644 --- a/test/algorithms/qrao/test_quantum_random_access_optimizer.py +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -33,7 +33,7 @@ QuantumRandomAccessOptimizationResult, QuantumRandomAccessOptimizer, RoundingContext, - SemideterministicRoundingResult, + RoundingResult, ) from qiskit_optimization.problems import QuadraticProgram @@ -166,7 +166,7 @@ def test_solve_numpy(self): self.assertAlmostEqual( results.relaxed_result.aux_operators_evaluated[2][0], 0.80178, places=5 ) - self.assertIsInstance(results.rounding_result, SemideterministicRoundingResult) + self.assertIsInstance(results.rounding_result, RoundingResult) self.assertAlmostEqual(results.rounding_result.expectation_values[0], 0.26726, places=5) self.assertAlmostEqual(results.rounding_result.expectation_values[1], 0.53452, places=5) self.assertAlmostEqual(results.rounding_result.expectation_values[2], 0.80178, places=5) diff --git a/test/algorithms/qrao/test_semideterministic_rounding.py b/test/algorithms/qrao/test_semideterministic_rounding.py index 7c5967274..80c609ca8 100644 --- a/test/algorithms/qrao/test_semideterministic_rounding.py +++ b/test/algorithms/qrao/test_semideterministic_rounding.py @@ -19,7 +19,7 @@ from qiskit_optimization.algorithms.qrao import ( QuantumRandomAccessEncoding, SemideterministicRounding, - SemideterministicRoundingResult, + RoundingResult, RoundingContext, ) from qiskit_optimization.algorithms import SolutionSample @@ -44,10 +44,10 @@ def test_semideterministic_rounding(self): result = rounding_scheme.round( RoundingContext(expectation_values=expectation_values, encoding=encoding) ) - self.assertIsInstance(result, SemideterministicRoundingResult) + self.assertIsInstance(result, RoundingResult) self.assertIsInstance(result.samples[0], SolutionSample) self.assertEqual(result.expectation_values, [1, -1, 0, 0.7, -0.3]) - np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 0, 0, 1]) + np.testing.assert_array_almost_equal(result.samples[0].x, [0, 1, 1, 0, 1]) self.assertEqual(result.samples[0].probability, 1.0) From d7513bb497493dd5665121a5f6ba504851779f86 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 18 May 2023 19:32:42 +0900 Subject: [PATCH 21/67] add explanations and reflect comments --- .../aux_files/magic_state_rounding.svg | 658 ++++++++++++++++++ docs/explanations/qraco_explanations.rst | 370 ++++++++++ qiskit_optimization/algorithms/__init__.py | 10 + .../algorithms/optimization_algorithm.py | 29 +- .../algorithms/qrao/__init__.py | 76 +- .../qrao/quantum_random_access_encoding.py | 2 - .../qrao/quantum_random_access_optimizer.py | 24 +- releasenotes/notes/qrao-89d5ff1d2927de64.yaml | 4 +- test/algorithms/qrao/test_magic_rounding.py | 50 +- .../test_quantum_random_access_encoding.py | 24 +- 10 files changed, 1176 insertions(+), 71 deletions(-) create mode 100644 docs/explanations/aux_files/magic_state_rounding.svg create mode 100644 docs/explanations/qraco_explanations.rst diff --git a/docs/explanations/aux_files/magic_state_rounding.svg b/docs/explanations/aux_files/magic_state_rounding.svg new file mode 100644 index 000000000..806fcf8ef --- /dev/null +++ b/docs/explanations/aux_files/magic_state_rounding.svg @@ -0,0 +1,658 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/docs/explanations/qraco_explanations.rst b/docs/explanations/qraco_explanations.rst new file mode 100644 index 000000000..de854971f --- /dev/null +++ b/docs/explanations/qraco_explanations.rst @@ -0,0 +1,370 @@ +Background on Quantum Random Access Optimization: *Quantum relaxations, quantum random access codes, rounding schemes* +====================================================================================================================== + +This material provides a deeper look into the concepts behind Quantum +Random Access Optimization. + +Relaxations +----------- + +Consider a binary optimization problem defined on binary variables +:math:`m_i \in \\{-1,1\\}`. The choice of using :math:`\pm 1` variables +instead of :math:`0/1` variables is not important, but will be +notationally convenient for us when we begin to re-cast this problem in +terms of quantum observables. We will be primarily interested in +`quadratic unconstrained binary optimization +(QUBO) `__ +problems, although the ideas in this document can readily extend to +problems with more than quadratic terms, and problems with non-binary or +constrained variables can often be recast as a QUBO (though this +conversion will incur some overhead). + +Within mathematical optimization, +`relaxation `__ +is the strategy of taking some hard problem and mapping it onto a +similar version of that problem which is (usually) easier to solve. The +core idea here is that for useful relaxations, the solution to the +relaxed problem can give information about the original problem and +allow one to heuristically find better solutions. An example of +relaxation could be something as simple as taking a discrete +optimization problem and allowing a solver to optimize the problem using +continuous variables. Once a solution is obtained for the relaxed +problem, the solver must find a strategy for extracting a discrete +solution from the relaxed solution of continuous values. This process of +mapping the relaxed solution back onto original problem’s set of +admissable solutions is often referred to as **rounding**. + +For a concrete example of relaxation and rounding, see the +`Goemans-Williamson Algorithm for +MaxCut `__. + +Without loss of generality, the rest of this document will consider a +`MaxCut `__ objective +function defined on a graph :math:`G = (V,E)`. Our goal is to find a +partitioning of our vertices :math:`V` into two sets (:math:`+1` and +:math:`-1`), such that we maximize the number of edges which connect +both sets. More concretely, each :math:`v_i \in V` will be assigned a +binary variable :math:`m_i \in \\{0,1\\}`, and we will define the *cut* +of a variable assignment as: + +.. math:: \text{cut}(m) = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-m_i m_j) + +Quantum Relaxation +------------------ + +Our goal is to define a relaxation of our MaxCut objective function. We +will do this by mapping our objective function’s binary variables into +the space of single qubit Pauli observables and by embedding the set of +feasible inputs to cut(:math:`m`) onto the space of single-qubit quantum +product states. Let us denote this embedding :math:`F` as: + +.. math:: F: \\{-1,1\\}^{M} \mapsto \mathcal{D}(\mathbb{C}^{2^n}), + +.. math:: \text{cut}(m) \mapsto \text{Tr}\big(H\cdot F(m)\big), + +where :math:`M = |V|`, and :math:`H` is a quantum Hamiltonian which +encodes our objective function. + +For this to be `a valid +relaxation `__ +of our problem, it must be the case that: + +.. math:: \text{cut}(m) \geq \text{Tr}\big(H\cdot F(m)\big)\qquad \forall m \in \\{-1,1\\}^M. + +In order to guarantee this is true, we will enforce the stronger +condition that our relaxation **commutes** with our objective function. +In other words, cut(:math:`m`) is equal to the relaxed objective +function for all :math:`m \in \\{-1,1\\}^M`, rather than simply upper +bounding it. This detail will become crucially important further down +when we explicitly define our quantum relaxation. + +A Simple Quantum Relaxation +--------------------------- + +Before explicating the full quantum relaxation scheme based on +single-qubit Quantum Random Access Codes (QRACs), it may be helpful to +first discuss `a version of quantum +optimization `__ +which users may be more familiar with, but discussed in the language of +quantum relaxation and rounding. + +Consider the embedding + +.. math:: F^{(1)}: m \in \\{-1,1\\}^M \mapsto \\{|0\rangle,|1\rangle\\}^{\otimes M}, + +.. math:: \text{cut}(m) \mapsto \text{Tr}\big(H^{(1)}F^{(1)}(m)\big),\quad H^{(1)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-Z_i Z_j), + +where :math:`Z_i` indicates the single qubit Pauli-Z observable defined +on the :math:`i`\ ’th qubit and Identity terms on all other qubits. It +is worth convincing yourself that this transformation is a valid +relaxation of our problem. In particular: + +.. math:: \text{cut}(m) = \text{Tr}\big(H^{(1)}F^{(1)}(m)\big) \quad \forall m \in \\{-1,1\\}^M + +This sort of embedding is currently used by many near-term quantum +optimization algorithms, including many `QAOA and VQE based +approaches `__. +Observe how although the relaxed version of our problem can exactly +reproduce the objective function cut(:math:`m`) for inputs of the form +:math:`\\{|0\rangle,|1\rangle\\}^{\otimes M}`, we are also free to +evaluate :math:`H^{(1)}` using a continuous superposition of such +states. This stands in analogy to how one might classically relax an +optimization problem such that they optimize the objective function +using continuous values. + +Crucially, a relaxation is only useful if there is some practical way to +**round** relaxed solutions back onto the original problem’s set of +admissable solutions. For this particular quantum relaxation, the +rounding scheme is simply given by measuring each qubit of our relaxed +solution in the :math:`Z`-basis. Measurement will project any quantum +state onto the set of computational basis states, and consequently, onto +the image of :math:`F^{(1)}`. + +Quantum Relaxations via Quantum Random Access Codes (QRACs) +----------------------------------------------------------- + +Quantum Random Access Codes were `first outlined in 1983 by Stephen +Wiesner +[2] `__ +and were used in the context of communication complexity theory. We will +not be using QRACs in the way they were originally concieved, instead we +are co-opting them to define our quantum relaxations. For this reason +will not provide a full introduction to RACs or QRACs, but encourage +interested readers to seek out more information about them. + +:math:`(1,1,1)`, :math:`(2,1,p)`, and :math:`(3,1,p)` Quantum Random Access Codes +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A :math:`(k,1,p)`-QRAC, is a scheme for embedding :math:`k` classical +bits into a 1-qubit state, such that given a single copy of this state, +you can recover any one of the :math:`k`-bits with probability :math:`p` +by performing some measurement. The simple quantum relaxation discussed +in the previous section is an example of a trivial :math:`(1,1,1)`-QRAC. +For convenience, we will write the :math:`(2,1,0.854)` and +:math:`(3,1,0.789)` QRACs as :math:`(2,1,p)` and :math:`(3,1,p)`, +respectively. + +As we generalize the simple example above, it will be helpful to write +out single qubit states decomposed in the Hermitian basis of Pauli +observables. + +.. math:: \rho = \frac{1}{2}\left(I + aX + bY + cZ \right),\quad |a|^2 + |b|^2 + |c|^2 = 1 + +The embeddings :math:`F^{(1)}`, :math:`F^{(2)}`, and :math:`F^{(3)}` +associated respectively with the :math:`(1,1,1), (2,1,p),` and +:math:`(3,1,p)` QRACs can now be written as follows: + +.. math:: + + \begin{array}{l|ll} \text{QRAC} & &\text{Embedding into } \rho = \vert \psi(m)\rangle\langle\psi(m)\vert \\ + \hline + (1,1,1)\qquad &F^{(1)}(m): \\{-1,1\\} &\mapsto\ \vert\psi^{(1)}_m\rangle \langle\psi^{(1)}_m\vert = \frac{1}{2}\Big(I + {m_0}Z \Big) \\ + (2,1,p)\qquad &F^{(2)}(m): \\{-1,1\\}^2 &\mapsto\ \vert\psi^{(2)}_m\rangle \langle\psi^{(2)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{2}}\big({m_0}X+ {m_1}Z \big)\right) \\ + (3,1,p)\qquad &F^{(3)}(m): \\{-1,1\\}^3 &\mapsto\ \vert\psi^{(3)}_m\rangle \langle\psi^{(3)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{3}}\big({m_0}X+ {m_1}Y + {m_2}Z\big)\right) \\ \end{array} + +  + +.. math:: \text{Table 1: Explicit QRAC States} + +Note that for when using a :math:`(k,1,p)`-QRAC with bistrings +:math:`m \in \\{-1,1\\}^M, M > k`, these embeddings scale naturally via +composition by tensor product. + +.. math:: m \in \\{-1,1\\}^6,\quad F^{(3)}(m) = F^{(3)}(m_0,m_1,m_2)\otimes F^{(3)}(m_3,m_4,m_5) + +Similarly, when :math:`k \nmid M`, we can simply pad our input bitstring +with the appropriate number of :math:`+1` values. + +.. math:: m \in \\{-1,1\\}^4,\quad F^{(3)}(m) = F^{(3)}(m_0,m_1,m_2)\otimes F^{(3)}(m_3,+1,+1) + +Recovering Encoded Bits +~~~~~~~~~~~~~~~~~~~~~~~ + +Given a QRAC state, we can recover the values of the encoded bits by +estimating the expectation value of each bit’s corresponding observable. +Note that there is a rescaling factor which depends on the density of +the QRAC. + +.. math:: + + \begin{array}{ll|l|l} + & \text{Embedding} & m_0 = & m_1 = & m_2 = &\\ + \hline + &\rho = F^{(1)}(m_0) &\text{Tr}\big(\rho Z\big) & & \\ + &\rho = F^{(2)}(m_0,m_1) &\sqrt{2}\cdot\text{Tr}\big(\rho X\big) &\sqrt{2}\cdot\text{Tr}\big(\rho Z\big) & \\ + &\rho = F^{(3)}(m_0,m_1,m_2) & \sqrt{3}\cdot\text{Tr}\big(\rho X\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Y\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Z\big) + \end{array} + +  + +.. math:: \text{Table 2: Bit recovery from QRAC States} + +Encoded Problem Hamiltonians +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Using the tools we have outlined above, we can explicitly write out the +Hamiltonians which encode the relaxed versions of our MaxCut problem. We +do this by substituting each decision variable with the unique +observable that has been assigned to that variable under the embedding +:math:`F`. + +.. math:: + + \begin{array}{l|ll} \text{QRAC} & \text{Problem Hamiltonian}\\ + \hline + (1,1,1)\qquad &H^{(1)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-Z_i Z_j)\\ + (2,1,p)\qquad &H^{(2)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-2\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \\{X,Z\\}\\ + (3,1,p)\qquad &H^{(3)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-3\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \\{X,Y,Z\\}\\ \end{array} + +  + +.. math:: \text{Table 3: Relaxed MaxCut Hamiltonians after QRAC Embedding} + +Note that here, :math:`P_{[i]}` indicates a single-qubit Pauli +observable corresponding to decision variable :math:`i`. The bracketed +index here is to make clear that :math:`P_{[i]}` will not necessarily be +defined on qubit :math:`i`, because the :math:`(2,1,p)` and +:math:`(3,1,p)` no longer have a 1:1 relationship between qubits and +decision variables. + +Commutation of Quantum Relaxation +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Note that for the :math:`(2,1,p)` and :math:`(3,1,p)` QRACs, we are +associating multiple decision variables to each qubit. This means that +each decision variable is assigned a *unique* single-qubit Pauli +observable and some subsets of these Pauli observables will be defined +on the same qubits. This can potentially pose a problem when trying to +ensure the commutativity condition discussed earlier + +Observe that under the :math:`(3,1,p)`-QRAC, any term in our objective +function of the form :math:`(1 - x_i x_j)` will map to a Hamiltonian +term of the form :math:`(1-3\cdot P_{[i]} P_{[j]})`. If both +:math:`P_{[i]}` and :math:`P_{[j]}` are defined on different qubits, +then :math:`P_{[i]}\cdot P_{[j]} = P_{[i]}\otimes P_{[j]}` and this term +of our Hamiltonian will behave as we expect. + +If however, :math:`P_{[i]}` and :math:`P_{[j]}` are defined on the same +qubit, the two Paulis will compose directly. Recall that the Pauli +matrices form a group and are self-inverse, thus we can deduce that the +product of two distinct Paulis will yield another element of the group +and it will not be the identity. + +Practically, this means that our commutation relationship will break and +:math:`\text{cut}(m) \not= \text{Tr}\big(H^{(1)}F^{(3)}(m)\big)` + +In order to restore the commutation of our encoding with our objective +function, we must introduce an additional constraint on the form of our +problem Hamiltonian. Specifically, we must guarantee that decision +variables which share an edge in our input graph :math:`G` are not +assigned to the same qubit under our embedding :math:`F` + +.. math:: \forall e_{ij} \in E,\quad F^{(3)}(\dots,m_i,\dots,m_j,\dots) = F^{(3)}(\dots,m_i,\dots)\otimes F^{(3)}(\dots,m_j,\dots) + +In [1] this is accomplished by finding a coloring of the graph G such +that no vertices with the same color share an edge, and then assigning +variables to the same qubit only if they have the same color. + +Quantum Rounding Schemes +------------------------ + +Because the final solution we obtain for the relaxed problem +:math:`\rho_\text{relax}` is unlikely to be in the image of :math:`F`, +we need a strategy for mapping :math:`\rho_\text{relax}` to the image of +:math:`F` so that we may extract a solution to our original problem. + +In [1] there are two strategies proposed for rounding +:math:`\rho_\text{relax}` back to :math:`m \in \\{-1,1\\}^M`. + +Semideterministic Rounding +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A natural choice for extracting a solution is to use the results of +Table :math:`2` and simply estimate +:math:`\text{Tr}(P_{[i]}\rho_\text{relax})` for all :math:`i` in order +to assign a value to each variable :math:`m_i`. The procedure described +in Table :math:`2` was intended for use on states in the image of +:math:`F`, however, we are now applying it to arbitrary input states. +The practical consequence is we will no longer measure a value close to +{:math:`\pm 1`}, {:math:`\pm \sqrt{2}`}, or {:math:`\pm \sqrt{3}`}, as +we would expect for the :math:`(1,1,1)`, :math:`(2,1,p)`, and +:math:`(3,1,p)` QRACs, respectively. + +We handle this by returning the sign of the expectation value, leading +to the following rounding scheme. + +.. math:: + + m_i = \left\\{\begin{array}{rl} + +1 & \text{Tr}(P_{[i]}\rho_\text{relax}) > 0 \\ + X \sim\\{-1,1\\} & \text{Tr}(P_{[i]}\rho_\text{relax}) = 0 \\ + -1 & \text{Tr}(P_{[i]}\rho_\text{relax}) < 0 + \end{array}\right. + +Where :math:`X` is a random variable which returns either -1 or 1 with +equal probability. + +Notice that Semideterministic rounding will faithfully recover :math:`m` +from :math:`F(m)` with a failure probability that decreases +exponentially with the number of shots used to estimate each +:math:`\text{Tr}(P_{[i]}\rho_\text{relax})` + +Magic State Rounding +~~~~~~~~~~~~~~~~~~~~ + +.. figure:: aux_files/magic_state_rounding.svg + :align: center + :width: 100% + + Figure 1: Three different encodings, the states and the measurement bases, of variables into a + single qubit. (a) One variable per qubit. (b) Two variables per qubit. (c) Three variables per + qubit. Taken from `[1] `__. + +Rather than seeking to independently distinguish each :math:`m_i`, magic +state rounding randomly selects a measurement basis which will perfectly +distinguish a particular pair of orthogonal QRAC states +:math:`\\{ F(m), F(\bar m)\\}`, where :math:`\bar m` indicates that +every bit of :math:`m` has been flipped. + +Let :math:`\mathcal{M}` be the randomized rounding procedure which takes +as input a state :math:`\rho_\text{relax}` and samples a bitstring +:math:`m` by measuring in a randomly selected magic-basis. + +.. math:: \mathcal{M}^{\otimes n}(\rho_\text{relax}) \rightarrow F(m) + +First, notice that for the :math:`(1,1,1)`-QRAC, there is only one basis +to choose and the magic state rounding scheme is essentially equivalent +to the semideterministic rounding scheme. + +For the :math:`(2,1,p)` and :math:`(3,1,p)` QRACs, if we apply the magic +state rounding scheme to an :math:`n`-qubit QRAC state :math:`F(m)`, we +will have a :math:`2^{-n}` and :math:`4^{-n}` probability of picking the +correct basis on each qubit to perfectly extract the solution :math:`m`. +Put differently, if we are given an unknown state :math:`F(m)` the +probability that :math:`\mathcal{M}^{\otimes n}(F(m))\mapsto F(m)` +decreases exponentially with the number of qubits measured – it is far +more likely to be mapped to some other :math:`F(m^*)`. Similarly, when +we perform magic rounding on an arbitrary state +:math:`\rho_\text{relax}`, we have similarly low odds of randomly +choosing the optimal magic basis for all :math:`n`-qubits. Fortunately +magic state rounding does offer a lower bound on the approximation ratio +under certain conditions. + +Let :math:`F(m^*)` be the highest energy state in the image of F, and +let :math:`\rho^\*` be the maximal eigenstate of H. + +.. math:: \forall \rho_\text{relax}\quad \text{st}\quad \text{Tr}\left(F(m^*)\cdot H\right) \leq \text{Tr}\left(\rho_\text{relax}\cdot H\right)\leq \text{Tr}\left(\rho^*\cdot H\right) + +.. math:: \frac{\text{expected fval}}{\text{optimal fval}} = \frac{\mathbb{E}\left[\text{Tr}\left(H\cdot \mathcal{M}^{\otimes n}(\rho_\text{relax})\right)\right]}{\text{Tr}\left(H\cdot F(m^*)\right)} \geq \frac{5}{9} + +References +---------- + +[1] B. Fuller, C. Hadfield, J. R. Glick, T. Imamichi, T. Itoko, R. J. +Thompson, Y. Jiao, M. M. Kagele, A. W. Blom-Schieber, R. Raymond, and A. +Mezzacapo, “Approximate solutions of combinatorial problems via quantum +relaxations,” (2021), `arXiv:2111.03167 `__, + +[2] Stephen Wiesner, “Conjugate coding,” SIGACT News, vol. 15, issue 1, +pp. 78–88, 1983. +`link `__ diff --git a/qiskit_optimization/algorithms/__init__.py b/qiskit_optimization/algorithms/__init__.py index c4ab6b0e8..63c35edb9 100644 --- a/qiskit_optimization/algorithms/__init__.py +++ b/qiskit_optimization/algorithms/__init__.py @@ -53,6 +53,8 @@ MinimumEigenOptimizationResult MinimumEigenOptimizer OptimizationResultStatus + QuantumRandomAccessOptimizationResult + QuantumRandomAccessOptimizer RecursiveMinimumEigenOptimizationResult RecursiveMinimumEigenOptimizer ScipyMilpOptimizer @@ -89,6 +91,12 @@ OptimizationResultStatus, SolutionSample, ) + +from .qrao import ( + QuantumRandomAccessOptimizer, + QuantumRandomAccessOptimizationResult, +) + from .recursive_minimum_eigen_optimizer import ( RecursiveMinimumEigenOptimizer, RecursiveMinimumEigenOptimizationResult, @@ -123,6 +131,8 @@ "MinimumEigenOptimizer", "MinimumEigenOptimizationResult", "MultiStartOptimizer", + "QuantumRandomAccessOptimizer", + "QuantumRandomAccessOptimizationResult", "RecursiveMinimumEigenOptimizer", "RecursiveMinimumEigenOptimizationResult", "IntermediateResult", diff --git a/qiskit_optimization/algorithms/optimization_algorithm.py b/qiskit_optimization/algorithms/optimization_algorithm.py index daf383204..078b806a3 100644 --- a/qiskit_optimization/algorithms/optimization_algorithm.py +++ b/qiskit_optimization/algorithms/optimization_algorithm.py @@ -11,12 +11,13 @@ # that they have been altered from the originals. """An abstract class for optimization algorithms in Qiskit's optimization module.""" +from __future__ import annotations from abc import ABC, abstractmethod from dataclasses import dataclass from enum import Enum from logging import getLogger -from typing import Any, Dict, List, Optional, Tuple, Type, Union, cast +from typing import Any, Dict, List, Tuple, Type, Union, cast import numpy as np from qiskit.opflow import DictStateFn, StateFn @@ -99,12 +100,12 @@ class OptimizationResult: def __init__( self, - x: Optional[Union[List[float], np.ndarray]], - fval: Optional[float], + x: Union[List[float], np.ndarray] | None, + fval: float | None, variables: List[Variable], status: OptimizationResultStatus, - raw_results: Optional[Any] = None, - samples: Optional[List[SolutionSample]] = None, + raw_results: Any | None, + samples: List[SolutionSample] | None, ) -> None: """ Args: @@ -216,7 +217,7 @@ def get_correlations(self) -> np.ndarray: return correlations @property - def x(self) -> Optional[np.ndarray]: + def x(self) -> np.ndarray | None: """Returns the variable values found in the optimization or None in case of FAILURE. Returns: @@ -225,7 +226,7 @@ def x(self) -> Optional[np.ndarray]: return self._x @property - def fval(self) -> Optional[float]: + def fval(self) -> float | None: """Returns the objective function value. Returns: @@ -375,8 +376,8 @@ def _get_feasibility_status( @staticmethod def _prepare_converters( - converters: Optional[Union[QuadraticProgramConverter, List[QuadraticProgramConverter]]], - penalty: Optional[float] = None, + converters: Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] | None, + penalty: float | None, ) -> List[QuadraticProgramConverter]: """Prepare a list of converters from the input. @@ -431,7 +432,7 @@ def _convert( @staticmethod def _check_converters( - converters: Optional[Union[QuadraticProgramConverter, List[QuadraticProgramConverter]]] + converters: Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] | None, ) -> List[QuadraticProgramConverter]: if converters is None: converters = [] @@ -446,9 +447,7 @@ def _interpret( cls, x: np.ndarray, problem: QuadraticProgram, - converters: Optional[ - Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] - ] = None, + converters: Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] | None = None, result_class: Type[OptimizationResult] = OptimizationResult, **kwargs, ) -> OptimizationResult: @@ -491,9 +490,7 @@ def _interpret_samples( cls, problem: QuadraticProgram, raw_samples: List[SolutionSample], - converters: Optional[ - Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] - ] = None, + converters: QuadraticProgramConverter | list[QuadraticProgramConverter] | None = None, ) -> Tuple[List[SolutionSample], SolutionSample]: """Interpret and sort all samples and return the raw sample corresponding to the best one""" converters = cls._check_converters(converters) diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index 2fa09dbec..0e71cf2e6 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -10,12 +10,86 @@ # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. -""" +r""" Quantum Random Access Optimization (:mod:`qiskit_optimization.algorithms.qrao`) =============================================================================== .. currentmodule:: qiskit_optimization.algorithms.qrao +The Quantum Random Access Optimization (QRAO) module is designed to enable users to leverage a new +quantum method for combinatorial optimization problems [1]. This approach incorporates +Quantum Random Access Codes (QRACs) as a tool to encode multiple classical binary variables into a +single qubit, thereby saving quantum resources and enabling exploration of larger problem instances +on a quantum computer. The encodings produce a local quantum Hamiltonian whose ground state can be +approximated with standard algorithms such as VQE, and then rounded to yield approximation solutions +of the original problem. + +QRAO through a series of 3 classes: +* The encoding class (:class:`~.QuantumRandomAccessEncoding`): This class encodes the original + problem into a relaxed problem that requires fewer resources to solve. +* The rounding schemes (:class:`~.SemideterministicRounding` and :class:`~.MagicRounding`): This + scheme is used to round the solution obtained from the relaxed problem back to a solution of + the original problem. +* The optimizer class (:class:`~.QuantumRandomAccessOptimizer`): This class performs the high-level + optimization algorithm, utilizing the capabilities of the encoding class and the rounding scheme. + +:class:`~.QuantumRandomAccessOptimizer` has two methods for solving problems, +:meth:`~.QuantumRandomAccessOptimizer.solve` and +:meth:`~.QuantumRandomAccessOptimizer.solve_relaxed`. The solve method provides a seamless +workflow by automatically managing the encoding and rounding procedures, as demonstrated in the +example below. This allows for a simplified and streamlined user experience. +On the other hand, the solve_relaxed method offers the flexibility to break the computation +process into distinct steps. This feature can be advantageous when we need to compare solutions +obtained from different rounding schemes applied to a potential ground state. + + +For example: + +.. code-block:: python + + from qiskit.algorithms.optimizers import COBYLA + from qiskit.algorithms.minimum_eigensolvers import VQE + from qiskit.circuit.library import RealAmplitudes + from qiskit.primitives import Estimator + + from qiskit_optimization.algorithms.qrao import ( + QuantumRandomAccessOptimizer, + QuantumRandomAccessEncoding, + SemideterministicRounding, + ) + from qiskit_optimization.problems import QuadraticProgram + + problem = QuadraticProgram() + problem.binary_var("x") + problem.binary_var("y") + problem.binary_var("z") + problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + + ansatz = RealAmplitudes(1) + vqe = VQE( + ansatz=ansatz, + optimizer=COBYLA(), + estimator=Estimator(), + ) + # solve() automatically performs the encoding, optimization, and rounding + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe) + result = qrao.solve(problem) + + # solve_relaxed() only performs the optimization. The encoding and rounding must be done manually. + # encoding + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) + encoding.encode(problem) + # optimization + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe) + relaxed_results, rounding_context = qrao.solve_relaxed(encoding=encoding) + # rounding + rounding = SemideterministicRounding() + result = rounding.round(rounding_context) + + +[1] Bryce Fuller et al., Approximate Solutions of Combinatorial Problems via Quantum Relaxations, +`arXiv:2111.03167 `_ + Quantum Random Access Encoding and Optimization =============================================== diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 0e126c68e..faa87abaf 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -20,7 +20,6 @@ import rustworkx as rx from qiskit import QuantumCircuit -from qiskit.opflow import PauliSumOp from qiskit.quantum_info import SparsePauliOp from qiskit_optimization.exceptions import QiskitOptimizationError @@ -341,7 +340,6 @@ def freeze(self): """ if not self._frozen: self._qubit_op = self._qubit_op.simplify() - self._qubit_op = PauliSumOp(self._qubit_op) self._frozen = True @property diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 1490092a2..bffeac61b 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -111,7 +111,8 @@ def __init__( min_eigen_solver: MinimumEigensolver, max_vars_per_qubit: int = 3, rounding_scheme: RoundingScheme | None = None, - **kwargs, + *, + penalty: float | None = None, ): """ Args: @@ -119,14 +120,23 @@ def __init__( max_vars_per_qubit: The maximum number of decision variables per qubit. rounding_scheme: The rounding scheme. If ``None`` is provided, ``SemideterministicRounding()`` will be used. + penalty: The penalty factor to use for the ``QuadraticProgramToQubo`` converter. + + Raises: + ValueError: If the maximum number of variables per qubit is not 1, 2, or 3. + TypeError: If the provided minimum eigensolver does not support auxiliary operators. """ + if max_vars_per_qubit not in (1, 2, 3): + raise ValueError("max_vars_per_qubit must be 1, 2, or 3") + self._max_vars_per_qubit = max_vars_per_qubit self.min_eigen_solver = min_eigen_solver # Use ``QuadraticProgramToQubo`` to convert the problem to a QUBO. + if rounding_scheme is None: + rounding_scheme = SemideterministicRounding() + self._rounding_scheme = rounding_scheme self._converters: QuadraticProgramConverter = QuadraticProgramToQubo( - penalty=kwargs.get("penalty") + penalty=penalty, ) - self._max_vars_per_qubit = max_vars_per_qubit - self.rounding_scheme = rounding_scheme @property def min_eigen_solver(self) -> MinimumEigensolver: @@ -159,10 +169,8 @@ def rounding_scheme(self) -> RoundingScheme: return self._rounding_scheme @rounding_scheme.setter - def rounding_scheme(self, rounding_scheme: RoundingScheme | None) -> None: + def rounding_scheme(self, rounding_scheme: RoundingScheme) -> None: """Set the rounding scheme.""" - if rounding_scheme is None: - rounding_scheme = SemideterministicRounding() self._rounding_scheme = rounding_scheme def get_compatibility_msg(self, problem: QuadraticProgram) -> str: @@ -256,7 +264,7 @@ def solve(self, problem: QuadraticProgram) -> QuantumRandomAccessOptimizationRes encoding.encode(qubo) # Solve the relaxed problem - (relaxed_result, rounding_context) = self.solve_relaxed(encoding) + relaxed_result, rounding_context = self.solve_relaxed(encoding) # Round the solution rounding_result = self.rounding_scheme.round(rounding_context) diff --git a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml index e1b297b84..7ea21ff9b 100644 --- a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml +++ b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml @@ -5,8 +5,8 @@ features: incorporates Quantum Random Access Codes (QRACs) as a tool to encode multiple classical binary variables into a single qubit, thereby saving quantum resources and enabling exploration of larger problem instances on a quantum computer. The encodings produce a local quantum - Hamiltonian whose ground state can be approximated with standard algorithms such as VQE and - QAOA, and then rounded to yield approximation solutions of the original problem. + Hamiltonian whose ground state can be approximated with standard algorithms such as VQE, + and then rounded to yield approximation solutions of the original problem. :class:`~.QuantumRandomAccessOptimizer` has two methods for solving problems, :meth:`~.QuantumRandomAccessOptimizer.solve` and diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 0628d984f..1efc36c13 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -70,25 +70,25 @@ def test_magic_rounding_round_uniform(self): rounding_result = magic_rounding.round(rounding_context) self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) - np.testing.assert_allclose(rounding_result.basis_shots, [2536, 2486, 2477, 2501]) + np.testing.assert_allclose(rounding_result.basis_shots, [2534, 2527, 2486, 2453]) expected_basis_counts = [ - {"0": 2436.0, "1": 100.0}, - {"0": 461.0, "1": 2025.0}, - {"0": 831.0, "1": 1646.0}, - {"0": 1259.0, "1": 1242.0}, + {"0": 2434.0, "1": 100.0}, + {"0": 469.0, "1": 2058.0}, + {"0": 833.0, "1": 1653.0}, + {"0": 1234.0, "1": 1219.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ - make_solution_sample(x=np.array([0, 0, 0]), probability=0.2436, problem=self.problem), - make_solution_sample(x=np.array([0, 0, 1]), probability=0.1242, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 0]), probability=0.1646, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 1]), probability=0.0461, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 0]), probability=0.2025, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 1]), probability=0.0831, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 0]), probability=0.1259, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 0]), probability=0.2434, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.1219, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1653, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0469, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.2058, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0833, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.1234, problem=self.problem), make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), ] for i, sample in enumerate(samples): @@ -110,26 +110,26 @@ def test_magic_rounding_round_weighted(self): rounding_result = magic_rounding.round(rounding_context) self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) - np.testing.assert_allclose(rounding_result.basis_shots, [4542, 2703, 1559, 1196]) + np.testing.assert_allclose(rounding_result.basis_shots, [4499, 2700, 1574, 1227]) expected_basis_counts = [ - {"0": 4393.0, "1": 149.0}, - {"0": 501.0, "1": 2202.0}, - {"0": 523.0, "1": 1036.0}, - {"0": 583.0, "1": 613.0}, + {"0": 4352.0, "1": 147.0}, + {"0": 500.0, "1": 2200.0}, + {"0": 528.0, "1": 1046.0}, + {"0": 597.0, "1": 630.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ - make_solution_sample(x=np.array([0, 0, 0]), probability=0.4393, problem=self.problem), - make_solution_sample(x=np.array([0, 0, 1]), probability=0.0613, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 0]), probability=0.1036, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 1]), probability=0.0501, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 0]), probability=0.2202, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 1]), probability=0.0523, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 0]), probability=0.0583, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 1]), probability=0.0149, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 0]), probability=0.4352, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.063, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1046, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.05, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.22, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0528, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.0597, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.0147, problem=self.problem), ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index a4eb06df2..2f4c36148 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -47,11 +47,8 @@ def test_31p_qrac_encoding(self): encoding = QuantumRandomAccessEncoding(3) self.assertFalse(encoding.frozen) # frozen is False encoding.encode(self.problem) - expected_op = PauliSumOp( - SparsePauliOp( - ["X", "Y", "Z"], coeffs=[-np.sqrt(3) / 2, 2 * -np.sqrt(3) / 2, 3 * -np.sqrt(3) / 2] - ), - coeff=1.0, + expected_op = SparsePauliOp( + ["X", "Y", "Z"], coeffs=[-np.sqrt(3) / 2, 2 * -np.sqrt(3) / 2, 3 * -np.sqrt(3) / 2] ) self.assertTrue(encoding.frozen) # frozen is True @@ -78,14 +75,10 @@ def test_21p_qrac_encoding(self): encoding = QuantumRandomAccessEncoding(2) self.assertFalse(encoding.frozen) # frozen is False encoding.encode(self.problem) - expected_op = PauliSumOp( - SparsePauliOp( - ["XI", "ZI", "IX"], - coeffs=[-np.sqrt(2) / 2, 2 * -np.sqrt(2) / 2, 3 * -np.sqrt(2) / 2], - ), - coeff=1.0, + expected_op = SparsePauliOp( + ["XI", "ZI", "IX"], + coeffs=[-np.sqrt(2) / 2, 2 * -np.sqrt(2) / 2, 3 * -np.sqrt(2) / 2], ) - self.assertTrue(encoding.frozen) # frozen is True self.assertEqual(encoding.qubit_op, expected_op) self.assertEqual(encoding.num_vars, 3) @@ -110,10 +103,7 @@ def test_11p_qrac_encoding(self): encoding = QuantumRandomAccessEncoding(1) self.assertFalse(encoding.frozen) # frozen is False encoding.encode(self.problem) - expected_op = PauliSumOp( - SparsePauliOp(["ZII", "IZI", "IIZ"], coeffs=[-0.5, -1.0, -1.5]), - coeff=1.0, - ) + expected_op = SparsePauliOp(["ZII", "IZI", "IIZ"], coeffs=[-0.5, -1.0, -1.5]) self.assertTrue(encoding.frozen) # frozen is True self.assertEqual(encoding.qubit_op, expected_op) @@ -184,7 +174,7 @@ def check_problem_commutation(self, problem: QuadraticProgram, max_vars_per_qubi verifier = EncodingCommutationVerifier(encoding) self.assertEqual(len(verifier), 2**encoding.num_vars) for _, obj_val, encoded_obj_val in verifier: - np.testing.assert_allclose(obj_val, encoded_obj_val) + np.testing.assert_allclose(obj_val, encoded_obj_val, atol=1e-5) def test_encoding_commutation_verifier(self): """Test EncodingCommutationVerifier""" From 558ee282e9e03379c04a17fb114b40ac282aebe8 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 19 May 2023 14:01:58 +0900 Subject: [PATCH 22/67] update codes --- .../13_quantum_random_access_optimizer.ipynb | 80 ++++++++----------- qiskit_optimization/algorithms/__init__.py | 18 ++--- .../algorithms/optimization_algorithm.py | 6 +- .../qrao/quantum_random_access_optimizer.py | 2 +- 4 files changed, 46 insertions(+), 60 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 848f16c67..82bfaad53 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -139,15 +139,9 @@ "output_type": "stream", "text": [ "Our encoded Hamiltonian is:\n", - "( 1.4999999999999998 * XX\n", - "+ 1.4999999999999998 * XY\n", - "+ 1.4999999999999998 * XZ\n", - "+ 1.4999999999999998 * YX\n", - "+ 1.4999999999999998 * ZX\n", - "+ 1.4999999999999998 * YY\n", - "+ 1.4999999999999998 * YZ\n", - "+ 1.4999999999999998 * ZY\n", - "+ 1.4999999999999998 * ZZ ).\n", + "( SparsePauliOp(['XX', 'XY', 'XZ', 'YX', 'ZX', 'YY', 'YZ', 'ZY', 'ZZ'],\n", + " coeffs=[1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j,\n", + " 1.5+0.j]) ).\n", "\n", "We achieve a compression ratio of (6 binary variables : 2 qubits) ≈ 3.0.\n", "\n" @@ -245,8 +239,8 @@ "output_type": "stream", "text": [ "The objective function value: 4.0\n", - "x: [1 0 0 0 1 0]\n", - "relaxed function value: 8.999999982036968\n", + "x: [0 1 0 0 0 1]\n", + "relaxed function value: 8.999999970637111\n", "\n" ] } @@ -285,7 +279,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [1 2 3 5] and nodes [0 4].\n" + "The obtained solution places a partition between nodes [0 2 3 4] and nodes [1 5].\n" ] } ], @@ -321,7 +315,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -351,7 +345,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([1, 0, 0, 0, 1, 0]), fval=4.0, probability=1.0, status=)]" + "[SolutionSample(x=array([0, 1, 0, 0, 0, 1]), fval=4.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -437,10 +431,10 @@ "Magic rounding is a quantum technique employed to map the ground state results of our encoded Hamiltonian back to a solution of the original problem. Unlike semideterministic rounding, magic rounding requires a quantum backend, which can be either hardware or a simulator. \n", "The backend is passed to the MagicRounding class through a `Sampler`, which also determines the total number of shots (samples) that magic rounding will utilize. Note that to specify the backend, you need to choose a `Sampler` from providers such as Aer or IBM Runtime. Consequently, we need to specify `Estimator` and `Sampler` for the optimizer and the rounding scheme, respectively.\n", "\n", - "In practice, users may choose to set a significantly higher number of magic rounding shots compared to the shots used by the minimum eigensolver for the relaxed problem. This difference arises because the minimum eigensolver estimates expectation values, while the magic rounding scheme returns the sample corresponding to the maximum function value found. When estimating an expectation value, increasing the number of shots enhances the convergence to the true value. However, when aiming to identify the largest possible function value, we often sample from the tail of a distribution of outcomes. As a result, until we observe the highest value outcome in our distribution, each additional shot increases the expected return value.\n", + "In practice, users may choose to set a significantly higher number of magic rounding shots compared to the shots used by the minimum eigensolver for the relaxed problem. This difference arises because the minimum eigensolver estimates expectation values, while the magic rounding scheme returns the sample corresponding to the maximum function value found. The number of magic rounding shots directly impacts the diversity of the computational basis we can generate.\n", + "When estimating an expectation value, increasing the number of shots enhances the convergence to the true value. However, when aiming to identify the largest possible function value, we often sample from the tail of a distribution of outcomes. As a result, until we observe the highest value outcome in our distribution, each additional shot increases the expected return value.\n", "\n", - "\n", - "In this tutorial, we use the `Estimator` and `Sampler` for solving the relaxed Hamiltonian and for performing magic rounding, respectively." + "In this tutorial, we use the `Estimator` for solving the relaxed Hamiltonian and the `Sampler` for performing magic rounding. Here, 10 times as many shots are used in the `Sampler`. As the number of qubits increases, you may need more shots or `weighted` basis sampling, as explained above.\"" ] }, { @@ -486,7 +480,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.9999905487688\n", + "relaxed function value: 8.99999412427944\n", "\n" ] } @@ -520,16 +514,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0085, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0102, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0207, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0217, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0225, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0207, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0201, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0211, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0202, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0212, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0088, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0106, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0202, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0212, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0201, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0211, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0196, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0206, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.020200000000000003, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0213, status=)\n" ] } ], @@ -590,7 +584,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -599,7 +593,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.99999314524776\n", + "relaxed function value: -8.999995916913132\n", "The number of distinct samples is 1.\n" ] } @@ -622,7 +616,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -631,7 +625,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.99999314524776\n", + "relaxed function value: -8.999995916913132\n", "The number of distinct samples is 56.\n" ] } @@ -665,7 +659,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -730,7 +724,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -739,15 +733,9 @@ "text": [ "Encoded Problem:\n", "=================\n", - "1.4999999999999998 * XX\n", - "+ 1.4999999999999998 * XY\n", - "+ 1.4999999999999998 * XZ\n", - "+ 1.4999999999999998 * YX\n", - "+ 1.4999999999999998 * ZX\n", - "+ 1.4999999999999998 * YY\n", - "+ 1.4999999999999998 * YZ\n", - "+ 1.4999999999999998 * ZY\n", - "+ 1.4999999999999998 * ZZ\n", + "SparsePauliOp(['XX', 'XY', 'XZ', 'YX', 'ZX', 'YY', 'YZ', 'ZY', 'ZZ'],\n", + " coeffs=[1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j, 1.5+0.j,\n", + " 1.5+0.j])\n", "Offset = -4.5\n", "Variables encoded on each qubit: [[0, 2, 5], [1, 3, 4]]\n" ] @@ -773,7 +761,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ @@ -799,7 +787,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 20, "metadata": { "scrolled": false }, @@ -807,7 +795,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed May 17 19:39:55 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Fri May 19 14:00:37 2023 JST
" ], "text/plain": [ "" diff --git a/qiskit_optimization/algorithms/__init__.py b/qiskit_optimization/algorithms/__init__.py index 63c35edb9..515dd1518 100644 --- a/qiskit_optimization/algorithms/__init__.py +++ b/qiskit_optimization/algorithms/__init__.py @@ -53,8 +53,6 @@ MinimumEigenOptimizationResult MinimumEigenOptimizer OptimizationResultStatus - QuantumRandomAccessOptimizationResult - QuantumRandomAccessOptimizer RecursiveMinimumEigenOptimizationResult RecursiveMinimumEigenOptimizer ScipyMilpOptimizer @@ -64,6 +62,14 @@ WarmStartQAOAOptimizer WarmStartQAOAFactory +Submodules +========== + +.. autosummary:: + :toctree: + + qrao + """ from .admm_optimizer import ( @@ -91,12 +97,6 @@ OptimizationResultStatus, SolutionSample, ) - -from .qrao import ( - QuantumRandomAccessOptimizer, - QuantumRandomAccessOptimizationResult, -) - from .recursive_minimum_eigen_optimizer import ( RecursiveMinimumEigenOptimizer, RecursiveMinimumEigenOptimizationResult, @@ -131,8 +131,6 @@ "MinimumEigenOptimizer", "MinimumEigenOptimizationResult", "MultiStartOptimizer", - "QuantumRandomAccessOptimizer", - "QuantumRandomAccessOptimizationResult", "RecursiveMinimumEigenOptimizer", "RecursiveMinimumEigenOptimizationResult", "IntermediateResult", diff --git a/qiskit_optimization/algorithms/optimization_algorithm.py b/qiskit_optimization/algorithms/optimization_algorithm.py index 078b806a3..f2fdd7e09 100644 --- a/qiskit_optimization/algorithms/optimization_algorithm.py +++ b/qiskit_optimization/algorithms/optimization_algorithm.py @@ -104,8 +104,8 @@ def __init__( fval: float | None, variables: List[Variable], status: OptimizationResultStatus, - raw_results: Any | None, - samples: List[SolutionSample] | None, + raw_results: Any | None = None, + samples: List[SolutionSample] | None = None, ) -> None: """ Args: @@ -377,7 +377,7 @@ def _get_feasibility_status( @staticmethod def _prepare_converters( converters: Union[QuadraticProgramConverter, List[QuadraticProgramConverter]] | None, - penalty: float | None, + penalty: float | None = None, ) -> List[QuadraticProgramConverter]: """Prepare a list of converters from the input. diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index bffeac61b..de28d8881 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -127,7 +127,7 @@ def __init__( TypeError: If the provided minimum eigensolver does not support auxiliary operators. """ if max_vars_per_qubit not in (1, 2, 3): - raise ValueError("max_vars_per_qubit must be 1, 2, or 3") + raise ValueError("max_vars_per_qubit must be 1, 2, or 3, but was {max_vars_per_qubit}.") self._max_vars_per_qubit = max_vars_per_qubit self.min_eigen_solver = min_eigen_solver # Use ``QuadraticProgramToQubo`` to convert the problem to a QUBO. From 02ec72ad49adfeb1ecea225a923e218654eb90ce Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 22 May 2023 17:53:55 +0900 Subject: [PATCH 23/67] fix Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- .pylintdict | 4 ++ docs/explanations/qraco_explanations.rst | 14 +++---- .../qrao/encoding_commutation_verifier.py | 14 ++----- .../algorithms/qrao/magic_rounding.py | 38 ++++++++++++++----- .../qrao/quantum_random_access_encoding.py | 6 +-- .../qrao/quantum_random_access_optimizer.py | 6 +-- .../test_quantum_random_access_encoding.py | 5 ++- .../test_quantum_random_access_optimizer.py | 27 +------------ 8 files changed, 52 insertions(+), 62 deletions(-) diff --git a/.pylintdict b/.pylintdict index 7b3e4cfa8..f64d61ccc 100644 --- a/.pylintdict +++ b/.pylintdict @@ -117,6 +117,8 @@ mdl milp minimizer minimumeigenoptimizer +mmp +mpm multiset mypy nannicini @@ -144,8 +146,10 @@ parikh pauli paulis peleato +pmm pooya pos +ppp pre preprint prepend diff --git a/docs/explanations/qraco_explanations.rst b/docs/explanations/qraco_explanations.rst index de854971f..46a79739d 100644 --- a/docs/explanations/qraco_explanations.rst +++ b/docs/explanations/qraco_explanations.rst @@ -162,7 +162,7 @@ associated respectively with the :math:`(1,1,1), (2,1,p),` and (2,1,p)\qquad &F^{(2)}(m): \\{-1,1\\}^2 &\mapsto\ \vert\psi^{(2)}_m\rangle \langle\psi^{(2)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{2}}\big({m_0}X+ {m_1}Z \big)\right) \\ (3,1,p)\qquad &F^{(3)}(m): \\{-1,1\\}^3 &\mapsto\ \vert\psi^{(3)}_m\rangle \langle\psi^{(3)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{3}}\big({m_0}X+ {m_1}Y + {m_2}Z\big)\right) \\ \end{array} -  + .. math:: \text{Table 1: Explicit QRAC States} @@ -195,7 +195,7 @@ the QRAC. &\rho = F^{(3)}(m_0,m_1,m_2) & \sqrt{3}\cdot\text{Tr}\big(\rho X\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Y\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Z\big) \end{array} -  + .. math:: \text{Table 2: Bit recovery from QRAC States} @@ -342,7 +342,7 @@ will have a :math:`2^{-n}` and :math:`4^{-n}` probability of picking the correct basis on each qubit to perfectly extract the solution :math:`m`. Put differently, if we are given an unknown state :math:`F(m)` the probability that :math:`\mathcal{M}^{\otimes n}(F(m))\mapsto F(m)` -decreases exponentially with the number of qubits measured – it is far +decreases exponentially with the number of qubits measured - it is far more likely to be mapped to some other :math:`F(m^*)`. Similarly, when we perform magic rounding on an arbitrary state :math:`\rho_\text{relax}`, we have similarly low odds of randomly @@ -360,11 +360,9 @@ let :math:`\rho^\*` be the maximal eigenstate of H. References ---------- -[1] B. Fuller, C. Hadfield, J. R. Glick, T. Imamichi, T. Itoko, R. J. -Thompson, Y. Jiao, M. M. Kagele, A. W. Blom-Schieber, R. Raymond, and A. -Mezzacapo, “Approximate solutions of combinatorial problems via quantum +[1] Bryce Fuller et al., “Approximate solutions of combinatorial problems via quantum relaxations,” (2021), `arXiv:2111.03167 `__, -[2] Stephen Wiesner, “Conjugate coding,” SIGACT News, vol. 15, issue 1, -pp. 78–88, 1983. +[2] Stephen Wiesner, “Conjugate coding,” SIGACT News, vol. 15, issue 1, +pp. 78-88, 1983. `link `__ diff --git a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py index b9338ee2f..dd74f0844 100644 --- a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py +++ b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py @@ -14,7 +14,7 @@ from __future__ import annotations -from qiskit.primitives import BaseEstimator, Estimator +from qiskit.primitives import BaseEstimator from qiskit_optimization.exceptions import QiskitOptimizationError @@ -24,20 +24,14 @@ class EncodingCommutationVerifier: """Class for verifying that the relaxation commutes with the objective function.""" - def __init__( - self, encoding: QuantumRandomAccessEncoding, estimator: BaseEstimator | None = None - ): + def __init__(self, encoding: QuantumRandomAccessEncoding, estimator: BaseEstimator): """ Args: encoding: The encoding to verify. - estimator: The estimator to use for the verification. If None, qiskit.primitives - Estimator will be used by default. + estimator: The estimator to use for the verification. """ self._encoding = encoding - if estimator is not None: - self._estimator = estimator - else: - self._estimator = Estimator() + self._estimator = estimator def __len__(self) -> int: return 2**self._encoding.num_vars diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 06badd91d..0b5b9cc0d 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -13,17 +13,18 @@ """Magic basis rounding module""" from __future__ import annotations -from dataclasses import dataclass - from collections import defaultdict +from dataclasses import dataclass import numpy as np from qiskit import QuantumCircuit from qiskit.algorithms.exceptions import AlgorithmError -from qiskit.primitives import Sampler +from qiskit.primitives import BaseSampler from qiskit.quantum_info import SparsePauliOp from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample +from qiskit_optimization.exceptions import QiskitOptimizationError + from .quantum_random_access_encoding import ( _z_to_21p_qrac_basis_circuit, _z_to_31p_qrac_basis_circuit, @@ -71,7 +72,7 @@ class MagicRounding(RoundingScheme): def __init__( self, - sampler: Sampler, + sampler: BaseSampler, basis_sampling: str = "uniform", seed: int | None = None, ): @@ -105,8 +106,8 @@ def __init__( super().__init__() @property - def sampler(self) -> Sampler: - """Returns the ``Sampler`` used to sample the magic bases.""" + def sampler(self) -> BaseSampler: + """Returns the Sampler used to sample the magic bases.""" return self._sampler @property @@ -169,6 +170,11 @@ def _evaluate_magic_bases( Raises: AlgorithmError: If the primitive job failed. + QiskitOptimizationError: If the number of circuits and the number of basis types are + not the same. + QiskitOptimizationError: If the number of circuits and the results from the primitive + job are not the same. + QiskitOptimizationError: If some of the results from the primitive job are not collected. """ circuits = self._make_circuits(circuit, bases, vars_per_qubit) # Execute each of the rotated circuits and collect the results @@ -177,7 +183,12 @@ def _evaluate_magic_bases( # using hardware. circuit_indices_by_shots: dict[int, list[int]] = defaultdict(list) basis_counts: list[dict[str, int] | None] = [None] * len(circuits) - assert len(circuits) == len(basis_shots) + if len(circuits) != len(basis_shots): + raise QiskitOptimizationError( + "The number of circuits and the number of basis types must be the same, " + f"{len(circuits)} != {len(basis_shots)}." + ) + for i, shots in enumerate(basis_shots): circuit_indices_by_shots[shots].append(i) @@ -187,15 +198,22 @@ def _evaluate_magic_bases( result = job.result() except Exception as exc: raise AlgorithmError( - "The primitive job to evaluate the magic state failed!" + "The primitive job to evaluate the magic state failed." ) from exc counts_list = [dist.binary_probabilities() for dist in result.quasi_dists] - assert len(indices) == len(counts_list) + if len(counts_list) != len(indices): + raise QiskitOptimizationError( + "The number of circuits and the results from the primitive job must be the same," + f"{len(indices)} != {len(counts_list)}." + ) for i, counts in zip(indices, counts_list): basis_counts[i] = counts - assert None not in basis_counts + if None in basis_counts: + raise QiskitOptimizationError( + "Some basis counts were not collected. Please check the primitive job." + ) basis_counts = [ {key: val * basis_shots[i] for key, val in counts.items()} diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index faa87abaf..1efd82415 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -451,7 +451,7 @@ def _generate_ising_coefficients( # convert linear parts of the objective function into Hamiltonian. linear = np.zeros(num_vars) for idx, coef in problem.objective.linear.to_dict().items(): - assert isinstance(idx, int) # hint for mypy + idx = int(idx) # hint for mypy weight = coef * sense / 2 linear[idx] -= weight offset += weight @@ -459,8 +459,8 @@ def _generate_ising_coefficients( # convert quadratic parts of the objective function into Hamiltonian. quad = np.zeros((num_vars, num_vars)) for (i, j), coef in problem.objective.quadratic.to_dict().items(): - assert isinstance(i, int) # hint for mypy - assert isinstance(j, int) # hint for mypy + i = int(i) # hint for mypy + j = int(j) # hint for mypy weight = coef * sense / 4 if i == j: linear[i] -= 2 * weight diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index de28d8881..6c55c3827 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -13,7 +13,7 @@ """Quantum Random Access Optimizer class.""" from __future__ import annotations -import time +import timeit from typing import cast import numpy as np @@ -213,11 +213,11 @@ def solve_relaxed( variable_ops = [encoding._term2op(i) for i in range(encoding.num_vars)] # Solve the relaxed problem - start_time_relaxed = time.time() + start_time_relaxed = timeit.default_timer() relaxed_result = self.min_eigen_solver.compute_minimum_eigenvalue( encoding.qubit_op, aux_operators=variable_ops ) - relaxed_result.time_taken = time.time() - start_time_relaxed + relaxed_result.time_taken = timeit.default_timer() - start_time_relaxed # Get auxiliary expectation values for rounding. if relaxed_result.aux_operators_evaluated is not None: diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index 2f4c36148..ded64f879 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -20,7 +20,7 @@ import networkx as nx from qiskit.circuit import QuantumCircuit -from qiskit.opflow import PauliSumOp +from qiskit.primitives import Estimator from qiskit.quantum_info import SparsePauliOp from qiskit_optimization.algorithms.qrao import ( @@ -171,7 +171,8 @@ def check_problem_commutation(self, problem: QuadraticProgram, max_vars_per_qubi """Utility function to check that the problem commutes with its encoding""" encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=max_vars_per_qubit) encoding.encode(problem) - verifier = EncodingCommutationVerifier(encoding) + estimator = Estimator() + verifier = EncodingCommutationVerifier(encoding, estimator) self.assertEqual(len(verifier), 2**encoding.num_vars) for _, obj_val, encoded_obj_val in verifier: np.testing.assert_allclose(obj_val, encoded_obj_val, atol=1e-5) diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py index 8bf8cc4d6..698ba5d5b 100644 --- a/test/algorithms/qrao/test_quantum_random_access_optimizer.py +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -22,7 +22,7 @@ VQEResult, ) from qiskit.algorithms.optimizers import COBYLA -from qiskit.circuit.library import QAOAAnsatz, RealAmplitudes +from qiskit.circuit.library import RealAmplitudes from qiskit.primitives import Estimator from qiskit.utils import algorithm_globals @@ -93,31 +93,6 @@ def test_solve_relaxed_vqe(self): self.assertAlmostEqual(rounding_context.expectation_values[1], 0, places=5) self.assertAlmostEqual(rounding_context.expectation_values[2], 0.94865, places=5) - def test_solve_relaxed_qaoa(self): - """Test QuantumRandomAccessOptimizer with QAOA.""" - qaoa_ansatz = QAOAAnsatz( - cost_operator=self.encoding.qubit_op, - ) - qaoa = VQE( - ansatz=qaoa_ansatz, - optimizer=COBYLA(), - estimator=Estimator(), - ) - qrao = QuantumRandomAccessOptimizer(min_eigen_solver=qaoa) - relaxed_results, rounding_context = qrao.solve_relaxed(encoding=self.encoding) - self.assertIsInstance(relaxed_results, VQEResult) - self.assertAlmostEqual(relaxed_results.eigenvalue, -3.24036, places=4) - self.assertEqual(len(relaxed_results.aux_operators_evaluated), 3) - self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[0][0], 0.26777, places=4) - self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[1][0], 0.53456, places=4) - self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[2][0], 0.80158, places=5) - self.assertIsInstance(rounding_context, RoundingContext) - self.assertEqual(rounding_context.circuit.num_qubits, self.ansatz.num_qubits) - self.assertEqual(rounding_context.encoding, self.encoding) - self.assertAlmostEqual(rounding_context.expectation_values[0], 0.26777, places=4) - self.assertAlmostEqual(rounding_context.expectation_values[1], 0.53456, places=4) - self.assertAlmostEqual(rounding_context.expectation_values[2], 0.80158, places=5) - def test_require_aux_operator_support(self): """Test whether the eigensolver supports auxiliary operator. If auxiliary operators are not supported, a TypeError should be raised. From da34116d842ec0f54fb12b837a7cab5e548843cf Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Tue, 23 May 2023 23:22:19 +0900 Subject: [PATCH 24/67] update the code --- ...explanations.rst => qrao_explanations.rst} | 0 .../algorithms/qrao/magic_rounding.py | 14 +++++----- .../qrao/quantum_random_access_encoding.py | 4 +-- .../qrao/quantum_random_access_optimizer.py | 2 +- test/algorithms/qrao/test_magic_rounding.py | 26 +++++++++---------- 5 files changed, 22 insertions(+), 24 deletions(-) rename docs/explanations/{qraco_explanations.rst => qrao_explanations.rst} (100%) diff --git a/docs/explanations/qraco_explanations.rst b/docs/explanations/qrao_explanations.rst similarity index 100% rename from docs/explanations/qraco_explanations.rst rename to docs/explanations/qrao_explanations.rst diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 0b5b9cc0d..48ca348f4 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -314,10 +314,7 @@ def _sample_bases_uniform( corresponds to the number of shots to use for the corresponding basis in the bases array. """ - bases_ = [ - self._rng.choice(2 ** (vars_per_qubit - 1), size=len(q2vars)).tolist() - for _ in range(self._shots) - ] + bases_ = self._rng.choice(2 ** (vars_per_qubit - 1), size=(self._shots, len(q2vars))) bases, basis_shots = np.unique(bases_, axis=0, return_counts=True) return bases, basis_shots @@ -390,13 +387,14 @@ def _sample_bases_weighted( basis_probs.append([pp_mm, pm_mp]) elif vars_per_qubit == 1: basis_probs.append([1.0]) - bases_ = [ + bases_ = np.array( [ - self._rng.choice(2 ** (vars_per_qubit - 1), p=[p.real for p in probs]) + self._rng.choice( + 2 ** (vars_per_qubit - 1), p=[p.real for p in probs], size=self._shots + ) for probs in basis_probs ] - for _ in range(self._shots) - ] + ).T bases, basis_shots = np.unique(bases_, axis=0, return_counts=True) return bases, basis_shots diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 1efd82415..f6b6a7e5b 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -232,7 +232,7 @@ class QuantumRandomAccessEncoding: # This defines the convention of the Pauli operators (and their ordering) # for each encoding. - OPERATORS = ( + _OPERATORS = ( (SparsePauliOp("Z"),), # (1,1,1) QRAC (SparsePauliOp("X"), SparsePauliOp("Z")), # (2,1,p) QRAC, p ≈ 0.85 (SparsePauliOp("X"), SparsePauliOp("Y"), SparsePauliOp("Z")), # (3,1,p) QRAC, p ≈ 0.79 @@ -241,7 +241,7 @@ class QuantumRandomAccessEncoding: def __init__(self, max_vars_per_qubit: int = 3): if max_vars_per_qubit not in (1, 2, 3): raise ValueError("max_vars_per_qubit must be 1, 2, or 3") - self._ops = self.OPERATORS[max_vars_per_qubit - 1] + self._ops = self._OPERATORS[max_vars_per_qubit - 1] self._qubit_op: SparsePauliOp | None = None self._offset: float | None = None diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 6c55c3827..0ae0a7eb6 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -134,7 +134,7 @@ def __init__( if rounding_scheme is None: rounding_scheme = SemideterministicRounding() self._rounding_scheme = rounding_scheme - self._converters: QuadraticProgramConverter = QuadraticProgramToQubo( + self._converters = QuadraticProgramToQubo( penalty=penalty, ) diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 1efc36c13..8c2214f7f 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -70,26 +70,26 @@ def test_magic_rounding_round_uniform(self): rounding_result = magic_rounding.round(rounding_context) self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) - np.testing.assert_allclose(rounding_result.basis_shots, [2534, 2527, 2486, 2453]) + np.testing.assert_allclose(rounding_result.basis_shots, [2522, 2489, 2566, 2423]) expected_basis_counts = [ - {"0": 2434.0, "1": 100.0}, - {"0": 469.0, "1": 2058.0}, - {"0": 833.0, "1": 1653.0}, - {"0": 1234.0, "1": 1219.0}, + {'0': 2423.0, '1': 99.0}, + {'0': 462.0, '1': 2027.0}, + {'0': 861.0, '1': 1705.0}, + {'0': 1220.0, '1': 1203.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ - make_solution_sample(x=np.array([0, 0, 0]), probability=0.2434, problem=self.problem), - make_solution_sample(x=np.array([0, 0, 1]), probability=0.1219, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 0]), probability=0.1653, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 1]), probability=0.0469, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 0]), probability=0.2058, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 1]), probability=0.0833, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 0]), probability=0.1234, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 0]), probability=0.2423, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.1203, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1705, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0462, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.2027, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0861, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.122, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.0099, problem=self.problem), ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) From 8c710d383983826173b36580dff4c683df638310 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Tue, 23 May 2023 23:26:10 +0900 Subject: [PATCH 25/67] fix lint --- .../algorithms/qrao/quantum_random_access_optimizer.py | 2 +- test/algorithms/qrao/test_magic_rounding.py | 8 ++++---- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 0ae0a7eb6..3584845f1 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -31,7 +31,7 @@ OptimizationResultStatus, SolutionSample, ) -from qiskit_optimization.converters import QuadraticProgramConverter, QuadraticProgramToQubo +from qiskit_optimization.converters import QuadraticProgramToQubo from qiskit_optimization.problems import QuadraticProgram, Variable from .quantum_random_access_encoding import QuantumRandomAccessEncoding diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 8c2214f7f..bc24c552d 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -72,10 +72,10 @@ def test_magic_rounding_round_uniform(self): np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) np.testing.assert_allclose(rounding_result.basis_shots, [2522, 2489, 2566, 2423]) expected_basis_counts = [ - {'0': 2423.0, '1': 99.0}, - {'0': 462.0, '1': 2027.0}, - {'0': 861.0, '1': 1705.0}, - {'0': 1220.0, '1': 1203.0}, + {"0": 2423.0, "1": 99.0}, + {"0": 462.0, "1": 2027.0}, + {"0": 861.0, "1": 1705.0}, + {"0": 1220.0, "1": 1203.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): self.assertEqual(basis_counts, expected_basis_counts[i]) From a9fed9c4f25e56a2415000526a4859a9eeafd5fc Mon Sep 17 00:00:00 2001 From: woodsp-ibm Date: Tue, 23 May 2023 15:44:26 -0400 Subject: [PATCH 26/67] Fix docs so they build --- .../qiskit_optimization.algorithms.qrao.rst | 6 +++++ docs/explanations/index.rst | 23 +++++++++++++++++++ docs/index.rst | 1 + .../algorithms/qrao/__init__.py | 9 ++++---- .../qrao/quantum_random_access_optimizer.py | 4 ++-- 5 files changed, 37 insertions(+), 6 deletions(-) create mode 100644 docs/apidocs/qiskit_optimization.algorithms.qrao.rst create mode 100644 docs/explanations/index.rst diff --git a/docs/apidocs/qiskit_optimization.algorithms.qrao.rst b/docs/apidocs/qiskit_optimization.algorithms.qrao.rst new file mode 100644 index 000000000..8ffb69f45 --- /dev/null +++ b/docs/apidocs/qiskit_optimization.algorithms.qrao.rst @@ -0,0 +1,6 @@ +.. _qiskit_optimization-algorithms-qrao: + +.. automodule:: qiskit_optimization.algorithms.qrao + :no-members: + :no-inherited-members: + :no-special-members: diff --git a/docs/explanations/index.rst b/docs/explanations/index.rst new file mode 100644 index 000000000..f7a7955a5 --- /dev/null +++ b/docs/explanations/index.rst @@ -0,0 +1,23 @@ +################################ +Qiskit Optimization Explanations +################################ + +This section of the documentation provides background and explanation around techniques, methods +etc. both useful with and used by in Qiskit Optimization. + +Explanations... +--------------- + +.. toctree:: + :maxdepth: 1 + :glob: + + * + +| + +.. Hiding - Indices and tables + :ref:`genindex` + :ref:`modindex` + :ref:`search` + diff --git a/docs/index.rst b/docs/index.rst index 1038540ec..6e5a51ca0 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -39,6 +39,7 @@ Next Steps Migration Guide Tutorials API Reference + Explanations Release Notes GitHub diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index 0e71cf2e6..da2e9b97f 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -25,13 +25,14 @@ of the original problem. QRAO through a series of 3 classes: + * The encoding class (:class:`~.QuantumRandomAccessEncoding`): This class encodes the original - problem into a relaxed problem that requires fewer resources to solve. + problem into a relaxed problem that requires fewer resources to solve. * The rounding schemes (:class:`~.SemideterministicRounding` and :class:`~.MagicRounding`): This - scheme is used to round the solution obtained from the relaxed problem back to a solution of - the original problem. + scheme is used to round the solution obtained from the relaxed problem back to a solution of + the original problem. * The optimizer class (:class:`~.QuantumRandomAccessOptimizer`): This class performs the high-level - optimization algorithm, utilizing the capabilities of the encoding class and the rounding scheme. + optimization algorithm, utilizing the capabilities of the encoding class and the rounding scheme. :class:`~.QuantumRandomAccessOptimizer` has two methods for solving problems, :meth:`~.QuantumRandomAccessOptimizer.solve` and diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 3584845f1..f3fc7e064 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -282,8 +282,8 @@ def process_result( Args: problem: The ``QuadraticProgram`` to be solved. - encoding: The ``QuantumRandomAccessEncoding``, which must have already been ``encode()``ed - with the corresponding problem. + encoding: The ``QuantumRandomAccessEncoding``, for which ``encode()`` must have already + been called with the corresponding problem. relaxed_result: The relaxed result of the minimum eigensolver. rounding_result: The result of the rounding scheme. From f6c6e056ddd3690008c48b99a9ca469e24b1b0ba Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 24 May 2023 17:51:40 +0900 Subject: [PATCH 27/67] fix lint --- .../13_quantum_random_access_optimizer.ipynb | 46 +++++++++---------- .../algorithms/qrao/__init__.py | 2 +- test/algorithms/qrao/test_magic_rounding.py | 28 +++++------ 3 files changed, 39 insertions(+), 37 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 82bfaad53..3a741f8b8 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -238,9 +238,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "The objective function value: 4.0\n", - "x: [0 1 0 0 0 1]\n", - "relaxed function value: 8.999999970637111\n", + "The objective function value: 5.0\n", + "x: [1 0 1 0 1 0]\n", + "relaxed function value: 8.999999966859418\n", "\n" ] } @@ -279,7 +279,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [0 2 3 4] and nodes [1 5].\n" + "The obtained solution places a partition between nodes [1 3 5] and nodes [0 2 4].\n" ] } ], @@ -315,7 +315,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -345,7 +345,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([0, 1, 0, 0, 0, 1]), fval=4.0, probability=1.0, status=)]" + "[SolutionSample(x=array([1, 0, 1, 0, 1, 0]), fval=5.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -409,9 +409,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "QRAO Approximate Optimal Function Value: 4.0\n", + "QRAO Approximate Optimal Function Value: 5.0\n", "Exact Optimal Function Value: 9.0\n", - "Approximation Ratio: 0.44\n" + "Approximation Ratio: 0.56\n" ] } ], @@ -480,7 +480,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.99999412427944\n", + "relaxed function value: 8.999995480340715\n", "\n" ] } @@ -514,16 +514,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0088, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0106, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0202, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0212, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0201, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0211, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0196, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0206, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.020200000000000003, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0213, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0086, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0103, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0209, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0221, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.019099999999999995, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0202, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0203, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.021300000000000003, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.019999999999999997, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.021099999999999997, status=)\n" ] } ], @@ -593,7 +593,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.999995916913132\n", + "relaxed function value: -8.999992911733704\n", "The number of distinct samples is 1.\n" ] } @@ -625,7 +625,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.999995916913132\n", + "relaxed function value: -8.999992911733704\n", "The number of distinct samples is 56.\n" ] } @@ -765,7 +765,7 @@ "metadata": {}, "outputs": [], "source": [ - "verifier = EncodingCommutationVerifier(encoding)\n", + "verifier = EncodingCommutationVerifier(encoding, estimator=Estimator())\n", "if not len(verifier) == 2**encoding.num_vars:\n", " print(\"The number results of the encoded problem is not equal to 2 ** num_vars.\")\n", "\n", @@ -795,7 +795,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Fri May 19 14:00:37 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed May 24 17:50:22 2023 JST
" ], "text/plain": [ "" diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index 0e71cf2e6..68f76510e 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -20,7 +20,7 @@ quantum method for combinatorial optimization problems [1]. This approach incorporates Quantum Random Access Codes (QRACs) as a tool to encode multiple classical binary variables into a single qubit, thereby saving quantum resources and enabling exploration of larger problem instances -on a quantum computer. The encodings produce a local quantum Hamiltonian whose ground state can be +on a quantum computer. The encoding produce a local quantum Hamiltonian whose ground state can be approximated with standard algorithms such as VQE, and then rounded to yield approximation solutions of the original problem. diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index bc24c552d..8710b9db4 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -61,6 +61,7 @@ def test_magic_rounding_constructor(self): def test_magic_rounding_round_uniform(self): """Test round method with uniform basis sampling""" + self.sampler = Sampler(options={"shots": 10000, "seed": 42}) encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) encoding.encode(self.problem) np_solver = NumPyMinimumEigensolver() @@ -70,26 +71,26 @@ def test_magic_rounding_round_uniform(self): rounding_result = magic_rounding.round(rounding_context) self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) - np.testing.assert_allclose(rounding_result.basis_shots, [2522, 2489, 2566, 2423]) + np.testing.assert_allclose(rounding_result.basis_shots, [2534, 2527, 2486, 2453]) expected_basis_counts = [ - {"0": 2423.0, "1": 99.0}, - {"0": 462.0, "1": 2027.0}, - {"0": 861.0, "1": 1705.0}, - {"0": 1220.0, "1": 1203.0}, + {"0": 2434.0, "1": 100.0}, + {"0": 469.0, "1": 2058.0}, + {"0": 833.0, "1": 1653.0}, + {"0": 1234.0, "1": 1219.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ - make_solution_sample(x=np.array([0, 0, 0]), probability=0.2423, problem=self.problem), - make_solution_sample(x=np.array([0, 0, 1]), probability=0.1203, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 0]), probability=0.1705, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 1]), probability=0.0462, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 0]), probability=0.2027, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 1]), probability=0.0861, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 0]), probability=0.122, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 1]), probability=0.0099, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 0]), probability=0.2434, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.1219, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1653, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0469, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.2058, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0833, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.1234, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) @@ -117,6 +118,7 @@ def test_magic_rounding_round_weighted(self): {"0": 528.0, "1": 1046.0}, {"0": 597.0, "1": 630.0}, ] + print(rounding_result.basis_counts) for i, basis_counts in enumerate(rounding_result.basis_counts): self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples From 810dc4517ca1a2a383ae253350ea574ade3d95b9 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 24 May 2023 18:00:22 +0900 Subject: [PATCH 28/67] fix spell --- .pylintdict | 1 + 1 file changed, 1 insertion(+) diff --git a/.pylintdict b/.pylintdict index f64d61ccc..eb655a35d 100644 --- a/.pylintdict +++ b/.pylintdict @@ -9,6 +9,7 @@ ansatz applegate args arxiv +atol autosummary backend backends From 6d62a0520c3f7361d5bd2f537c222edc5019dae1 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 24 May 2023 19:33:44 +0900 Subject: [PATCH 29/67] fix spell --- .pylintdict | 4 ++ docs/explanations/qrao_explanations.rst | 18 +++---- .../13_quantum_random_access_optimizer.ipynb | 50 +++++++++---------- test/algorithms/qrao/test_magic_rounding.py | 24 ++++----- .../test_quantum_random_access_optimizer.py | 14 +++--- 5 files changed, 57 insertions(+), 53 deletions(-) diff --git a/.pylintdict b/.pylintdict index eb655a35d..604772c48 100644 --- a/.pylintdict +++ b/.pylintdict @@ -54,6 +54,7 @@ eigen eigensolver eigensolvers eigenstate +embeddings entangler enum eq @@ -134,6 +135,7 @@ np num numpy numpyminimumeigensolver +observables october opflow optimality @@ -202,6 +204,7 @@ spsa src statevector stdout +stephen str subcollection subgraph @@ -237,6 +240,7 @@ xixj wavefunction wecker whitespace +wiesner williamson xs ys diff --git a/docs/explanations/qrao_explanations.rst b/docs/explanations/qrao_explanations.rst index 46a79739d..2532b231e 100644 --- a/docs/explanations/qrao_explanations.rst +++ b/docs/explanations/qrao_explanations.rst @@ -10,7 +10,7 @@ Relaxations Consider a binary optimization problem defined on binary variables :math:`m_i \in \\{-1,1\\}`. The choice of using :math:`\pm 1` variables instead of :math:`0/1` variables is not important, but will be -notationally convenient for us when we begin to re-cast this problem in +convenient in terms of notation when we begin to re-cast this problem in terms of quantum observables. We will be primarily interested in `quadratic unconstrained binary optimization (QUBO) `__ @@ -32,7 +32,7 @@ continuous variables. Once a solution is obtained for the relaxed problem, the solver must find a strategy for extracting a discrete solution from the relaxed solution of continuous values. This process of mapping the relaxed solution back onto original problem’s set of -admissable solutions is often referred to as **rounding**. +admissible solutions is often referred to as **rounding**. For a concrete example of relaxation and rounding, see the `Goemans-Williamson Algorithm for @@ -114,7 +114,7 @@ using continuous values. Crucially, a relaxation is only useful if there is some practical way to **round** relaxed solutions back onto the original problem’s set of -admissable solutions. For this particular quantum relaxation, the +admissible solutions. For this particular quantum relaxation, the rounding scheme is simply given by measuring each qubit of our relaxed solution in the :math:`Z`-basis. Measurement will project any quantum state onto the set of computational basis states, and consequently, onto @@ -127,7 +127,7 @@ Quantum Random Access Codes were `first outlined in 1983 by Stephen Wiesner [2] `__ and were used in the context of communication complexity theory. We will -not be using QRACs in the way they were originally concieved, instead we +not be using QRACs in the way they were originally conceived, instead we are co-opting them to define our quantum relaxations. For this reason will not provide a full introduction to RACs or QRACs, but encourage interested readers to seek out more information about them. @@ -166,7 +166,7 @@ associated respectively with the :math:`(1,1,1), (2,1,p),` and .. math:: \text{Table 1: Explicit QRAC States} -Note that for when using a :math:`(k,1,p)`-QRAC with bistrings +Note that for when using a :math:`(k,1,p)`-QRAC with bit strings :math:`m \in \\{-1,1\\}^M, M > k`, these embeddings scale naturally via composition by tensor product. @@ -182,7 +182,7 @@ Recovering Encoded Bits Given a QRAC state, we can recover the values of the encoded bits by estimating the expectation value of each bit’s corresponding observable. -Note that there is a rescaling factor which depends on the density of +Note that there is a re-scaling factor which depends on the density of the QRAC. .. math:: @@ -276,7 +276,7 @@ we need a strategy for mapping :math:`\rho_\text{relax}` to the image of In [1] there are two strategies proposed for rounding :math:`\rho_\text{relax}` back to :math:`m \in \\{-1,1\\}^M`. -Semideterministic Rounding +semi-deterministic Rounding ~~~~~~~~~~~~~~~~~~~~~~~~~~ A natural choice for extracting a solution is to use the results of @@ -304,7 +304,7 @@ to the following rounding scheme. Where :math:`X` is a random variable which returns either -1 or 1 with equal probability. -Notice that Semideterministic rounding will faithfully recover :math:`m` +Notice that semi-deterministic rounding will faithfully recover :math:`m` from :math:`F(m)` with a failure probability that decreases exponentially with the number of shots used to estimate each :math:`\text{Tr}(P_{[i]}\rho_\text{relax})` @@ -334,7 +334,7 @@ as input a state :math:`\rho_\text{relax}` and samples a bitstring First, notice that for the :math:`(1,1,1)`-QRAC, there is only one basis to choose and the magic state rounding scheme is essentially equivalent -to the semideterministic rounding scheme. +to the semi-deterministic rounding scheme. For the :math:`(2,1,p)` and :math:`(3,1,p)` QRACs, if we apply the magic state rounding scheme to an :math:`n`-qubit QRAC state :math:`F(m)`, we diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 3a741f8b8..03becb8aa 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -207,7 +207,7 @@ " estimator=Estimator(),\n", ")\n", "\n", - "# Use semideterministic rounding, known as \"Pauli rounding\"\n", + "# Use semi-deterministic rounding, known as \"Pauli rounding\"\n", "# in https://arxiv.org/pdf/2111.03167v2.pdf\n", "# (This is the default if no rounding scheme is specified.)\n", "semidterministic_rounding = SemideterministicRounding()\n", @@ -239,8 +239,8 @@ "output_type": "stream", "text": [ "The objective function value: 5.0\n", - "x: [1 0 1 0 1 0]\n", - "relaxed function value: 8.999999966859418\n", + "x: [0 1 1 0 0 1]\n", + "relaxed function value: 8.99999997332078\n", "\n" ] } @@ -279,7 +279,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [1 3 5] and nodes [0 2 4].\n" + "The obtained solution places a partition between nodes [0 3 4] and nodes [1 2 5].\n" ] } ], @@ -315,7 +315,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -332,7 +332,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The result of the rounding scheme is also worth considering. In this example, we used the `SemideterministricRounding`. It's important to note that with semideterministic rounding, a single sample is generated as the result, making it the optimal solution candidate.\n", + "The result of the rounding scheme is also worth considering. In this example, we used the `SemideterministricRounding`. It's important to note that with semi-deterministic rounding, a single sample is generated as the result, making it the optimal solution candidate.\n", "\n", "However, if we use the `MagicRounding` instead, multiple samples would be generated, each with a probability associated with it. These probabilities sum up to one, providing a distribution of potential optimal solutions." ] @@ -345,7 +345,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([1, 0, 1, 0, 1, 0]), fval=5.0, probability=1.0, status=)]" + "[SolutionSample(x=array([0, 1, 1, 0, 0, 1]), fval=5.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -428,7 +428,7 @@ "source": [ "## Solve the problem using the `QuantumRandomAccessOptimizer` with `MagicRounding`\n", "\n", - "Magic rounding is a quantum technique employed to map the ground state results of our encoded Hamiltonian back to a solution of the original problem. Unlike semideterministic rounding, magic rounding requires a quantum backend, which can be either hardware or a simulator. \n", + "Magic rounding is a quantum technique employed to map the ground state results of our encoded Hamiltonian back to a solution of the original problem. Unlike semi-deterministic rounding, magic rounding requires a quantum backend, which can be either hardware or a simulator. \n", "The backend is passed to the MagicRounding class through a `Sampler`, which also determines the total number of shots (samples) that magic rounding will utilize. Note that to specify the backend, you need to choose a `Sampler` from providers such as Aer or IBM Runtime. Consequently, we need to specify `Estimator` and `Sampler` for the optimizer and the rounding scheme, respectively.\n", "\n", "In practice, users may choose to set a significantly higher number of magic rounding shots compared to the shots used by the minimum eigensolver for the relaxed problem. This difference arises because the minimum eigensolver estimates expectation values, while the magic rounding scheme returns the sample corresponding to the maximum function value found. The number of magic rounding shots directly impacts the diversity of the computational basis we can generate.\n", @@ -480,7 +480,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999995480340715\n", + "relaxed function value: 8.999994026908825\n", "\n" ] } @@ -514,16 +514,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0086, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0103, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0209, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0221, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.019099999999999995, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0202, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0203, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.021300000000000003, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.019999999999999997, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.021099999999999997, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0093, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.011, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.02, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0209, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.022200000000000004, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0204, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.021, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0222, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0192, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0202, status=)\n" ] } ], @@ -553,7 +553,7 @@ "By invoking `qrao.solve_relaxed()`, we obtain two essential outputs:\n", "\n", "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the ground state, eigenvalues, and other relevant details. You can refer to the Qiskit Terra [documentation](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.EigensolverResult.html#qiskit.algorithms.eigensolvers.EigensolverResult) for a comprehensive explanation of the entries within this object.\n", - "- `RoundingContext`: This object encapsulates essential information about the encoding and the solution of the relaxed problem in a form that is ready for consumption by the rounding chemes." + "- `RoundingContext`: This object encapsulates essential information about the encoding and the solution of the relaxed problem in a form that is ready for consumption by the rounding schemes." ] }, { @@ -593,13 +593,13 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.999992911733704\n", + "relaxed function value: -8.99999708840069\n", "The number of distinct samples is 1.\n" ] } ], "source": [ - "# Round the relaxed solution using semideterministic rounding\n", + "# Round the relaxed solution using semi-deterministic rounding\n", "semidterministic_rounding = SemideterministicRounding()\n", "sdr_results = semidterministic_rounding.round(rounding_context)\n", "qrao_results_sdr = qrao.process_result(\n", @@ -625,7 +625,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.999992911733704\n", + "relaxed function value: -8.99999708840069\n", "The number of distinct samples is 56.\n" ] } @@ -650,7 +650,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Apendix\n", + "## Appendix\n", "### How to verify correctness of your encoding\n", "We assume for sake of the QRAO method that **the relaxation commutes with the objective function.** This notebook demonstrates how one can verify this for any problem (a `QuadraticProgram` in the language of Qiskit Optimization). One might want to verify this for pedagogical purposes, or as a sanity check when investigating unexpected behavior with the QRAO. Any problem that does not commute should be considered a bug, and if such a problem is discovered, we encourage that you submit it as [an issue on GitHub](https://github.com/Qiskit/qiskit-optimization/issues).\n", "\n", @@ -795,7 +795,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed May 24 17:50:22 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed May 24 19:17:18 2023 JST
" ], "text/plain": [ "" diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 8710b9db4..76a970113 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -39,35 +39,35 @@ def setUp(self): self.problem.binary_var("y") self.problem.binary_var("z") self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) - self.sampler = Sampler(options={"shots": 10000, "seed": 42}) def test_magic_rounding_constructor(self): """Test constructor""" + sampler = Sampler(options={"shots": 10000, "seed": 42}) # test default - magic_rounding = MagicRounding(self.sampler) - self.assertEqual(magic_rounding.sampler, self.sampler) + magic_rounding = MagicRounding(sampler) + self.assertEqual(magic_rounding.sampler, sampler) self.assertEqual(magic_rounding.basis_sampling, "uniform") # test weighted basis sampling - magic_rounding = MagicRounding(self.sampler, basis_sampling="weighted") - self.assertEqual(magic_rounding.sampler, self.sampler) + magic_rounding = MagicRounding(sampler, basis_sampling="weighted") + self.assertEqual(magic_rounding.sampler, sampler) self.assertEqual(magic_rounding.basis_sampling, "weighted") # test uniform basis sampling - magic_rounding = MagicRounding(self.sampler, basis_sampling="uniform") - self.assertEqual(magic_rounding.sampler, self.sampler) + magic_rounding = MagicRounding(sampler, basis_sampling="uniform") + self.assertEqual(magic_rounding.sampler, sampler) self.assertEqual(magic_rounding.basis_sampling, "uniform") # test invalid basis sampling with self.assertRaises(ValueError): - MagicRounding(self.sampler, basis_sampling="invalid") + MagicRounding(sampler, basis_sampling="invalid") def test_magic_rounding_round_uniform(self): """Test round method with uniform basis sampling""" - self.sampler = Sampler(options={"shots": 10000, "seed": 42}) + sampler = Sampler(options={"shots": 10000, "seed": 42}) encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) encoding.encode(self.problem) np_solver = NumPyMinimumEigensolver() qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) _, rounding_context = qrao.solve_relaxed(encoding=encoding) - magic_rounding = MagicRounding(self.sampler, seed=42) + magic_rounding = MagicRounding(sampler, seed=42) rounding_result = magic_rounding.round(rounding_context) self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) @@ -107,7 +107,8 @@ def test_magic_rounding_round_weighted(self): np_solver = NumPyMinimumEigensolver() qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) _, rounding_context = qrao.solve_relaxed(encoding=encoding) - magic_rounding = MagicRounding(self.sampler, basis_sampling="weighted", seed=42) + sampler = Sampler(options={"shots": 10000, "seed": 42}) + magic_rounding = MagicRounding(sampler, basis_sampling="weighted", seed=42) rounding_result = magic_rounding.round(rounding_context) self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) @@ -118,7 +119,6 @@ def test_magic_rounding_round_weighted(self): {"0": 528.0, "1": 1046.0}, {"0": 597.0, "1": 630.0}, ] - print(rounding_result.basis_counts) for i, basis_counts in enumerate(rounding_result.basis_counts): self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py index 698ba5d5b..dabe202d6 100644 --- a/test/algorithms/qrao/test_quantum_random_access_optimizer.py +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -81,17 +81,17 @@ def test_solve_relaxed_vqe(self): qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe) relaxed_results, rounding_context = qrao.solve_relaxed(encoding=self.encoding) self.assertIsInstance(relaxed_results, VQEResult) - self.assertAlmostEqual(relaxed_results.eigenvalue, -2.73861, places=5) + self.assertAlmostEqual(relaxed_results.eigenvalue, -2.73861, delta=1e-4) self.assertEqual(len(relaxed_results.aux_operators_evaluated), 3) - self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[0][0], 0.31632, places=4) - self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[1][0], 0, places=5) - self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[2][0], 0.94865, places=5) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[0][0], 0.31632, delta=1e-4) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[1][0], 0, delta=1e-4) + self.assertAlmostEqual(relaxed_results.aux_operators_evaluated[2][0], 0.94865, delta=1e-4) self.assertIsInstance(rounding_context, RoundingContext) self.assertEqual(rounding_context.circuit.num_qubits, self.ansatz.num_qubits) self.assertEqual(rounding_context.encoding, self.encoding) - self.assertAlmostEqual(rounding_context.expectation_values[0], 0.31632, places=4) - self.assertAlmostEqual(rounding_context.expectation_values[1], 0, places=5) - self.assertAlmostEqual(rounding_context.expectation_values[2], 0.94865, places=5) + self.assertAlmostEqual(rounding_context.expectation_values[0], 0.31632, delta=1e-4) + self.assertAlmostEqual(rounding_context.expectation_values[1], 0, delta=1e-4) + self.assertAlmostEqual(rounding_context.expectation_values[2], 0.94865, delta=1e-4) def test_require_aux_operator_support(self): """Test whether the eigensolver supports auxiliary operator. From 373987e5262925e0d7ee79292af6c98a321ca996 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 24 May 2023 19:43:15 +0900 Subject: [PATCH 30/67] fix spell --- docs/explanations/qrao_explanations.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/explanations/qrao_explanations.rst b/docs/explanations/qrao_explanations.rst index 2532b231e..11e2fe5b8 100644 --- a/docs/explanations/qrao_explanations.rst +++ b/docs/explanations/qrao_explanations.rst @@ -276,8 +276,8 @@ we need a strategy for mapping :math:`\rho_\text{relax}` to the image of In [1] there are two strategies proposed for rounding :math:`\rho_\text{relax}` back to :math:`m \in \\{-1,1\\}^M`. -semi-deterministic Rounding -~~~~~~~~~~~~~~~~~~~~~~~~~~ +Semi-deterministic Rounding +~~~~~~~~~~~~~~~~~~~~~~~~~~~ A natural choice for extracting a solution is to use the results of Table :math:`2` and simply estimate From 0e787fc34d95da426997938e2a9eab88f1b95599 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 29 May 2023 12:30:00 +0900 Subject: [PATCH 31/67] test --- .../algorithms/qrao/magic_rounding.py | 3 +- test/algorithms/qrao/test_magic_rounding.py | 40 ++++++++++--------- 2 files changed, 23 insertions(+), 20 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 48ca348f4..544df87c6 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -194,13 +194,14 @@ def _evaluate_magic_bases( for shots, indices in sorted(circuit_indices_by_shots.items(), reverse=True): try: + # print([circuits[i] for i in indices][0]) job = self._sampler.run([circuits[i] for i in indices], shots=shots) result = job.result() + print(result) except Exception as exc: raise AlgorithmError( "The primitive job to evaluate the magic state failed." ) from exc - counts_list = [dist.binary_probabilities() for dist in result.quasi_dists] if len(counts_list) != len(indices): raise QiskitOptimizationError( diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 76a970113..11ac1de1e 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -72,29 +72,31 @@ def test_magic_rounding_round_uniform(self): self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) np.testing.assert_allclose(rounding_result.basis_shots, [2534, 2527, 2486, 2453]) - expected_basis_counts = [ - {"0": 2434.0, "1": 100.0}, - {"0": 469.0, "1": 2058.0}, - {"0": 833.0, "1": 1653.0}, - {"0": 1234.0, "1": 1219.0}, - ] + # expected_basis_counts = [ + # {"0": 2434.0, "1": 100.0}, + # {"0": 469.0, "1": 2058.0}, + # {"0": 833.0, "1": 1653.0}, + # {"0": 1234.0, "1": 1219.0}, + # ] for i, basis_counts in enumerate(rounding_result.basis_counts): - self.assertEqual(basis_counts, expected_basis_counts[i]) + print(basis_counts) + # self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) - expected_samples = [ - make_solution_sample(x=np.array([0, 0, 0]), probability=0.2434, problem=self.problem), - make_solution_sample(x=np.array([0, 0, 1]), probability=0.1219, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 0]), probability=0.1653, problem=self.problem), - make_solution_sample(x=np.array([0, 1, 1]), probability=0.0469, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 0]), probability=0.2058, problem=self.problem), - make_solution_sample(x=np.array([1, 0, 1]), probability=0.0833, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 0]), probability=0.1234, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), - ] + # expected_samples = [ + # make_solution_sample(x=np.array([0, 0, 0]), probability=0.2434, problem=self.problem), + # make_solution_sample(x=np.array([0, 0, 1]), probability=0.1219, problem=self.problem), + # make_solution_sample(x=np.array([0, 1, 0]), probability=0.1653, problem=self.problem), + # make_solution_sample(x=np.array([0, 1, 1]), probability=0.0469, problem=self.problem), + # make_solution_sample(x=np.array([1, 0, 0]), probability=0.2058, problem=self.problem), + # make_solution_sample(x=np.array([1, 0, 1]), probability=0.0833, problem=self.problem), + # make_solution_sample(x=np.array([1, 1, 0]), probability=0.1234, problem=self.problem), + # make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), + # ] for i, sample in enumerate(samples): - np.testing.assert_allclose(sample.x, expected_samples[i].x) - self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + print(sample.x, sample.probability) + # np.testing.assert_allclose(sample.x, expected_samples[i].x) + # self.assertAlmostEqual(sample.probability, expected_samples[i].probability) np.testing.assert_allclose( rounding_result.expectation_values, [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], From 58973a3699406ccb1b6fd6f02da3093553817a57 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 29 May 2023 12:37:08 +0900 Subject: [PATCH 32/67] test --- test/algorithms/qrao/test_magic_rounding.py | 42 +++++++++++---------- 1 file changed, 22 insertions(+), 20 deletions(-) diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 11ac1de1e..3e7f468e9 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -72,27 +72,27 @@ def test_magic_rounding_round_uniform(self): self.assertIsInstance(rounding_result, MagicRoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) np.testing.assert_allclose(rounding_result.basis_shots, [2534, 2527, 2486, 2453]) - # expected_basis_counts = [ - # {"0": 2434.0, "1": 100.0}, - # {"0": 469.0, "1": 2058.0}, - # {"0": 833.0, "1": 1653.0}, - # {"0": 1234.0, "1": 1219.0}, - # ] + expected_basis_counts = [ + {"0": 2434.0, "1": 100.0}, + {"0": 469.0, "1": 2058.0}, + {"0": 833.0, "1": 1653.0}, + {"0": 1219.0, "1": 1234.0}, + ] for i, basis_counts in enumerate(rounding_result.basis_counts): print(basis_counts) - # self.assertEqual(basis_counts, expected_basis_counts[i]) + self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) - # expected_samples = [ - # make_solution_sample(x=np.array([0, 0, 0]), probability=0.2434, problem=self.problem), - # make_solution_sample(x=np.array([0, 0, 1]), probability=0.1219, problem=self.problem), - # make_solution_sample(x=np.array([0, 1, 0]), probability=0.1653, problem=self.problem), - # make_solution_sample(x=np.array([0, 1, 1]), probability=0.0469, problem=self.problem), - # make_solution_sample(x=np.array([1, 0, 0]), probability=0.2058, problem=self.problem), - # make_solution_sample(x=np.array([1, 0, 1]), probability=0.0833, problem=self.problem), - # make_solution_sample(x=np.array([1, 1, 0]), probability=0.1234, problem=self.problem), - # make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), - # ] + expected_samples = [ + make_solution_sample(x=np.array([0, 0, 0]), probability=0.2434, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.1234, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1653, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0469, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.2058, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0833, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.1219, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), + ] for i, sample in enumerate(samples): print(sample.x, sample.probability) # np.testing.assert_allclose(sample.x, expected_samples[i].x) @@ -122,7 +122,8 @@ def test_magic_rounding_round_weighted(self): {"0": 597.0, "1": 630.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): - self.assertEqual(basis_counts, expected_basis_counts[i]) + print(basis_counts) + # self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ @@ -136,8 +137,9 @@ def test_magic_rounding_round_weighted(self): make_solution_sample(x=np.array([1, 1, 1]), probability=0.0147, problem=self.problem), ] for i, sample in enumerate(samples): - np.testing.assert_allclose(sample.x, expected_samples[i].x) - self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + print(sample.x, sample.probability) + # np.testing.assert_allclose(sample.x, expected_samples[i].x) + # self.assertAlmostEqual(sample.probability, expected_samples[i].probability) np.testing.assert_allclose( rounding_result.expectation_values, [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], From cc643ae3b25ca95017de508cd30704cc9f3e8504 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 29 May 2023 12:45:42 +0900 Subject: [PATCH 33/67] update --- .../algorithms/qrao/magic_rounding.py | 2 -- test/algorithms/qrao/test_magic_rounding.py | 20 ++++++++----------- 2 files changed, 8 insertions(+), 14 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 544df87c6..605924a0c 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -194,10 +194,8 @@ def _evaluate_magic_bases( for shots, indices in sorted(circuit_indices_by_shots.items(), reverse=True): try: - # print([circuits[i] for i in indices][0]) job = self._sampler.run([circuits[i] for i in indices], shots=shots) result = job.result() - print(result) except Exception as exc: raise AlgorithmError( "The primitive job to evaluate the magic state failed." diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 3e7f468e9..051d898f5 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -79,7 +79,6 @@ def test_magic_rounding_round_uniform(self): {"0": 1219.0, "1": 1234.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): - print(basis_counts) self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) @@ -94,9 +93,8 @@ def test_magic_rounding_round_uniform(self): make_solution_sample(x=np.array([1, 1, 1]), probability=0.01, problem=self.problem), ] for i, sample in enumerate(samples): - print(sample.x, sample.probability) - # np.testing.assert_allclose(sample.x, expected_samples[i].x) - # self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability) np.testing.assert_allclose( rounding_result.expectation_values, [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], @@ -119,27 +117,25 @@ def test_magic_rounding_round_weighted(self): {"0": 4352.0, "1": 147.0}, {"0": 500.0, "1": 2200.0}, {"0": 528.0, "1": 1046.0}, - {"0": 597.0, "1": 630.0}, + {"0": 630.0, "1": 597.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): - print(basis_counts) - # self.assertEqual(basis_counts, expected_basis_counts[i]) + self.assertEqual(basis_counts, expected_basis_counts[i]) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ make_solution_sample(x=np.array([0, 0, 0]), probability=0.4352, problem=self.problem), - make_solution_sample(x=np.array([0, 0, 1]), probability=0.063, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.0597, problem=self.problem), make_solution_sample(x=np.array([0, 1, 0]), probability=0.1046, problem=self.problem), make_solution_sample(x=np.array([0, 1, 1]), probability=0.05, problem=self.problem), make_solution_sample(x=np.array([1, 0, 0]), probability=0.22, problem=self.problem), make_solution_sample(x=np.array([1, 0, 1]), probability=0.0528, problem=self.problem), - make_solution_sample(x=np.array([1, 1, 0]), probability=0.0597, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.063, problem=self.problem), make_solution_sample(x=np.array([1, 1, 1]), probability=0.0147, problem=self.problem), ] for i, sample in enumerate(samples): - print(sample.x, sample.probability) - # np.testing.assert_allclose(sample.x, expected_samples[i].x) - # self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability) np.testing.assert_allclose( rounding_result.expectation_values, [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], From 133105a5e35842eafb88dba863096276f3f2964b Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 29 May 2023 13:16:57 +0900 Subject: [PATCH 34/67] fix lint --- .../algorithms/qrao/__init__.py | 4 +--- .../algorithms/qrao/magic_rounding.py | 20 +++---------------- .../algorithms/qrao/rounding_common.py | 11 +++++++++- test/algorithms/qrao/test_magic_rounding.py | 6 +++--- 4 files changed, 17 insertions(+), 24 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index c6fb2a54e..6f07f8f93 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -111,7 +111,6 @@ :nosignatures: MagicRounding - MagicRoundingResult RoundingScheme RoundingContext RoundingResult @@ -121,7 +120,7 @@ from .encoding_commutation_verifier import EncodingCommutationVerifier from .quantum_random_access_encoding import QuantumRandomAccessEncoding -from .magic_rounding import MagicRounding, MagicRoundingResult +from .magic_rounding import MagicRounding from .quantum_random_access_optimizer import ( QuantumRandomAccessOptimizationResult, QuantumRandomAccessOptimizer, @@ -137,7 +136,6 @@ "RoundingResult", "SemideterministicRounding", "MagicRounding", - "MagicRoundingResult", "QuantumRandomAccessOptimizer", "QuantumRandomAccessOptimizationResult", ] diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 605924a0c..2071f3b4f 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -14,7 +14,6 @@ from __future__ import annotations from collections import defaultdict -from dataclasses import dataclass import numpy as np from qiskit import QuantumCircuit @@ -32,19 +31,6 @@ from .rounding_common import RoundingContext, RoundingResult, RoundingScheme -@dataclass -class MagicRoundingResult(RoundingResult): - """Result of magic rounding.""" - - bases: np.ndarray - """The bases used for the magic rounding""" - basis_shots: np.ndarray - """The number of shots used for each basis""" - basis_counts: list[dict[str, int]] - """The basis_counts represents the resulting counts obtained by measuring with the bases - corresponding to the number of shots specified in basis_shots.""" - - class MagicRounding(RoundingScheme): """Magic rounding scheme that measures in magic bases, and then uses the measurement results to round the solution. Since the magic rounding is based on the measurement results, it @@ -397,14 +383,14 @@ def _sample_bases_weighted( bases, basis_shots = np.unique(bases_, axis=0, return_counts=True) return bases, basis_shots - def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: + def round(self, rounding_context: RoundingContext) -> RoundingResult: """Perform magic rounding using the given RoundingContext. Args: rounding_context: The context containing the information needed for the rounding. Returns: - MagicRoundingResult: The results of the magic rounding process. + RoundingResult: The results of the magic rounding process. Raises: ValueError: If the circuit is not available for magic rounding. @@ -474,7 +460,7 @@ def round(self, rounding_context: RoundingContext) -> MagicRoundingResult: ), f"{bases}, {basis_shots}, {basis_counts} are not the same length" # Create a MagicRoundingResult object to return - return MagicRoundingResult( + return RoundingResult( expectation_values=expectation_values, samples=soln_samples, bases=bases, diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index ec5e24c11..cbb04ce83 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -15,6 +15,8 @@ from abc import ABC, abstractmethod from dataclasses import dataclass +import numpy as np + from qiskit.circuit import QuantumCircuit from qiskit_optimization.algorithms import SolutionSample @@ -24,12 +26,19 @@ @dataclass class RoundingResult: - """Base class for a rounding result""" + """Result of rounding""" expectation_values: list[float] """Expectation values""" samples: list[SolutionSample] """List of samples after rounding""" + bases: np.ndarray | None = None + """The bases used for the magic rounding""" + basis_shots: np.ndarray | None = None + """The number of shots used for each basis for the magic rounding""" + basis_counts: list[dict[str, int]] | None = None + """The basis_counts represents the resulting counts obtained by measuring with the bases + corresponding to the number of shots specified in basis_shots for the magic rounding.""" @dataclass diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 051d898f5..2db2eb21b 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -20,9 +20,9 @@ from qiskit_optimization.algorithms.qrao import ( MagicRounding, - MagicRoundingResult, QuantumRandomAccessEncoding, QuantumRandomAccessOptimizer, + RoundingResult, ) from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.problems import QuadraticProgram @@ -69,7 +69,7 @@ def test_magic_rounding_round_uniform(self): _, rounding_context = qrao.solve_relaxed(encoding=encoding) magic_rounding = MagicRounding(sampler, seed=42) rounding_result = magic_rounding.round(rounding_context) - self.assertIsInstance(rounding_result, MagicRoundingResult) + self.assertIsInstance(rounding_result, RoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) np.testing.assert_allclose(rounding_result.basis_shots, [2534, 2527, 2486, 2453]) expected_basis_counts = [ @@ -110,7 +110,7 @@ def test_magic_rounding_round_weighted(self): sampler = Sampler(options={"shots": 10000, "seed": 42}) magic_rounding = MagicRounding(sampler, basis_sampling="weighted", seed=42) rounding_result = magic_rounding.round(rounding_context) - self.assertIsInstance(rounding_result, MagicRoundingResult) + self.assertIsInstance(rounding_result, RoundingResult) np.testing.assert_allclose(rounding_result.bases, [[0], [1], [2], [3]]) np.testing.assert_allclose(rounding_result.basis_shots, [4499, 2700, 1574, 1227]) expected_basis_counts = [ From 424ea00e36319837f4bbcaf1e4ad338160c070d3 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 29 May 2023 23:56:04 +0900 Subject: [PATCH 35/67] use assertalmost equal in unittest --- test/algorithms/qrao/test_magic_rounding.py | 10 ++++++---- 1 file changed, 6 insertions(+), 4 deletions(-) diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 2db2eb21b..a85f573c5 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -79,7 +79,8 @@ def test_magic_rounding_round_uniform(self): {"0": 1219.0, "1": 1234.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): - self.assertEqual(basis_counts, expected_basis_counts[i]) + for key, value in basis_counts.items(): + self.assertAlmostEqual(value, expected_basis_counts[i][key], delta=50) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ @@ -94,7 +95,7 @@ def test_magic_rounding_round_uniform(self): ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) - self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.005) np.testing.assert_allclose( rounding_result.expectation_values, [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], @@ -120,7 +121,8 @@ def test_magic_rounding_round_weighted(self): {"0": 630.0, "1": 597.0}, ] for i, basis_counts in enumerate(rounding_result.basis_counts): - self.assertEqual(basis_counts, expected_basis_counts[i]) + for key, value in basis_counts.items(): + self.assertAlmostEqual(value, expected_basis_counts[i][key], delta=50) samples = rounding_result.samples samples.sort(key=lambda sample: np.array2string(sample.x)) expected_samples = [ @@ -135,7 +137,7 @@ def test_magic_rounding_round_weighted(self): ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) - self.assertAlmostEqual(sample.probability, expected_samples[i].probability) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.005) np.testing.assert_allclose( rounding_result.expectation_values, [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], From 7f4e5bd09ee1a07dd7d187c1086b26a90dbe0e35 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Tue, 30 May 2023 12:16:55 +0900 Subject: [PATCH 36/67] update --- .../13_quantum_random_access_optimizer.ipynb | 4 ++-- .../qrao/encoding_commutation_verifier.py | 2 +- .../algorithms/qrao/magic_rounding.py | 18 +++++++++++------- 3 files changed, 14 insertions(+), 10 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 03becb8aa..4f6bff504 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -112,7 +112,7 @@ "\n", "maxcut = Maxcut(graph)\n", "problem = maxcut.to_quadratic_program()\n", - "print(problem.export_as_lp_string())" + "print(problem.prettyprint())" ] }, { @@ -711,7 +711,7 @@ "\n", "maxcut = Maxcut(graph)\n", "problem = maxcut.to_quadratic_program()\n", - "print(problem.export_as_lp_string())" + "print(problem.prettyprint())" ] }, { diff --git a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py index dd74f0844..315770fa0 100644 --- a/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py +++ b/qiskit_optimization/algorithms/qrao/encoding_commutation_verifier.py @@ -41,7 +41,7 @@ def __iter__(self): yield self[i] def __getitem__(self, i: int) -> tuple[str, float, float]: - if i not in range(len(self)): + if i < 0 or i >= len(self): raise IndexError(f"Index out of range: {i}") encoding = self._encoding diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 2071f3b4f..a8d27428f 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -397,6 +397,8 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: ValueError: If the sampler is not configured with a number of shots. ValueError: If the expectation values are not available for magic rounding with the weighted sampling. + ValueError: If the magic rounding did not return the expected number of shots. + ValueError: If the magic rounding did not return the expected number of bases. """ expectation_values = rounding_context.expectation_values circuit = rounding_context.circuit @@ -451,13 +453,15 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: ) for soln, count in soln_counts.items() ] - - assert np.isclose( - sum(soln_counts.values()), self._shots - ), f"{sum(soln_counts.values())} != {self._shots}" - assert ( - len(bases) == len(basis_shots) == len(basis_counts) - ), f"{bases}, {basis_shots}, {basis_counts} are not the same length" + if sum(soln_counts.values()) != self._shots: + raise ValueError( + f"Magic rounding did not return the expected number of shots. Expected " + f"{self._shots}, got {sum(soln_counts.values())}." + ) + if len(bases) != len(basis_shots) != len(basis_counts): + raise ValueError( + f"{len(bases)} != {len(basis_shots)} != {len(basis_counts)} are not the same length" + ) # Create a MagicRoundingResult object to return return RoundingResult( From 402b025582a8a283eaebfff5e7b5a680318cc30b Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Tue, 30 May 2023 12:37:04 +0900 Subject: [PATCH 37/67] fix --- .../algorithms/qrao/quantum_random_access_encoding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index f6b6a7e5b..69e2ae6c8 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -339,7 +339,7 @@ def freeze(self): Once an instance of this class is frozen, ``encode`` can no longer be called. """ if not self._frozen: - self._qubit_op = self._qubit_op.simplify() + self._qubit_op = self._qubit_op.simplify(atol=0) self._frozen = True @property From f76c50bec84eba96e8b9b3b95516ef724a4b9f5b Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 2 Jun 2023 12:57:17 +0900 Subject: [PATCH 38/67] rerun tutorial --- .../13_quantum_random_access_optimizer.ipynb | 88 ++++++++----------- 1 file changed, 35 insertions(+), 53 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 4f6bff504..a9d632c8f 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -65,27 +65,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "\\ This file has been generated by DOcplex\n", - "\\ ENCODING=ISO-8859-1\n", - "\\Problem name: Max-cut\n", + "Problem name: Max-cut\n", "\n", "Maximize\n", - " obj: 3 x_0 + 3 x_1 + 3 x_2 + 3 x_3 + 3 x_4 + 3 x_5 + [ - 4 x_0*x_1 - 4 x_0*x_3\n", - " - 4 x_0*x_4 - 4 x_1*x_2 - 4 x_1*x_5 - 4 x_2*x_3 - 4 x_2*x_4 - 4 x_3*x_5\n", - " - 4 x_4*x_5 ]/2\n", - "Subject To\n", + " -2*x_0*x_1 - 2*x_0*x_3 - 2*x_0*x_4 - 2*x_1*x_2 - 2*x_1*x_5 - 2*x_2*x_3\n", + " - 2*x_2*x_4 - 2*x_3*x_5 - 2*x_4*x_5 + 3*x_0 + 3*x_1 + 3*x_2 + 3*x_3 + 3*x_4\n", + " + 3*x_5\n", "\n", - "Bounds\n", - " 0 <= x_0 <= 1\n", - " 0 <= x_1 <= 1\n", - " 0 <= x_2 <= 1\n", - " 0 <= x_3 <= 1\n", - " 0 <= x_4 <= 1\n", - " 0 <= x_5 <= 1\n", + "Subject to\n", + " No constraints\n", "\n", - "Binaries\n", - " x_0 x_1 x_2 x_3 x_4 x_5\n", - "End\n", + " Binary variables (6)\n", + " x_0 x_1 x_2 x_3 x_4 x_5\n", "\n" ] }, @@ -239,8 +230,8 @@ "output_type": "stream", "text": [ "The objective function value: 5.0\n", - "x: [0 1 1 0 0 1]\n", - "relaxed function value: 8.99999997332078\n", + "x: [0 1 1 0 1 0]\n", + "relaxed function value: 8.999999983259919\n", "\n" ] } @@ -279,7 +270,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [0 3 4] and nodes [1 2 5].\n" + "The obtained solution places a partition between nodes [0 3 5] and nodes [1 2 4].\n" ] } ], @@ -315,7 +306,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -345,7 +336,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([0, 1, 1, 0, 0, 1]), fval=5.0, probability=1.0, status=)]" + "[SolutionSample(x=array([0, 1, 1, 0, 1, 0]), fval=5.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -480,7 +471,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999994026908825\n", + "relaxed function value: 8.999998136072591\n", "\n" ] } @@ -514,16 +505,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0093, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.011, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.02, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0209, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.022200000000000004, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0204, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.021, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0222, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0192, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0202, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.009500000000000001, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.011300000000000001, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0188, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0198, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0205, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0215, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0201, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0212, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0211, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0223, status=)\n" ] } ], @@ -593,7 +584,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.99999708840069\n", + "relaxed function value: -8.99999274486882\n", "The number of distinct samples is 1.\n" ] } @@ -625,7 +616,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.99999708840069\n", + "relaxed function value: -8.99999274486882\n", "The number of distinct samples is 56.\n" ] } @@ -666,27 +657,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "\\ This file has been generated by DOcplex\n", - "\\ ENCODING=ISO-8859-1\n", - "\\Problem name: Max-cut\n", + "Problem name: Max-cut\n", "\n", "Maximize\n", - " obj: 3 x_0 + 3 x_1 + 3 x_2 + 3 x_3 + 3 x_4 + 3 x_5 + [ - 4 x_0*x_1 - 4 x_0*x_3\n", - " - 4 x_0*x_4 - 4 x_1*x_2 - 4 x_1*x_5 - 4 x_2*x_3 - 4 x_2*x_4 - 4 x_3*x_5\n", - " - 4 x_4*x_5 ]/2\n", - "Subject To\n", + " -2*x_0*x_1 - 2*x_0*x_3 - 2*x_0*x_4 - 2*x_1*x_2 - 2*x_1*x_5 - 2*x_2*x_3\n", + " - 2*x_2*x_4 - 2*x_3*x_5 - 2*x_4*x_5 + 3*x_0 + 3*x_1 + 3*x_2 + 3*x_3 + 3*x_4\n", + " + 3*x_5\n", "\n", - "Bounds\n", - " 0 <= x_0 <= 1\n", - " 0 <= x_1 <= 1\n", - " 0 <= x_2 <= 1\n", - " 0 <= x_3 <= 1\n", - " 0 <= x_4 <= 1\n", - " 0 <= x_5 <= 1\n", + "Subject to\n", + " No constraints\n", "\n", - "Binaries\n", - " x_0 x_1 x_2 x_3 x_4 x_5\n", - "End\n", + " Binary variables (6)\n", + " x_0 x_1 x_2 x_3 x_4 x_5\n", "\n" ] }, @@ -795,7 +777,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.23.3
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed May 24 19:17:18 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.25.0.dev0+788b89d
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Fri Jun 02 12:56:21 2023 JST
" ], "text/plain": [ "" From 02c0a7c4233368cbce34d3420cd2ce6970b5e306 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 5 Jun 2023 17:26:32 +0900 Subject: [PATCH 39/67] add unittests for max per qubit= 2 and 1 --- .../qrao/quantum_random_access_encoding.py | 2 +- .../algorithms/qrao/rounding_common.py | 2 +- test/algorithms/qrao/test_magic_rounding.py | 190 +++++++++++++++++- 3 files changed, 187 insertions(+), 7 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 69e2ae6c8..5d57c9c2f 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -73,7 +73,7 @@ def _z_to_21p_qrac_basis_circuit(bases: list[int], bit_flip: int = 0) -> Quantum Raises: ValueError: if the basis is not 0 or 1 """ - circ = QuantumCircuit(1) + circ = QuantumCircuit(len(bases)) for i, base in enumerate(reversed(bases)): if bit_flip: diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index cbb04ce83..3d9562897 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -47,7 +47,7 @@ class RoundingContext: encoding: QuantumRandomAccessEncoding """Encoding containing the problem information.""" - expectation_values: list[float] + expectation_values: list[float] | None = None """Expectation values for the relaxed Hamiltonian.""" circuit: QuantumCircuit | None = None """Circuit corresponding to the encoding and expectation values.""" diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index a85f573c5..45eaa5107 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -15,6 +15,7 @@ from test.optimization_test_case import QiskitOptimizationTestCase import numpy as np +from qiskit.circuit import QuantumCircuit from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver from qiskit.primitives import Sampler @@ -23,6 +24,7 @@ QuantumRandomAccessEncoding, QuantumRandomAccessOptimizer, RoundingResult, + RoundingContext, ) from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.problems import QuadraticProgram @@ -59,8 +61,150 @@ def test_magic_rounding_constructor(self): with self.assertRaises(ValueError): MagicRounding(sampler, basis_sampling="invalid") - def test_magic_rounding_round_uniform(self): - """Test round method with uniform basis sampling""" + def test_magic_rounding_round_uniform_1_1_qrac(self): + """Test round method with uniform basis sampling for max_vars_per_qubit=1""" + sampler = Sampler(options={"shots": 10000, "seed": 42}) + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=1) + encoding.encode(self.problem) + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + _, rounding_context = qrao.solve_relaxed(encoding=encoding) + magic_rounding = MagicRounding(sampler, seed=42) + rounding_result = magic_rounding.round(rounding_context) + self.assertIsInstance(rounding_result, RoundingResult) + np.testing.assert_allclose(rounding_result.bases, [[0, 0, 0]]) + np.testing.assert_allclose(rounding_result.basis_shots, [10000]) + expected_basis_counts = [{"000": 10000}] + for i, basis_counts in enumerate(rounding_result.basis_counts): + for key, value in basis_counts.items(): + self.assertAlmostEqual(value, expected_basis_counts[i][key], delta=50) + samples = rounding_result.samples + samples.sort(key=lambda sample: np.array2string(sample.x)) + expected_samples = [ + make_solution_sample(x=np.array([0, 0, 0]), probability=1, problem=self.problem), + ] + for i, sample in enumerate(samples): + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.05) + np.testing.assert_allclose( + rounding_result.expectation_values, + [1, 1, 1], + ) + + def test_magic_rounding_round_weighted_1_1_qrac(self): + """Test round method with uniform basis sampling for max_vars_per_qubit=1""" + sampler = Sampler(options={"shots": 10000, "seed": 42}) + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=1) + encoding.encode(self.problem) + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + _, rounding_context = qrao.solve_relaxed(encoding=encoding) + magic_rounding = MagicRounding(sampler, basis_sampling="weighted", seed=42) + rounding_result = magic_rounding.round(rounding_context) + self.assertIsInstance(rounding_result, RoundingResult) + np.testing.assert_allclose(rounding_result.bases, [[0, 0, 0]]) + np.testing.assert_allclose(rounding_result.basis_shots, [10000]) + expected_basis_counts = [{"000": 10000}] + for i, basis_counts in enumerate(rounding_result.basis_counts): + for key, value in basis_counts.items(): + self.assertAlmostEqual(value, expected_basis_counts[i][key], delta=50) + samples = rounding_result.samples + samples.sort(key=lambda sample: np.array2string(sample.x)) + expected_samples = [ + make_solution_sample(x=np.array([0, 0, 0]), probability=1, problem=self.problem), + ] + for i, sample in enumerate(samples): + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.05) + np.testing.assert_allclose( + rounding_result.expectation_values, + [1, 1, 1], + ) + + def test_magic_rounding_round_uniform_2_1_qrac(self): + """Test round method with uniform basis sampling for max_vars_per_qubit=2""" + sampler = Sampler(options={"shots": 10000, "seed": 42}) + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=2) + encoding.encode(self.problem) + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + _, rounding_context = qrao.solve_relaxed(encoding=encoding) + magic_rounding = MagicRounding(sampler, seed=42) + rounding_result = magic_rounding.round(rounding_context) + self.assertIsInstance(rounding_result, RoundingResult) + np.testing.assert_allclose(rounding_result.bases, [[0, 0], [0, 1], [1, 0], [1, 1]]) + np.testing.assert_allclose(rounding_result.basis_shots, [2575, 2482, 2440, 2503]) + expected_basis_counts = [ + {"00": 2154.0, "01": 367, "10": 44.0, "11": 10.0}, + {"00": 2076.0, "01": 357.0, "10": 45.0, "11": 4.0}, + {"00": 689.0, "01": 137.0, "10": 1401.0, "11": 213.0}, + {"00": 708.0, "01": 110.0, "10": 1446.0, "11": 239.0}, + ] + for i, basis_counts in enumerate(rounding_result.basis_counts): + for key, value in basis_counts.items(): + self.assertAlmostEqual(value, expected_basis_counts[i][key], delta=50) + samples = rounding_result.samples + samples.sort(key=lambda sample: np.array2string(sample.x)) + expected_samples = [ + make_solution_sample(x=np.array([0, 0, 0]), probability=0.423, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.0724, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.1397, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0247, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.2847, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0452, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.0089, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.0014, problem=self.problem), + ] + for i, sample in enumerate(samples): + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.05) + np.testing.assert_allclose( + rounding_result.expectation_values, + [0.44721359549995743, 0.8944271909999162, 1], + ) + + def test_magic_rounding_round_weighted_2_1_qrac(self): + """Test round method with weighted basis sampling for max_vars_per_qubit=2""" + sampler = Sampler(options={"shots": 10000, "seed": 42}) + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=2) + encoding.encode(self.problem) + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + _, rounding_context = qrao.solve_relaxed(encoding=encoding) + magic_rounding = MagicRounding(sampler, basis_sampling="weighted", seed=42) + rounding_result = magic_rounding.round(rounding_context) + self.assertIsInstance(rounding_result, RoundingResult) + np.testing.assert_allclose(rounding_result.bases, [[0, 0], [1, 0]]) + np.testing.assert_allclose(rounding_result.basis_shots, [7058, 2942]) + expected_basis_counts = [ + {"00": 5858.0, "01": 1036.0, "10": 137.0, "11": 27.0}, + {"00": 832.0, "01": 131.0, "10": 1698.0, "11": 281.0}, + ] + for i, basis_counts in enumerate(rounding_result.basis_counts): + for key, value in basis_counts.items(): + self.assertAlmostEqual(value, expected_basis_counts[i][key], delta=50) + samples = rounding_result.samples + samples.sort(key=lambda sample: np.array2string(sample.x)) + expected_samples = [ + make_solution_sample(x=np.array([0, 0, 0]), probability=0.5858, problem=self.problem), + make_solution_sample(x=np.array([0, 0, 1]), probability=0.1036, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 0]), probability=0.0832, problem=self.problem), + make_solution_sample(x=np.array([0, 1, 1]), probability=0.0131, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 0]), probability=0.1698, problem=self.problem), + make_solution_sample(x=np.array([1, 0, 1]), probability=0.0281, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 0]), probability=0.0137, problem=self.problem), + make_solution_sample(x=np.array([1, 1, 1]), probability=0.0027, problem=self.problem), + ] + for i, sample in enumerate(samples): + np.testing.assert_allclose(sample.x, expected_samples[i].x) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.05) + np.testing.assert_allclose( + rounding_result.expectation_values, + [0.44721359549995743, 0.8944271909999162, 1], + ) + + def test_magic_rounding_round_uniform_3_1_qrac(self): + """Test round method with uniform basis sampling for max_vars_per_qubit=3""" sampler = Sampler(options={"shots": 10000, "seed": 42}) encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) encoding.encode(self.problem) @@ -95,14 +239,14 @@ def test_magic_rounding_round_uniform(self): ] for i, sample in enumerate(samples): np.testing.assert_allclose(sample.x, expected_samples[i].x) - self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.005) + self.assertAlmostEqual(sample.probability, expected_samples[i].probability, delta=0.05) np.testing.assert_allclose( rounding_result.expectation_values, [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], ) - def test_magic_rounding_round_weighted(self): - """Test round method with weighted basis sampling""" + def test_magic_rounding_round_weighted_3_1_qrac(self): + """Test round method with weighted basis sampling for max_vars_per_qubit=3""" encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) encoding.encode(self.problem) np_solver = NumPyMinimumEigensolver() @@ -143,6 +287,42 @@ def test_magic_rounding_round_weighted(self): [0.2672612419124245, 0.5345224838248487, 0.8017837257372733], ) + def test_magic_rounding_exceptions(self): + """Test exceptions in the MagicRounding class""" + encoding = QuantumRandomAccessEncoding(max_vars_per_qubit=3) + encoding.encode(self.problem) + + with self.assertRaises(ValueError): + # circuit is None + sampler = Sampler(options={"shots": 10000, "seed": 42}) + magic_rounding = MagicRounding(sampler=sampler) + rounding_context = RoundingContext(encoding, expectation_values=[1, 1, 1], circuit=None) + magic_rounding.round(rounding_context) + + with self.assertRaises(ValueError): + # sampler without shots + sampler = Sampler() + magic_rounding = MagicRounding(sampler=sampler) + rounding_context = RoundingContext( + encoding, expectation_values=[1, 1, 1], circuit=QuantumCircuit(1) + ) + magic_rounding.round(rounding_context) + + with self.assertRaises(ValueError): + # expectation_values is None for weighted basis sampling + sampler = Sampler() + magic_rounding = MagicRounding(sampler=sampler, basis_sampling="weighted") + rounding_context = RoundingContext( + encoding, expectation_values=None, circuit=QuantumCircuit(1) + ) + magic_rounding.round(rounding_context) + + with self.assertRaises(ValueError): + # vars_per_qubit is invalid + sampler = Sampler(options={"shots": 10000, "seed": 42}) + magic_rounding = MagicRounding(sampler=sampler) + magic_rounding._make_circuits(circuit=QuantumCircuit(1), bases=[[0]], vars_per_qubit=4) + def make_solution_sample( x: np.ndarray, probability: float, problem: QuadraticProgram From 3523a447d45f49ebd20712abea029e851872d4c4 Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Wed, 7 Jun 2023 15:59:55 +0900 Subject: [PATCH 40/67] Update docs/tutorials/13_quantum_random_access_optimizer.ipynb Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com> --- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index a9d632c8f..f12c3c994 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -53,7 +53,7 @@ "Note that once our problem is represented as a `QuadraticProgram`, it needs to be converted into the appropriate format for QRAO, which is a [quadratic unconstrained binary optimization (QUBO)](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization) problem. While a `QuadraticProgram` generated by `Maxcut` is already in QUBO form, if you define your own problem, make sure to convert it into a QUBO before proceeding. You can refer to this [tutorial](https://qiskit.org/documentation/optimization/tutorials/02_converters_for_quadratic_programs.html) for guidance on converting QuadraticPrograms.\n", "\n", "Note that once our problem has been represented as a `QuadraticProgram`, it will need to be converted to the correct type, a [quadratic unconstrained binary optimization (QUBO)](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization) problem, so that it is compatible with QRAO.\n", - "A `QuadraticProgram` generated by `Maxcut`is already a QUBO, but if you define your own problem be sure you convert it to a QUBO before proceeding. Here is [a tutorial](https://qiskit.org/documentation/optimization/tutorials/02_converters_for_quadratic_programs.html) on converting `QuadraticPrograms`." + "A `QuadraticProgram` generated by `Maxcut` is already a QUBO, but if you define your own problem be sure you convert it to a QUBO before proceeding. Here is [a tutorial](https://qiskit.org/documentation/optimization/tutorials/02_converters_for_quadratic_programs.html) on converting `QuadraticPrograms`." ] }, { From a8be7b44abea8828ed87985ef46c4b8a728e2970 Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Wed, 7 Jun 2023 16:00:48 +0900 Subject: [PATCH 41/67] Update docs/tutorials/13_quantum_random_access_optimizer.ipynb Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com> --- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index f12c3c994..c547998a1 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -217,7 +217,7 @@ "The result is provides us as a `QuantumRandomAccessOptimizationResult`.\n", "The `x` contains the binary values representing the best solution found, while the `fval` contains the corresponding objective value.\n", "\n", - "The `relaxed_fval` provides the expectation value of the relaxed Hamiltonian, adjusted to be in the units of the original optimization problem. For maximization problems, the best possible relaxed function value will always be greater than or equal to the best possible function value of the original problem. In practice, this often holds true for the best found value and best found function value as well." + "The `relaxed_fval` provides the expectation value of the relaxed Hamiltonian, adjusted to be in the units of the original optimization problem. For maximization problems, the best possible relaxed function value will always be greater than or equal to the best possible objective function value of the original problem. In practice, this often holds true for the best found value and best found objective function value as well." ] }, { From 1e8bc6f553ca3cf044d04cb38616df4610be7b93 Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Wed, 7 Jun 2023 16:01:32 +0900 Subject: [PATCH 42/67] Update docs/tutorials/13_quantum_random_access_optimizer.ipynb Co-authored-by: Takashi Imamichi <31178928+t-imamichi@users.noreply.github.com> --- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index c547998a1..93c6ce4a1 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -420,7 +420,7 @@ "## Solve the problem using the `QuantumRandomAccessOptimizer` with `MagicRounding`\n", "\n", "Magic rounding is a quantum technique employed to map the ground state results of our encoded Hamiltonian back to a solution of the original problem. Unlike semi-deterministic rounding, magic rounding requires a quantum backend, which can be either hardware or a simulator. \n", - "The backend is passed to the MagicRounding class through a `Sampler`, which also determines the total number of shots (samples) that magic rounding will utilize. Note that to specify the backend, you need to choose a `Sampler` from providers such as Aer or IBM Runtime. Consequently, we need to specify `Estimator` and `Sampler` for the optimizer and the rounding scheme, respectively.\n", + "The backend is passed to the `MagicRounding` class through a `Sampler`, which also determines the total number of shots (samples) that magic rounding will utilize. Note that to specify the backend, you need to choose a `Sampler` from providers such as Aer or IBM Runtime. Consequently, we need to specify `Estimator` and `Sampler` for the optimizer and the rounding scheme, respectively.\n", "\n", "In practice, users may choose to set a significantly higher number of magic rounding shots compared to the shots used by the minimum eigensolver for the relaxed problem. This difference arises because the minimum eigensolver estimates expectation values, while the magic rounding scheme returns the sample corresponding to the maximum function value found. The number of magic rounding shots directly impacts the diversity of the computational basis we can generate.\n", "When estimating an expectation value, increasing the number of shots enhances the convergence to the true value. However, when aiming to identify the largest possible function value, we often sample from the tail of a distribution of outcomes. As a result, until we observe the highest value outcome in our distribution, each additional shot increases the expected return value.\n", From dfde28bc5230643c9e62dac7d19db137202324a4 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 7 Jun 2023 17:00:12 +0900 Subject: [PATCH 43/67] fix docs --- .../{qrao_explanations.rst => qrao.rst} | 67 ++++++++++-------- .../13_quantum_random_access_optimizer.ipynb | 68 +++++++++++-------- 2 files changed, 77 insertions(+), 58 deletions(-) rename docs/explanations/{qrao_explanations.rst => qrao.rst} (85%) diff --git a/docs/explanations/qrao_explanations.rst b/docs/explanations/qrao.rst similarity index 85% rename from docs/explanations/qrao_explanations.rst rename to docs/explanations/qrao.rst index 11e2fe5b8..04cd65e38 100644 --- a/docs/explanations/qrao_explanations.rst +++ b/docs/explanations/qrao.rst @@ -8,7 +8,7 @@ Relaxations ----------- Consider a binary optimization problem defined on binary variables -:math:`m_i \in \\{-1,1\\}`. The choice of using :math:`\pm 1` variables +:math:`m_i \in \{-1,1\}`. The choice of using :math:`\pm 1` variables instead of :math:`0/1` variables is not important, but will be convenient in terms of notation when we begin to re-cast this problem in terms of quantum observables. We will be primarily interested in @@ -44,7 +44,7 @@ function defined on a graph :math:`G = (V,E)`. Our goal is to find a partitioning of our vertices :math:`V` into two sets (:math:`+1` and :math:`-1`), such that we maximize the number of edges which connect both sets. More concretely, each :math:`v_i \in V` will be assigned a -binary variable :math:`m_i \in \\{0,1\\}`, and we will define the *cut* +binary variable :math:`m_i \in \{-1, 1\}`, and we will define the *cut* of a variable assignment as: .. math:: \text{cut}(m) = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-m_i m_j) @@ -58,7 +58,7 @@ the space of single qubit Pauli observables and by embedding the set of feasible inputs to cut(:math:`m`) onto the space of single-qubit quantum product states. Let us denote this embedding :math:`F` as: -.. math:: F: \\{-1,1\\}^{M} \mapsto \mathcal{D}(\mathbb{C}^{2^n}), +.. math:: F: \{-1,1\}^{M} \mapsto \mathcal{D}(\mathbb{C}^{2^n}), .. math:: \text{cut}(m) \mapsto \text{Tr}\big(H\cdot F(m)\big), @@ -69,12 +69,12 @@ For this to be `a valid relaxation `__ of our problem, it must be the case that: -.. math:: \text{cut}(m) \geq \text{Tr}\big(H\cdot F(m)\big)\qquad \forall m \in \\{-1,1\\}^M. +.. math:: \text{cut}(m) \geq \text{Tr}\big(H\cdot F(m)\big)\qquad \forall m \in \{-1,1\}^M. In order to guarantee this is true, we will enforce the stronger condition that our relaxation **commutes** with our objective function. In other words, cut(:math:`m`) is equal to the relaxed objective -function for all :math:`m \in \\{-1,1\\}^M`, rather than simply upper +function for all :math:`m \in \{-1,1\}^M`, rather than simply upper bounding it. This detail will become crucially important further down when we explicitly define our quantum relaxation. @@ -90,23 +90,23 @@ quantum relaxation and rounding. Consider the embedding -.. math:: F^{(1)}: m \in \\{-1,1\\}^M \mapsto \\{|0\rangle,|1\rangle\\}^{\otimes M}, +.. math:: F^{(1)}: m \in \{-1,1\}^M \mapsto \{|0\rangle,|1\rangle\}^{\otimes M}, .. math:: \text{cut}(m) \mapsto \text{Tr}\big(H^{(1)}F^{(1)}(m)\big),\quad H^{(1)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-Z_i Z_j), where :math:`Z_i` indicates the single qubit Pauli-Z observable defined -on the :math:`i`\ ’th qubit and Identity terms on all other qubits. It +on the :math:`i`\ ’th qubit and identity terms on all other qubits. It is worth convincing yourself that this transformation is a valid relaxation of our problem. In particular: -.. math:: \text{cut}(m) = \text{Tr}\big(H^{(1)}F^{(1)}(m)\big) \quad \forall m \in \\{-1,1\\}^M +.. math:: \text{cut}(m) = \text{Tr}\big(H^{(1)}F^{(1)}(m)\big) \quad \forall m \in \{-1,1\}^M This sort of embedding is currently used by many near-term quantum optimization algorithms, including many `QAOA and VQE based approaches `__. Observe how although the relaxed version of our problem can exactly reproduce the objective function cut(:math:`m`) for inputs of the form -:math:`\\{|0\rangle,|1\rangle\\}^{\otimes M}`, we are also free to +:math:`\{|0\rangle,|1\rangle\}^{\otimes M}`, we are also free to evaluate :math:`H^{(1)}` using a continuous superposition of such states. This stands in analogy to how one might classically relax an optimization problem such that they optimize the objective function @@ -142,7 +142,9 @@ by performing some measurement. The simple quantum relaxation discussed in the previous section is an example of a trivial :math:`(1,1,1)`-QRAC. For convenience, we will write the :math:`(2,1,0.854)` and :math:`(3,1,0.789)` QRACs as :math:`(2,1,p)` and :math:`(3,1,p)`, -respectively. +respectively. It is worth noting :math:`(4, 1, p)`-QRAC :math:`(p > 1/2)` +has been `proven to be impossible. +[3] `__ As we generalize the simple example above, it will be helpful to write out single qubit states decomposed in the Hermitian basis of Pauli @@ -158,24 +160,24 @@ associated respectively with the :math:`(1,1,1), (2,1,p),` and \begin{array}{l|ll} \text{QRAC} & &\text{Embedding into } \rho = \vert \psi(m)\rangle\langle\psi(m)\vert \\ \hline - (1,1,1)\qquad &F^{(1)}(m): \\{-1,1\\} &\mapsto\ \vert\psi^{(1)}_m\rangle \langle\psi^{(1)}_m\vert = \frac{1}{2}\Big(I + {m_0}Z \Big) \\ - (2,1,p)\qquad &F^{(2)}(m): \\{-1,1\\}^2 &\mapsto\ \vert\psi^{(2)}_m\rangle \langle\psi^{(2)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{2}}\big({m_0}X+ {m_1}Z \big)\right) \\ - (3,1,p)\qquad &F^{(3)}(m): \\{-1,1\\}^3 &\mapsto\ \vert\psi^{(3)}_m\rangle \langle\psi^{(3)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{3}}\big({m_0}X+ {m_1}Y + {m_2}Z\big)\right) \\ \end{array} + (1,1,1)\qquad &F^{(1)}(m): \{-1,1\} &\mapsto\ \vert\psi^{(1)}_m\rangle \langle\psi^{(1)}_m\vert = \frac{1}{2}\Big(I + {m_0}Z \Big) \\ + (2,1,p)\qquad &F^{(2)}(m): \{-1,1\}^2 &\mapsto\ \vert\psi^{(2)}_m\rangle \langle\psi^{(2)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{2}}\big({m_0}X+ {m_1}Z \big)\right) \\ + (3,1,p)\qquad &F^{(3)}(m): \{-1,1\}^3 &\mapsto\ \vert\psi^{(3)}_m\rangle \langle\psi^{(3)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{3}}\big({m_0}X+ {m_1}Y + {m_2}Z\big)\right) \\ \end{array} .. math:: \text{Table 1: Explicit QRAC States} Note that for when using a :math:`(k,1,p)`-QRAC with bit strings -:math:`m \in \\{-1,1\\}^M, M > k`, these embeddings scale naturally via +:math:`m \in \{-1,1\}^M, M > k`, these embeddings scale naturally via composition by tensor product. -.. math:: m \in \\{-1,1\\}^6,\quad F^{(3)}(m) = F^{(3)}(m_0,m_1,m_2)\otimes F^{(3)}(m_3,m_4,m_5) +.. math:: m \in \{-1,1\}^6,\quad F^{(3)}(m) = F^{(3)}(m_0,m_1,m_2)\otimes F^{(3)}(m_3,m_4,m_5) Similarly, when :math:`k \nmid M`, we can simply pad our input bitstring with the appropriate number of :math:`+1` values. -.. math:: m \in \\{-1,1\\}^4,\quad F^{(3)}(m) = F^{(3)}(m_0,m_1,m_2)\otimes F^{(3)}(m_3,+1,+1) +.. math:: m \in \{-1,1\}^4,\quad F^{(3)}(m) = F^{(3)}(m_0,m_1,m_2)\otimes F^{(3)}(m_3,+1,+1) Recovering Encoded Bits ~~~~~~~~~~~~~~~~~~~~~~~ @@ -188,10 +190,10 @@ the QRAC. .. math:: \begin{array}{ll|l|l} - & \text{Embedding} & m_0 = & m_1 = & m_2 = &\\ + & \text{Embedding} & m_0 = & m_1 = & m_2 = &\ \hline - &\rho = F^{(1)}(m_0) &\text{Tr}\big(\rho Z\big) & & \\ - &\rho = F^{(2)}(m_0,m_1) &\sqrt{2}\cdot\text{Tr}\big(\rho X\big) &\sqrt{2}\cdot\text{Tr}\big(\rho Z\big) & \\ + &\rho = F^{(1)}(m_0) &\text{Tr}\big(\rho Z\big) & & \ + &\rho = F^{(2)}(m_0,m_1) &\sqrt{2}\cdot\text{Tr}\big(\rho X\big) &\sqrt{2}\cdot\text{Tr}\big(\rho Z\big) & \ &\rho = F^{(3)}(m_0,m_1,m_2) & \sqrt{3}\cdot\text{Tr}\big(\rho X\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Y\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Z\big) \end{array} @@ -210,11 +212,11 @@ observable that has been assigned to that variable under the embedding .. math:: - \begin{array}{l|ll} \text{QRAC} & \text{Problem Hamiltonian}\\ + \begin{array}{l|ll} \text{QRAC} & \text{Problem Hamiltonian}\ \hline (1,1,1)\qquad &H^{(1)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-Z_i Z_j)\\ - (2,1,p)\qquad &H^{(2)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-2\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \\{X,Z\\}\\ - (3,1,p)\qquad &H^{(3)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-3\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \\{X,Y,Z\\}\\ \end{array} + (2,1,p)\qquad &H^{(2)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-2\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \{X,Z\}\\ + (3,1,p)\qquad &H^{(3)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-3\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \{X,Y,Z\}\\ \end{array}   @@ -223,7 +225,7 @@ observable that has been assigned to that variable under the embedding Note that here, :math:`P_{[i]}` indicates a single-qubit Pauli observable corresponding to decision variable :math:`i`. The bracketed index here is to make clear that :math:`P_{[i]}` will not necessarily be -defined on qubit :math:`i`, because the :math:`(2,1,p)` and +acting on qubit :math:`i`, because the :math:`(2,1,p)` and :math:`(3,1,p)` no longer have a 1:1 relationship between qubits and decision variables. @@ -240,11 +242,11 @@ ensure the commutativity condition discussed earlier Observe that under the :math:`(3,1,p)`-QRAC, any term in our objective function of the form :math:`(1 - x_i x_j)` will map to a Hamiltonian term of the form :math:`(1-3\cdot P_{[i]} P_{[j]})`. If both -:math:`P_{[i]}` and :math:`P_{[j]}` are defined on different qubits, +:math:`P_{[i]}` and :math:`P_{[j]}` are acting on different qubits, then :math:`P_{[i]}\cdot P_{[j]} = P_{[i]}\otimes P_{[j]}` and this term of our Hamiltonian will behave as we expect. -If however, :math:`P_{[i]}` and :math:`P_{[j]}` are defined on the same +If however, :math:`P_{[i]}` and :math:`P_{[j]}` are acting on the same qubit, the two Paulis will compose directly. Recall that the Pauli matrices form a group and are self-inverse, thus we can deduce that the product of two distinct Paulis will yield another element of the group @@ -274,7 +276,7 @@ we need a strategy for mapping :math:`\rho_\text{relax}` to the image of :math:`F` so that we may extract a solution to our original problem. In [1] there are two strategies proposed for rounding -:math:`\rho_\text{relax}` back to :math:`m \in \\{-1,1\\}^M`. +:math:`\rho_\text{relax}` back to :math:`m \in \{-1,1\}^M`. Semi-deterministic Rounding ~~~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -295,9 +297,9 @@ to the following rounding scheme. .. math:: - m_i = \left\\{\begin{array}{rl} + m_i = \left\{\begin{array}{rl} +1 & \text{Tr}(P_{[i]}\rho_\text{relax}) > 0 \\ - X \sim\\{-1,1\\} & \text{Tr}(P_{[i]}\rho_\text{relax}) = 0 \\ + X \sim\{-1,1\} & \text{Tr}(P_{[i]}\rho_\text{relax}) = 0 \\ -1 & \text{Tr}(P_{[i]}\rho_\text{relax}) < 0 \end{array}\right. @@ -316,14 +318,14 @@ Magic State Rounding :align: center :width: 100% - Figure 1: Three different encodings, the states and the measurement bases, of variables into a + Three different encodings, the states and the measurement bases, of variables into a single qubit. (a) One variable per qubit. (b) Two variables per qubit. (c) Three variables per qubit. Taken from `[1] `__. Rather than seeking to independently distinguish each :math:`m_i`, magic state rounding randomly selects a measurement basis which will perfectly distinguish a particular pair of orthogonal QRAC states -:math:`\\{ F(m), F(\bar m)\\}`, where :math:`\bar m` indicates that +:math:`\{ F(m), F(\bar m)\}`, where :math:`\bar m` indicates that every bit of :math:`m` has been flipped. Let :math:`\mathcal{M}` be the randomized rounding procedure which takes @@ -366,3 +368,8 @@ relaxations,” (2021), `arXiv:2111.03167 [2] Stephen Wiesner, “Conjugate coding,” SIGACT News, vol. 15, issue 1, pp. 78-88, 1983. `link `__ + +[3] Masahito Hayashi, Kazuo Iwama, Harumichi Nishimura, Rudy Raymond, and Shigeru Yamashita, +“(4,1)-Quantum random access coding does not exist—one qubit is not enough to recover +one of four bits,” New Journal of Physics, vol. 8, number 8, pp. 129, 2006. +`link `__ diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 93c6ce4a1..e483d79ef 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -115,7 +115,7 @@ "\n", "Once we have appropriately configured our problem, we proceed to encode it using the `QuantumRandomAccessEncoding` class from the `qrao` module. This encoding step allows us to generate a quantum Hamiltonian operator that represents our problem. In particular, we employ a Quantum Random Access Code (QRAC) to encode multiple classical binary variables (corresponding to the nodes of our max-cut graph) into each qubit.\n", "\n", - "It's important to note that the resulting \"relaxed\" Hamiltonian, produced by this encoding, will not be diagonal. This differs from the standard workflow in `qiskit-optimization`, which typically generates a diagonal (Ising) Hamiltonian suitable for optimization using a [`MinimumEigenOptimizer`](https://qiskit.org/documentation/optimization/tutorials/03_minimum_eigen_optimizer.html).\n", + "It's important to note that the resulting \"relaxed\" Hamiltonian, produced by this encoding, will not be diagonal. This differs from the standard workflow in `qiskit-optimization`, which typically generates a diagonal (Ising) Hamiltonian suitable for optimization using a `MinimumEigenOptimizer`. You can find a tutorial on the `MinimumEigenOptimizer` [here](https://qiskit.org/documentation/optimization/tutorials/03_minimum_eigen_optimizer.html).\n", "\n", "In our encoding process, we employ a $(3,1,p)-$QRAC, where each qubit can accommodate a maximum of 3 classical binary variables. The parameter $p$ represents the bit recovery probability achieved through measurement. Depending on the nature of the problem, some qubits may have fewer than 3 classical variables assigned to them. To evaluate the compression achieved, we can examine the `compression_ratio` attribute of the encoding, which provides the ratio between the number of original binary variables and the number of qubits used (at best, a factor of 3)." ] @@ -229,9 +229,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "The objective function value: 5.0\n", - "x: [0 1 1 0 1 0]\n", - "relaxed function value: 8.999999983259919\n", + "The objective function value: 9.0\n", + "x: [1 0 1 0 0 1]\n", + "relaxed function value: 8.999999969451725\n", "\n" ] } @@ -270,17 +270,27 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [0 3 5] and nodes [1 2 4].\n" + "The obtained solution places a partition between nodes [1, 3, 4] and nodes [0, 2, 5].\n" ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ - "import numpy as np\n", - "\n", + "maxcut_partition = maxcut.interpret(results)\n", "print(\n", - " f\"The obtained solution places a partition between nodes {np.where(results.x == 0)[0]} \"\n", - " f\"and nodes {np.where(results.x == 1)[0]}.\"\n", - ")" + " f\"The obtained solution places a partition between nodes {maxcut_partition[0]} \"\n", + " f\"and nodes {maxcut_partition[1]}.\"\n", + ")\n", + "maxcut.draw(results, pos=nx.spring_layout(graph, seed=seed))" ] }, { @@ -295,7 +305,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The [`MinimumEigensolverResult`](https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html) that results from performing VQE on the relaxed Hamiltonian is available:" + "The `MinimumEigensolverResult` ([details](https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html)) that results from performing VQE on the relaxed Hamiltonian is available:" ] }, { @@ -306,7 +316,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -336,7 +346,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([0, 1, 1, 0, 1, 0]), fval=5.0, probability=1.0, status=)]" + "[SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -385,10 +395,11 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "The approximation ratio (QRAO's approximate optimal function value divided by the exact optimal function value) tells us how closely QRAO approximated the optimal solution to the problem." + "The approximation ratio (QRAO's objective function value divided by the optimal objective function value) tells us how closely QRAO approximated the optimal solution to the problem." ] }, { @@ -400,9 +411,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "QRAO Approximate Optimal Function Value: 5.0\n", + "QRAO Approximate Optimal Function Value: 9.0\n", "Exact Optimal Function Value: 9.0\n", - "Approximation Ratio: 0.56\n" + "Approximation Ratio: 1.00\n" ] } ], @@ -471,7 +482,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999998136072591\n", + "relaxed function value: 8.999994326560426\n", "\n" ] } @@ -505,16 +516,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.009500000000000001, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.011300000000000001, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0188, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0198, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0205, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0215, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.012100000000000001, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0097, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.021, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0222, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0219, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0201, status=)\n", "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0201, status=)\n", "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0212, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0211, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0223, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0199, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0209, status=)\n" ] } ], @@ -584,7 +595,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.99999274486882\n", + "relaxed function value: -8.999997502617678\n", "The number of distinct samples is 1.\n" ] } @@ -616,7 +627,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.99999274486882\n", + "relaxed function value: -8.999997502617678\n", "The number of distinct samples is 56.\n" ] } @@ -747,6 +758,7 @@ "metadata": {}, "outputs": [], "source": [ + "import numpy as np\n", "verifier = EncodingCommutationVerifier(encoding, estimator=Estimator())\n", "if not len(verifier) == 2**encoding.num_vars:\n", " print(\"The number results of the encoded problem is not equal to 2 ** num_vars.\")\n", @@ -777,7 +789,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.25.0.dev0+788b89d
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Fri Jun 02 12:56:21 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+8a52d88
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed Jun 07 16:59:56 2023 JST
" ], "text/plain": [ "" From cdc675d618a031881fa133d042f792f7f33c04b0 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 7 Jun 2023 17:17:43 +0900 Subject: [PATCH 44/67] lint --- .pylintdict | 2 ++ docs/explanations/qrao.rst | 2 +- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 3 ++- 3 files changed, 5 insertions(+), 2 deletions(-) diff --git a/.pylintdict b/.pylintdict index 604772c48..475fbf9a1 100644 --- a/.pylintdict +++ b/.pylintdict @@ -84,6 +84,7 @@ hamilton hamiltonian hamiltonians hastings +hayashi hoyer ibm ide @@ -111,6 +112,7 @@ lp lucas macos makefile +masahito matplotlib maxcut maxfun diff --git a/docs/explanations/qrao.rst b/docs/explanations/qrao.rst index 04cd65e38..20da84437 100644 --- a/docs/explanations/qrao.rst +++ b/docs/explanations/qrao.rst @@ -369,7 +369,7 @@ relaxations,” (2021), `arXiv:2111.03167 pp. 78-88, 1983. `link `__ -[3] Masahito Hayashi, Kazuo Iwama, Harumichi Nishimura, Rudy Raymond, and Shigeru Yamashita, +[3] Masahito Hayashi et al., “(4,1)-Quantum random access coding does not exist—one qubit is not enough to recover one of four bits,” New Journal of Physics, vol. 8, number 8, pp. 129, 2006. `link `__ diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index e483d79ef..ef1c26834 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -290,7 +290,7 @@ " f\"The obtained solution places a partition between nodes {maxcut_partition[0]} \"\n", " f\"and nodes {maxcut_partition[1]}.\"\n", ")\n", - "maxcut.draw(results, pos=nx.spring_layout(graph, seed=seed))" + "maxcut.draw(results, pos=nx.spring_layout(graph, seed=seed))" ] }, { @@ -759,6 +759,7 @@ "outputs": [], "source": [ "import numpy as np\n", + "\n", "verifier = EncodingCommutationVerifier(encoding, estimator=Estimator())\n", "if not len(verifier) == 2**encoding.num_vars:\n", " print(\"The number results of the encoded problem is not equal to 2 ** num_vars.\")\n", From 948152d87c8594e867398cab2e7fdee157e476ca Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 7 Jun 2023 21:55:29 +0900 Subject: [PATCH 45/67] add unittest quadratic objective --- .../test_quantum_random_access_encoding.py | 85 +++++++++++++++++++ 1 file changed, 85 insertions(+) diff --git a/test/algorithms/qrao/test_quantum_random_access_encoding.py b/test/algorithms/qrao/test_quantum_random_access_encoding.py index ded64f879..b15b680d6 100644 --- a/test/algorithms/qrao/test_quantum_random_access_encoding.py +++ b/test/algorithms/qrao/test_quantum_random_access_encoding.py @@ -41,6 +41,12 @@ def setUp(self): self.problem.binary_var("y") self.problem.binary_var("z") self.problem.minimize(linear={"x": 1, "y": 2, "z": 3}) + # quadratic objective + self.problem2 = QuadraticProgram() + self.problem2.binary_var("x") + self.problem2.binary_var("y") + self.problem2.binary_var("z") + self.problem2.maximize(linear={"x": 1, "y": 2, "z": 3}, quadratic={("y", "z"): -4}) def test_31p_qrac_encoding(self): """Test (3,1,p) QRAC""" @@ -70,6 +76,31 @@ def test_31p_qrac_encoding(self): self.assertEqual(encoding.minimum_recovery_probability, (1 + 1 / np.sqrt(3)) / 2) self.assertEqual(encoding.problem, self.problem) + def test_31p_qrac_encoding_quadratic(self): + """Test (3,1,p) QRAC""" + encoding = QuantumRandomAccessEncoding(3) + self.assertFalse(encoding.frozen) # frozen is False + encoding.encode(self.problem2) + expected_op = SparsePauliOp(["XI", "IX", "YX"], coeffs=[np.sqrt(3) / 2, np.sqrt(3) / 2, 3]) + self.assertTrue(encoding.frozen) # frozen is True + self.assertEqual(encoding.qubit_op, expected_op) + self.assertEqual(encoding.num_vars, 3) + self.assertEqual(encoding.num_qubits, 2) + self.assertEqual(encoding.offset, -2) + self.assertEqual(encoding.max_vars_per_qubit, 3) + self.assertEqual(encoding.q2vars, [[0, 1], [2]]) + self.assertEqual( + encoding.var2op, + { + 0: (0, SparsePauliOp(["X"], coeffs=[1.0])), + 1: (0, SparsePauliOp(["Y"], coeffs=[1.0])), + 2: (1, SparsePauliOp(["X"], coeffs=[1.0])), + }, + ) + self.assertEqual(encoding.compression_ratio, 1.5) + self.assertEqual(encoding.minimum_recovery_probability, (1 + 1 / np.sqrt(3)) / 2) + self.assertEqual(encoding.problem, self.problem2) + def test_21p_qrac_encoding(self): """Test (2,1,p) QRAC""" encoding = QuantumRandomAccessEncoding(2) @@ -98,6 +129,34 @@ def test_21p_qrac_encoding(self): self.assertEqual(encoding.minimum_recovery_probability, (1 + 1 / np.sqrt(2)) / 2) self.assertEqual(encoding.problem, self.problem) + def test_21p_qrac_encoding_quadratic(self): + """Test (2,1,p) QRAC""" + encoding = QuantumRandomAccessEncoding(2) + self.assertFalse(encoding.frozen) # frozen is False + encoding.encode(self.problem2) + expected_op = SparsePauliOp( + ["XI", "IX", "ZX"], + coeffs=[np.sqrt(2) / 2, np.sqrt(2) / 2, 2], + ) + self.assertTrue(encoding.frozen) # frozen is True + self.assertEqual(encoding.qubit_op, expected_op) + self.assertEqual(encoding.num_vars, 3) + self.assertEqual(encoding.num_qubits, 2) + self.assertEqual(encoding.offset, -2) + self.assertEqual(encoding.max_vars_per_qubit, 2) + self.assertEqual(encoding.q2vars, [[0, 1], [2]]) + self.assertEqual( + encoding.var2op, + { + 0: (0, SparsePauliOp(["X"], coeffs=[1.0])), + 1: (0, SparsePauliOp(["Z"], coeffs=[1.0])), + 2: (1, SparsePauliOp(["X"], coeffs=[1.0])), + }, + ) + self.assertEqual(encoding.compression_ratio, 1.5) + self.assertEqual(encoding.minimum_recovery_probability, (1 + 1 / np.sqrt(2)) / 2) + self.assertEqual(encoding.problem, self.problem2) + def test_11p_qrac_encoding(self): """Test (1,1,p) QRAC""" encoding = QuantumRandomAccessEncoding(1) @@ -124,6 +183,32 @@ def test_11p_qrac_encoding(self): self.assertEqual(encoding.minimum_recovery_probability, 1) self.assertEqual(encoding.problem, self.problem) + def test_11p_qrac_encoding_quadratic(self): + """Test (1,1,p) QRAC""" + encoding = QuantumRandomAccessEncoding(1) + self.assertFalse(encoding.frozen) # frozen is False + encoding.encode(self.problem2) + expected_op = SparsePauliOp(["ZII", "IIZ", "IZZ"], coeffs=[0.5, 0.5, 1]) + + self.assertTrue(encoding.frozen) # frozen is True + self.assertEqual(encoding.qubit_op, expected_op) + self.assertEqual(encoding.num_vars, 3) + self.assertEqual(encoding.num_qubits, 3) + self.assertEqual(encoding.offset, -2) + self.assertEqual(encoding.max_vars_per_qubit, 1) + self.assertEqual(encoding.q2vars, [[0], [1], [2]]) + self.assertEqual( + encoding.var2op, + { + 0: (0, SparsePauliOp(["Z"], coeffs=[1.0])), + 1: (1, SparsePauliOp(["Z"], coeffs=[1.0])), + 2: (2, SparsePauliOp(["Z"], coeffs=[1.0])), + }, + ) + self.assertEqual(encoding.compression_ratio, 1) + self.assertEqual(encoding.minimum_recovery_probability, 1) + self.assertEqual(encoding.problem, self.problem2) + def test_qrac_state_prep(self): """Test that state preparation circuit is correct""" dvars = [0, 1, 1] From e71f660650472545326b9a54398693ab084f4b63 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 7 Jun 2023 22:31:49 +0900 Subject: [PATCH 46/67] update optimizer unittest --- .../test_quantum_random_access_optimizer.py | 35 +++++++++++++++++++ 1 file changed, 35 insertions(+) diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py index dabe202d6..00fd08cf7 100644 --- a/test/algorithms/qrao/test_quantum_random_access_optimizer.py +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -147,6 +147,41 @@ def test_solve_numpy(self): self.assertAlmostEqual(results.rounding_result.expectation_values[2], 0.80178, places=5) self.assertIsInstance(results.rounding_result.samples[0], SolutionSample) + def test_solve_quadratic(self): + """Test QuantumRandomAccessOptimizer with a quadratic objective function.""" + # quadratic objective + problem2 = QuadraticProgram() + problem2.binary_var("x") + problem2.binary_var("y") + problem2.binary_var("z") + problem2.maximize(linear={"x": 1, "y": 2, "z": 3}, quadratic={("y", "z"): -4}) + np_solver = NumPyMinimumEigensolver() + qrao = QuantumRandomAccessOptimizer(min_eigen_solver=np_solver) + results = qrao.solve(problem2) + self.assertIsInstance(results, QuantumRandomAccessOptimizationResult) + self.assertEqual(results.fval, 4) + self.assertEqual(len(results.samples), 1) + np.testing.assert_array_almost_equal(results.samples[0].x, [1, 0, 1]) + self.assertAlmostEqual(results.samples[0].fval, 4) + self.assertAlmostEqual(results.samples[0].probability, 1.0) + self.assertEqual(results.samples[0].status, OptimizationResultStatus.SUCCESS) + self.assertAlmostEqual(results.relaxed_fval, -5.98852, places=5) + self.assertIsInstance(results.relaxed_result, NumPyMinimumEigensolverResult) + self.assertAlmostEqual(results.relaxed_result.eigenvalue, -3.98852, places=5) + self.assertEqual(len(results.relaxed_result.aux_operators_evaluated), 3) + self.assertAlmostEqual( + results.relaxed_result.aux_operators_evaluated[0][0], -0.27735, places=5 + ) + self.assertAlmostEqual( + results.relaxed_result.aux_operators_evaluated[1][0], 0.96077, places=5 + ) + self.assertAlmostEqual(results.relaxed_result.aux_operators_evaluated[2][0], -1, places=5) + self.assertIsInstance(results.rounding_result, RoundingResult) + self.assertAlmostEqual(results.rounding_result.expectation_values[0], -0.27735, places=5) + self.assertAlmostEqual(results.rounding_result.expectation_values[1], 0.96077, places=5) + self.assertAlmostEqual(results.rounding_result.expectation_values[2], -1, places=5) + self.assertIsInstance(results.rounding_result.samples[0], SolutionSample) + def test_empty_encoding(self): """Test the encoding is empty.""" np_solver = NumPyMinimumEigensolver() From 7b3c9e3317357b988f27a13ce3251d3bbd1dcbc1 Mon Sep 17 00:00:00 2001 From: Takashi Imamichi Date: Mon, 12 Jun 2023 14:37:33 +0900 Subject: [PATCH 47/67] replaces rustworkx with networkx - updates type cast --- qiskit_optimization/algorithms/qrao/__init__.py | 2 +- .../qrao/quantum_random_access_encoding.py | 16 ++++++++-------- .../algorithms/qrao/rounding_common.py | 1 - .../qrao/semideterministic_rounding.py | 7 ++----- 4 files changed, 11 insertions(+), 15 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index 6f07f8f93..85f758534 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -119,8 +119,8 @@ """ from .encoding_commutation_verifier import EncodingCommutationVerifier -from .quantum_random_access_encoding import QuantumRandomAccessEncoding from .magic_rounding import MagicRounding +from .quantum_random_access_encoding import QuantumRandomAccessEncoding from .quantum_random_access_optimizer import ( QuantumRandomAccessOptimizationResult, QuantumRandomAccessOptimizer, diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 5d57c9c2f..753759418 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -15,10 +15,10 @@ from collections import defaultdict from functools import reduce +from typing import cast +import networkx as nx import numpy as np -import rustworkx as rx - from qiskit import QuantumCircuit from qiskit.quantum_info import SparsePauliOp @@ -451,7 +451,7 @@ def _generate_ising_coefficients( # convert linear parts of the objective function into Hamiltonian. linear = np.zeros(num_vars) for idx, coef in problem.objective.linear.to_dict().items(): - idx = int(idx) # hint for mypy + idx = cast(int, idx) weight = coef * sense / 2 linear[idx] -= weight offset += weight @@ -459,8 +459,8 @@ def _generate_ising_coefficients( # convert quadratic parts of the objective function into Hamiltonian. quad = np.zeros((num_vars, num_vars)) for (i, j), coef in problem.objective.quadratic.to_dict().items(): - i = int(i) # hint for mypy - j = int(j) # hint for mypy + i = cast(int, i) + j = cast(int, j) weight = coef * sense / 4 if i == j: linear[i] -= 2 * weight @@ -486,10 +486,10 @@ def _find_variable_partition(quad: np.ndarray) -> dict[int, list[int]]: # pylint: disable=E1101 color2node: dict[int, list[int]] = defaultdict(list) num_nodes = quad.shape[0] - graph = rx.PyGraph() + graph = nx.Graph() graph.add_nodes_from(range(num_nodes)) - graph.add_edges_from_no_data(list(zip(*np.where(quad != 0)))) - node2color = rx.graph_greedy_color(graph) + graph.add_edges_from(list(zip(*np.where(quad != 0)))) + node2color = nx.greedy_color(graph) for node, color in sorted(node2color.items()): color2node[color].append(node) return color2node diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index 3d9562897..0aae64120 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -16,7 +16,6 @@ from dataclasses import dataclass import numpy as np - from qiskit.circuit import QuantumCircuit from qiskit_optimization.algorithms import SolutionSample diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 901469b6c..4d638c318 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -17,11 +17,8 @@ from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.exceptions import QiskitOptimizationError -from .rounding_common import ( - RoundingScheme, - RoundingContext, - RoundingResult, -) + +from .rounding_common import RoundingContext, RoundingResult, RoundingScheme class SemideterministicRounding(RoundingScheme): From 0d6e7cef48f4cf24a8b63a9702297072be0b6fe2 Mon Sep 17 00:00:00 2001 From: Takashi Imamichi Date: Mon, 12 Jun 2023 15:07:23 +0900 Subject: [PATCH 48/67] minor updates of explanation --- docs/explanations/qrao.rst | 46 ++++++++++++++++++-------------------- 1 file changed, 22 insertions(+), 24 deletions(-) diff --git a/docs/explanations/qrao.rst b/docs/explanations/qrao.rst index 20da84437..a06785b2a 100644 --- a/docs/explanations/qrao.rst +++ b/docs/explanations/qrao.rst @@ -158,15 +158,15 @@ associated respectively with the :math:`(1,1,1), (2,1,p),` and .. math:: - \begin{array}{l|ll} \text{QRAC} & &\text{Embedding into } \rho = \vert \psi(m)\rangle\langle\psi(m)\vert \\ + \begin{array}{l|ll} + \text{QRAC} & &\text{Embedding into } \rho = \vert \psi(m)\rangle\langle\psi(m)\vert \\ \hline - (1,1,1)\qquad &F^{(1)}(m): \{-1,1\} &\mapsto\ \vert\psi^{(1)}_m\rangle \langle\psi^{(1)}_m\vert = \frac{1}{2}\Big(I + {m_0}Z \Big) \\ - (2,1,p)\qquad &F^{(2)}(m): \{-1,1\}^2 &\mapsto\ \vert\psi^{(2)}_m\rangle \langle\psi^{(2)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{2}}\big({m_0}X+ {m_1}Z \big)\right) \\ - (3,1,p)\qquad &F^{(3)}(m): \{-1,1\}^3 &\mapsto\ \vert\psi^{(3)}_m\rangle \langle\psi^{(3)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{3}}\big({m_0}X+ {m_1}Y + {m_2}Z\big)\right) \\ \end{array} - - + (1,1,1)&F^{(1)}(m): \{-1,1\} &\mapsto\ \vert\psi^{(1)}_m\rangle \langle\psi^{(1)}_m\vert = \frac{1}{2}\Big(I + {m_0}Z \Big) \\ + (2,1,p)&F^{(2)}(m): \{-1,1\}^2 &\mapsto\ \vert\psi^{(2)}_m\rangle \langle\psi^{(2)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{2}}\big({m_0}X+ {m_1}Z \big)\right) \\ + (3,1,p)&F^{(3)}(m): \{-1,1\}^3 &\mapsto\ \vert\psi^{(3)}_m\rangle \langle\psi^{(3)}_m\vert = \frac{1}{2}\left(I + \frac{1}{\sqrt{3}}\big({m_0}X+ {m_1}Y + {m_2}Z\big)\right) \\ + \end{array} -.. math:: \text{Table 1: Explicit QRAC States} +.. math:: \text{Table 1: QRAC states} Note that for when using a :math:`(k,1,p)`-QRAC with bit strings :math:`m \in \{-1,1\}^M, M > k`, these embeddings scale naturally via @@ -189,17 +189,15 @@ the QRAC. .. math:: - \begin{array}{ll|l|l} - & \text{Embedding} & m_0 = & m_1 = & m_2 = &\ + \begin{array}{l|l|l|l} + \text{Embedding} & m_0 & m_1 & m_2\\ \hline - &\rho = F^{(1)}(m_0) &\text{Tr}\big(\rho Z\big) & & \ - &\rho = F^{(2)}(m_0,m_1) &\sqrt{2}\cdot\text{Tr}\big(\rho X\big) &\sqrt{2}\cdot\text{Tr}\big(\rho Z\big) & \ - &\rho = F^{(3)}(m_0,m_1,m_2) & \sqrt{3}\cdot\text{Tr}\big(\rho X\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Y\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Z\big) + \rho = F^{(1)}(m_0) &\text{Tr}\big(\rho Z\big) & & \\ + \rho = F^{(2)}(m_0,m_1) &\sqrt{2}\cdot\text{Tr}\big(\rho X\big) &\sqrt{2}\cdot\text{Tr}\big(\rho Z\big) & \\ + \rho = F^{(3)}(m_0,m_1,m_2) & \sqrt{3}\cdot\text{Tr}\big(\rho X\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Y\big) & \sqrt{3}\cdot\text{Tr}\big(\rho Z\big) \end{array} - - -.. math:: \text{Table 2: Bit recovery from QRAC States} +.. math:: \text{Table 2: Bit recovery from QRAC states} Encoded Problem Hamiltonians ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -212,15 +210,15 @@ observable that has been assigned to that variable under the embedding .. math:: - \begin{array}{l|ll} \text{QRAC} & \text{Problem Hamiltonian}\ + \begin{array}{l|ll} + \text{QRAC} & \text{Problem Hamiltonian}\\ \hline - (1,1,1)\qquad &H^{(1)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-Z_i Z_j)\\ - (2,1,p)\qquad &H^{(2)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-2\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \{X,Z\}\\ - (3,1,p)\qquad &H^{(3)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-3\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \{X,Y,Z\}\\ \end{array} - -  + (1,1,1)&H^{(1)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-Z_i Z_j)\\ + (2,1,p)&H^{(2)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-2\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \{X,Z\}\\ + (3,1,p)&H^{(3)} = \sum_{ij; e_{ij} \in E} \frac{1}{2}(1-3\cdot P_{[i]} P_{[j]}),\quad P_{[i]} \in \{X,Y,Z\}\\ + \end{array} -.. math:: \text{Table 3: Relaxed MaxCut Hamiltonians after QRAC Embedding} +.. math:: \text{Table 3: Relaxed MaxCut Hamiltonians after QRAC embedding} Note that here, :math:`P_{[i]}` indicates a single-qubit Pauli observable corresponding to decision variable :math:`i`. The bracketed @@ -353,9 +351,9 @@ magic state rounding does offer a lower bound on the approximation ratio under certain conditions. Let :math:`F(m^*)` be the highest energy state in the image of F, and -let :math:`\rho^\*` be the maximal eigenstate of H. +let :math:`\rho^*` be the maximal eigenstate of H. -.. math:: \forall \rho_\text{relax}\quad \text{st}\quad \text{Tr}\left(F(m^*)\cdot H\right) \leq \text{Tr}\left(\rho_\text{relax}\cdot H\right)\leq \text{Tr}\left(\rho^*\cdot H\right) +.. math:: \forall \rho_\text{relax}\quad \text{s.t.}\quad \text{Tr}\left(F(m^*)\cdot H\right) \leq \text{Tr}\left(\rho_\text{relax}\cdot H\right)\leq \text{Tr}\left(\rho^*\cdot H\right) .. math:: \frac{\text{expected fval}}{\text{optimal fval}} = \frac{\mathbb{E}\left[\text{Tr}\left(H\cdot \mathcal{M}^{\otimes n}(\rho_\text{relax})\right)\right]}{\text{Tr}\left(H\cdot F(m^*)\right)} \geq \frac{5}{9} From da4142ea7c1000373f67ae9697deebda1fcbacee Mon Sep 17 00:00:00 2001 From: Takashi Imamichi Date: Tue, 13 Jun 2023 23:03:12 +0900 Subject: [PATCH 49/67] fix docstrings --- .../algorithms/qrao/magic_rounding.py | 15 ++++++----- .../qrao/quantum_random_access_encoding.py | 15 ++++++----- .../qrao/quantum_random_access_optimizer.py | 27 +++++++++++-------- .../qrao/semideterministic_rounding.py | 2 +- 4 files changed, 34 insertions(+), 25 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index a8d27428f..8e7ab7cd3 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -36,7 +36,7 @@ class MagicRounding(RoundingScheme): to round the solution. Since the magic rounding is based on the measurement results, it requires a quantum backend, which can be either hardware or a simulator. - The details are described in https://arxiv.org/abs/2111.03167v2. + The details are described in https://arxiv.org/abs/2111.03167. """ _DECODING = { @@ -68,11 +68,11 @@ def __init__( basis_sampling: Method to use for sampling the magic bases. Must be either ``"uniform"`` (default) or ``"weighted"``. ``"uniform"`` samples all magic bases uniformly, and is the - method described in https://arxiv.org/abs/2111.03167v2. + method described in https://arxiv.org/abs/2111.03167. ``"weighted"`` attempts to choose bases strategically using the Pauli expectation values from the minimum eigensolver. However, the approximation bounds given in - https://arxiv.org/abs/2111.03167v2 apply only to ``"uniform"`` + https://arxiv.org/abs/2111.03167 apply only to ``"uniform"`` sampling. seed: Seed for random number generator, which is used to sample the magic bases. @@ -408,13 +408,15 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: if circuit is None: raise ValueError( - "Magic rounding requires a circuit to be available. Perhaps try " - "Semideterministic rounding instead." + "No circuit was provided in the rounding context. " + "Magic rounding requires a circuit to be available. " + "Perhaps try Semi-deterministic rounding instead." ) if self._sampler.options.get("shots") is None: raise ValueError( - "Magic rounding requires the sampler to be configured with a number of shots." + "No number of shots was provided in the rounding context. " + "Magic rounding requires a sampler configured with a number of shots." ) self._shots = self._sampler.options.shots @@ -425,6 +427,7 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: # weighted sampling if expectation_values is None: raise ValueError( + "No expectation values were provided in the rounding context. " "Magic rounding with weighted sampling requires the expectation values of the " "``RoundingContext`` to be available, but they are not." ) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py index 753759418..c438134f2 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_encoding.py @@ -126,7 +126,7 @@ def _qrac_state_prep_1q(bit_list: list[int]) -> QuantumCircuit: base_index0 = bit_list[1] ^ bit_list[2] base_index1 = bit_list[0] ^ bit_list[2] - # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf + # This is a convention chosen to be consistent with https://arxiv.org/abs/2111.03167 # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| base = [2 * base_index0 + base_index1] circ = _z_to_31p_qrac_basis_circuit(base, bit_flip) @@ -138,7 +138,7 @@ def _qrac_state_prep_1q(bit_list: list[int]) -> QuantumCircuit: # (00,11) or (01,10) base_index0 = bit_list[0] ^ bit_list[1] - # This is a convention chosen to be consistent with https://arxiv.org/pdf/2111.03167v2.pdf + # This is a convention chosen to be consistent with https://arxiv.org/abs/2111.03167 # # See SI:4 second paragraph and observe that π+ = |0X0|, π- = |1X1| base = [base_index0] circ = _z_to_21p_qrac_basis_circuit(base, bit_flip) @@ -224,10 +224,6 @@ class QuantumRandomAccessEncoding: the binary variables of a QUBO (quadratic unconstrained binary optimization problem). - Args: - max_vars_per_qubit: maximum possible compression ratio. - Supported values are 1, 2, or 3. - """ # This defines the convention of the Pauli operators (and their ordering) @@ -239,6 +235,11 @@ class QuantumRandomAccessEncoding: ) def __init__(self, max_vars_per_qubit: int = 3): + """ + Args: + max_vars_per_qubit: The maximum number of decision variables per qubit. + Integer values 1, 2 and 3 are supported (default to 3). + """ if max_vars_per_qubit not in (1, 2, 3): raise ValueError("max_vars_per_qubit must be 1, 2, or 3") self._ops = self._OPERATORS[max_vars_per_qubit - 1] @@ -396,7 +397,7 @@ def _add_term(self, w: float, *variables: int) -> None: weight: the coefficient for the term *variables: the list of variables for the term """ - # Eq. (31) in https://arxiv.org/abs/2111.03167v2 assumes a weight-2 + # Eq. (31) in https://arxiv.org/abs/2111.03167 assumes a weight-2 # Pauli operator. To generalize, we replace the `d` in that equation # with `d_prime`, defined as follows: d_prime = np.sqrt(self.max_vars_per_qubit) ** len(variables) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index f3fc7e064..31d84e62c 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -118,9 +118,10 @@ def __init__( Args: min_eigen_solver: The minimum eigensolver to use for solving the relaxed problem. max_vars_per_qubit: The maximum number of decision variables per qubit. + Integer values 1, 2 and 3 are supported (default to 3). rounding_scheme: The rounding scheme. If ``None`` is provided, - ``SemideterministicRounding()`` will be used. - penalty: The penalty factor to use for the ``QuadraticProgramToQubo`` converter. + :class:`~.SemideterministicRounding` will be used. + penalty: The penalty factor to use for the :class:`~.QuadraticProgramToQubo` converter. Raises: ValueError: If the maximum number of variables per qubit is not 1, 2, or 3. @@ -193,15 +194,19 @@ def solve_relaxed( ) -> tuple[MinimumEigensolverResult, RoundingContext]: """Solve the relaxed Hamiltonian given by the encoding. + .. note:: + This method uses the encoding instance given as ``encoding`` and + ignores :meth:`max_vars_per_qubit`. + Args: - encoding: The ``QuantumRandomAccessEncoding``, which must have already been ``encode()``ed - with a ``QuadraticProgram``. + encoding: An encoding instance for which :meth:`~QuantumRandomAccessEncoding.encode` + has already been called so it has been encoded with a :class:`~.QuadraticProgram`. Returns: The result of the minimum eigensolver, and the rounding context. Raises: - ValueError: If the encoding has not been encoded with a ``QuadraticProgram``. + ValueError: If the encoding has not been encoded with a :class:`~.QuadraticProgram`. """ if not encoding.frozen: raise ValueError( @@ -245,16 +250,16 @@ def solve_relaxed( def solve(self, problem: QuadraticProgram) -> QuantumRandomAccessOptimizationResult: """Solve the relaxed Hamiltonian given by the encoding and round the solution by the given - rounding scheme. + rounding scheme. Args: - problem: The ``QuadraticProgram`` to be solved. + problem: The :class:`~.QuadraticProgram` to be solved. Returns: The result of the quantum random access optimization. Raises: - ValueError: If the encoding has not been encoded with a ``QuadraticProgram``. + ValueError: If the encoding has not been encoded with a :class:`~.QuadraticProgram`. """ # Convert the problem to a QUBO self._verify_compatibility(problem) @@ -281,9 +286,9 @@ def process_result( """Process the relaxed result of the minimum eigensolver and rounding scheme. Args: - problem: The ``QuadraticProgram`` to be solved. - encoding: The ``QuantumRandomAccessEncoding``, for which ``encode()`` must have already - been called with the corresponding problem. + problem: The :class:`~.QuadraticProgram` to be solved. + encoding: An encoding instance for which :meth:`~QuantumRandomAccessEncoding.encode` + has already been called so it has been encoded with a :class:`~.QuadraticProgram`. relaxed_result: The relaxed result of the minimum eigensolver. rounding_result: The result of the rounding scheme. diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 4d638c318..724bec17d 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -25,7 +25,7 @@ class SemideterministicRounding(RoundingScheme): """Semi-deterministic rounding scheme This is referred to as "Pauli rounding" in - https://arxiv.org/abs/2111.03167v2. + https://arxiv.org/abs/2111.03167. """ def __init__(self, *, atol: float = 1e-8, seed: int | None = None): From 8b13f0c06a1f296bce8bdb77618058210f045649 Mon Sep 17 00:00:00 2001 From: Takashi Imamichi Date: Wed, 14 Jun 2023 22:35:08 +0900 Subject: [PATCH 50/67] update an error message --- qiskit_optimization/algorithms/qrao/magic_rounding.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 8e7ab7cd3..ee72972db 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -429,7 +429,8 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: raise ValueError( "No expectation values were provided in the rounding context. " "Magic rounding with weighted sampling requires the expectation values of the " - "``RoundingContext`` to be available, but they are not." + "``RoundingContext`` to be available, but they are not. " + 'Try `basis_sampling="uniform"` instead.' ) bases, basis_shots = self._sample_bases_weighted( q2vars, expectation_values, vars_per_qubit From d4585608084d5e747588c6eb688322f5ed34d3ab Mon Sep 17 00:00:00 2001 From: Takashi Imamichi Date: Thu, 15 Jun 2023 16:17:23 +0900 Subject: [PATCH 51/67] update error messages --- .../algorithms/qrao/magic_rounding.py | 40 +++++++++---------- .../qrao/semideterministic_rounding.py | 2 +- test/algorithms/qrao/test_magic_rounding.py | 4 -- 3 files changed, 19 insertions(+), 27 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index ee72972db..fb4a96332 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -79,6 +79,7 @@ def __init__( Raises: ValueError: If ``basis_sampling`` is not ``"uniform"`` or ``"weighted"``. + ValueError: If the sampler is not configured with a number of shots. """ if basis_sampling not in ("uniform", "weighted"): raise ValueError( @@ -88,7 +89,9 @@ def __init__( self._sampler = sampler self._rng = np.random.default_rng(seed) self._basis_sampling = basis_sampling - self._shots = None + if self._sampler.options.get("shots") is None: + raise ValueError("Magic rounding requires a sampler configured with a number of shots.") + self._shots = sampler.options.shots super().__init__() @property @@ -171,7 +174,7 @@ def _evaluate_magic_bases( basis_counts: list[dict[str, int] | None] = [None] * len(circuits) if len(circuits) != len(basis_shots): raise QiskitOptimizationError( - "The number of circuits and the number of basis types must be the same, " + "Internal error: The number of circuits and the number of basis types must be the same, " f"{len(circuits)} != {len(basis_shots)}." ) @@ -189,7 +192,7 @@ def _evaluate_magic_bases( counts_list = [dist.binary_probabilities() for dist in result.quasi_dists] if len(counts_list) != len(indices): raise QiskitOptimizationError( - "The number of circuits and the results from the primitive job must be the same," + "Internal error: The number of circuits and the results from the primitive job must be the same," f"{len(indices)} != {len(counts_list)}." ) for i, counts in zip(indices, counts_list): @@ -197,7 +200,7 @@ def _evaluate_magic_bases( if None in basis_counts: raise QiskitOptimizationError( - "Some basis counts were not collected. Please check the primitive job." + "Internal error: Some basis counts were not collected. Please check the primitive job." ) basis_counts = [ @@ -393,12 +396,11 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: RoundingResult: The results of the magic rounding process. Raises: - ValueError: If the circuit is not available for magic rounding. - ValueError: If the sampler is not configured with a number of shots. - ValueError: If the expectation values are not available for magic rounding with the + ValueError: If the rounding context has no circuits. + ValueError: If the rounding context has no expectation values for magic rounding with the weighted sampling. - ValueError: If the magic rounding did not return the expected number of shots. - ValueError: If the magic rounding did not return the expected number of bases. + QiskitOptimizationError: If the magic rounding did not return the expected number of shots. + QiskitOptimizationError: If the magic rounding did not return the expected number of bases. """ expectation_values = rounding_context.expectation_values circuit = rounding_context.circuit @@ -413,13 +415,6 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: "Perhaps try Semi-deterministic rounding instead." ) - if self._sampler.options.get("shots") is None: - raise ValueError( - "No number of shots was provided in the rounding context. " - "Magic rounding requires a sampler configured with a number of shots." - ) - self._shots = self._sampler.options.shots - if self.basis_sampling == "uniform": # uniform sampling bases, basis_shots = self._sample_bases_uniform(q2vars, vars_per_qubit) @@ -458,13 +453,14 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: for soln, count in soln_counts.items() ] if sum(soln_counts.values()) != self._shots: - raise ValueError( - f"Magic rounding did not return the expected number of shots. Expected " - f"{self._shots}, got {sum(soln_counts.values())}." + raise QiskitOptimizationError( + f"Internal error: Magic rounding did not return the expected number of shots. " + f"Expected {self._shots}, got {sum(soln_counts.values())}." ) - if len(bases) != len(basis_shots) != len(basis_counts): - raise ValueError( - f"{len(bases)} != {len(basis_shots)} != {len(basis_counts)} are not the same length" + if not (len(bases) == len(basis_shots) == len(basis_counts)): + raise QiskitOptimizationError( + f"Internal error: sizes of bases({len(bases)}), basis_shots({len(basis_shots)}), " + f"and basis_counts({len(basis_counts)}) are not equal." ) # Create a MagicRoundingResult object to return diff --git a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py index 724bec17d..017a94066 100644 --- a/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/semideterministic_rounding.py @@ -53,7 +53,7 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: """ if rounding_context.expectation_values is None: raise QiskitOptimizationError( - "Semideterministric rounding requires the expectation values of the ", + "Semi-deterministic rounding requires the expectation values of the ", "``RoundingContext`` to be available, but they are not.", ) diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 45eaa5107..685bc2c69 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -303,10 +303,6 @@ def test_magic_rounding_exceptions(self): # sampler without shots sampler = Sampler() magic_rounding = MagicRounding(sampler=sampler) - rounding_context = RoundingContext( - encoding, expectation_values=[1, 1, 1], circuit=QuantumCircuit(1) - ) - magic_rounding.round(rounding_context) with self.assertRaises(ValueError): # expectation_values is None for weighted basis sampling From 638010759df7b205dea3f9983c61d494f9ad9720 Mon Sep 17 00:00:00 2001 From: Takashi Imamichi Date: Thu, 15 Jun 2023 16:21:04 +0900 Subject: [PATCH 52/67] fix lint --- qiskit_optimization/algorithms/qrao/magic_rounding.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index fb4a96332..19d7761f1 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -192,8 +192,8 @@ def _evaluate_magic_bases( counts_list = [dist.binary_probabilities() for dist in result.quasi_dists] if len(counts_list) != len(indices): raise QiskitOptimizationError( - "Internal error: The number of circuits and the results from the primitive job must be the same," - f"{len(indices)} != {len(counts_list)}." + "Internal error: The number of circuits and the results from the primitive job " + f"must be the same, {len(indices)} != {len(counts_list)}." ) for i, counts in zip(indices, counts_list): basis_counts[i] = counts @@ -457,7 +457,7 @@ def round(self, rounding_context: RoundingContext) -> RoundingResult: f"Internal error: Magic rounding did not return the expected number of shots. " f"Expected {self._shots}, got {sum(soln_counts.values())}." ) - if not (len(bases) == len(basis_shots) == len(basis_counts)): + if not len(bases) == len(basis_shots) == len(basis_counts): raise QiskitOptimizationError( f"Internal error: sizes of bases({len(bases)}), basis_shots({len(basis_shots)}), " f"and basis_counts({len(basis_counts)}) are not equal." From ff8ee8e5fc7d81e526eddbc9a423838dffc6b2d1 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Mon, 4 Sep 2023 13:53:15 +0900 Subject: [PATCH 53/67] update tutorial and qiskit_algorithms --- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 6 ++---- .../algorithms/qrao/quantum_random_access_optimizer.py | 4 ++-- 2 files changed, 4 insertions(+), 6 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index ef1c26834..2518ea91f 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -21,7 +21,7 @@ "3. The optimizer class (`QuantumRandomAccessOptimizer`): This class performs the high-level optimization algorithm, utilizing the capabilities of the encoding class and the rounding scheme.\n", "\n", "\n", - "### References\n", + "*References*\n", "\n", "[1] Bryce Fuller et al., *Approximate Solutions of Combinatorial Problems via Quantum Relaxations,* [arXiv:2111.03167](https://arxiv.org/abs/2111.03167)" ] @@ -50,8 +50,6 @@ "\n", "To begin, we utilize the `Maxcut` class from Qiskit Optimization's application module. It allows us to generate a `QuadraticProgram` representation of the given graph.\n", "\n", - "Note that once our problem is represented as a `QuadraticProgram`, it needs to be converted into the appropriate format for QRAO, which is a [quadratic unconstrained binary optimization (QUBO)](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization) problem. While a `QuadraticProgram` generated by `Maxcut` is already in QUBO form, if you define your own problem, make sure to convert it into a QUBO before proceeding. You can refer to this [tutorial](https://qiskit.org/documentation/optimization/tutorials/02_converters_for_quadratic_programs.html) for guidance on converting QuadraticPrograms.\n", - "\n", "Note that once our problem has been represented as a `QuadraticProgram`, it will need to be converted to the correct type, a [quadratic unconstrained binary optimization (QUBO)](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization) problem, so that it is compatible with QRAO.\n", "A `QuadraticProgram` generated by `Maxcut` is already a QUBO, but if you define your own problem be sure you convert it to a QUBO before proceeding. Here is [a tutorial](https://qiskit.org/documentation/optimization/tutorials/02_converters_for_quadratic_programs.html) on converting `QuadraticPrograms`." ] @@ -654,7 +652,7 @@ "source": [ "## Appendix\n", "### How to verify correctness of your encoding\n", - "We assume for sake of the QRAO method that **the relaxation commutes with the objective function.** This notebook demonstrates how one can verify this for any problem (a `QuadraticProgram` in the language of Qiskit Optimization). One might want to verify this for pedagogical purposes, or as a sanity check when investigating unexpected behavior with the QRAO. Any problem that does not commute should be considered a bug, and if such a problem is discovered, we encourage that you submit it as [an issue on GitHub](https://github.com/Qiskit/qiskit-optimization/issues).\n", + "We assume for sake of the QRAO method that **the relaxation commutes with the objective function.** This notebook demonstrates how one can verify this for any problem (a `QuadraticProgram` in the language of Qiskit Optimization). One might want to verify this for pedagogical purposes, or as a sanity check when investigating unexpected behavior with the QRAO. Any problem that does not commute should be considered a bug, and if such a problem is discovered, we encourage that you submit it as [an issue on GitHub](https://github.com/qiskit-community/qiskit-optimization/issues).\n", "\n", "The `EncodingCommutationVerifier` class allows one to conveniently iterate over all decision variable states and compare each objective value with the corresponding encoded objective value, in order to identify any discrepancy." ] diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 31d84e62c..970e724f9 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -18,8 +18,8 @@ import numpy as np from qiskit import QuantumCircuit -from qiskit.algorithms import VariationalResult -from qiskit.algorithms.minimum_eigensolvers import ( +from qiskit_algorithms import VariationalResult +from qiskit_algorithms.minimum_eigensolvers import ( MinimumEigensolver, MinimumEigensolverResult, NumPyMinimumEigensolver, From caac634111752808007d1993d29fa6f8dfb442fc Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Wed, 6 Sep 2023 22:42:25 +0900 Subject: [PATCH 54/67] update --- .../13_quantum_random_access_optimizer.ipynb | 104 ++++++++++++------ .../algorithms/qrao/magic_rounding.py | 4 +- .../qrao/quantum_random_access_optimizer.py | 20 ++-- .../algorithms/qrao/rounding_common.py | 4 +- test/algorithms/qrao/test_magic_rounding.py | 2 +- .../test_quantum_random_access_optimizer.py | 4 +- 6 files changed, 88 insertions(+), 50 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 2518ea91f..53361c76c 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -177,8 +177,8 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.algorithms.optimizers import COBYLA\n", - "from qiskit.algorithms.minimum_eigensolvers import VQE\n", + "from qiskit_algorithms.optimizers import COBYLA\n", + "from qiskit_algorithms.minimum_eigensolvers import VQE\n", "from qiskit.circuit.library import RealAmplitudes\n", "from qiskit.primitives import Estimator\n", "\n", @@ -227,9 +227,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "The objective function value: 9.0\n", - "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999999969451725\n", + "The objective function value: 6.0\n", + "x: [1 0 1 1 0 1]\n", + "relaxed function value: 8.999999989370085\n", "\n" ] } @@ -268,12 +268,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [1, 3, 4] and nodes [0, 2, 5].\n" + "The obtained solution places a partition between nodes [1, 4] and nodes [0, 2, 3, 5].\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -314,7 +314,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -344,7 +344,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=1.0, status=)]" + "[SolutionSample(x=array([1, 0, 1, 1, 0, 1]), fval=6.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -409,9 +409,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "QRAO Approximate Optimal Function Value: 9.0\n", + "QRAO Approximate Optimal Function Value: 6.0\n", "Exact Optimal Function Value: 9.0\n", - "Approximation Ratio: 1.00\n" + "Approximation Ratio: 0.67\n" ] } ], @@ -480,7 +480,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999994326560426\n", + "relaxed function value: 8.999996668583572\n", "\n" ] } @@ -514,16 +514,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.012100000000000001, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0097, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.021, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0222, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0219, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0201, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0201, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0212, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0199, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0209, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.009, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0107, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0202, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0212, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.020799999999999996, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.022, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0211, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0223, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0213, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0214, status=)\n" ] } ], @@ -552,7 +552,7 @@ "\n", "By invoking `qrao.solve_relaxed()`, we obtain two essential outputs:\n", "\n", - "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the ground state, eigenvalues, and other relevant details. You can refer to the Qiskit Terra [documentation](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.EigensolverResult.html#qiskit.algorithms.eigensolvers.EigensolverResult) for a comprehensive explanation of the entries within this object.\n", + "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the ground state, eigenvalues, and other relevant details. You can refer to the Qiskit [documentation](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.EigensolverResult.html#qiskit.algorithms.eigensolvers.EigensolverResult) for a comprehensive explanation of the entries within this object.\n", "- `RoundingContext`: This object encapsulates essential information about the encoding and the solution of the relaxed problem in a form that is ready for consumption by the rounding schemes." ] }, @@ -570,6 +570,46 @@ "relaxed_results, rounding_context = qrao.solve_relaxed(encoding)" ] }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "aux_operators_evaluated: [(0.010980469912106938, {'variance': 0.9999999972816058, 'shots': 1000}), (0.02592971014759554, {'variance': 0.9999999972817522, 'shots': 1000}), (0.010449337841060821, {'variance': 1.0000000000000002, 'shots': 1000}), (-0.04120945001189342, {'variance': 1.0000000000000002, 'shots': 1000}), (0.028653133992095906, {'variance': 0.9999999994586152, 'shots': 1000}), (0.014092338840393742, {'variance': 0.9999999994587615, 'shots': 1000})]\n", + "combine: >\n", + "cost_function_evals: 118\n", + "eigenvalue: -4.499996371675237\n", + "optimal_circuit: ┌──────────────────────────────────────────────────────────┐\n", + "q_0: ┤0 ├\n", + " │ RealAmplitudes(θ[0],θ[1],θ[2],θ[3],θ[4],θ[5],θ[6],θ[7]) │\n", + "q_1: ┤1 ├\n", + " └──────────────────────────────────────────────────────────┘\n", + "optimal_parameters: {ParameterVectorElement(θ[0]): 0.3532646937914269, ParameterVectorElement(θ[1]): 2.4273161830112815, ParameterVectorElement(θ[2]): -0.8428005493659728, ParameterVectorElement(θ[3]): -0.4310546814880949, ParameterVectorElement(θ[4]): 2.0803783002882614, ParameterVectorElement(θ[5]): -1.767912211852171, ParameterVectorElement(θ[6]): 0.6592719674949016, ParameterVectorElement(θ[7]): 4.230855465332269}\n", + "optimal_point: [ 0.35326469 2.42731618 -0.84280055 -0.43105468 2.0803783 -1.76791221\n", + " 0.65927197 4.23085547]\n", + "optimal_value: -4.499996371675237\n", + "optimizer_evals: None\n", + "optimizer_result: { 'fun': -4.499996371675237,\n", + " 'jac': None,\n", + " 'nfev': 118,\n", + " 'nit': None,\n", + " 'njev': None,\n", + " 'x': array([ 0.35326469, 2.42731618, -0.84280055, -0.43105468, 2.0803783 ,\n", + " -1.76791221, 0.65927197, 4.23085547])}\n", + "optimizer_time: 0.22208309173583984\n" + ] + } + ], + "source": [ + "for k in dir(relaxed_results):\n", + " if not k.startswith(\"_\"):\n", + " print(f\"{k}: {getattr(relaxed_results, k)}\")" + ] + }, { "attachments": {}, "cell_type": "markdown", @@ -584,7 +624,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -593,7 +633,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.999997502617678\n", + "relaxed function value: -8.999996371675238\n", "The number of distinct samples is 1.\n" ] } @@ -616,7 +656,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -625,7 +665,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.999997502617678\n", + "relaxed function value: -8.999996371675238\n", "The number of distinct samples is 56.\n" ] } @@ -659,7 +699,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -715,7 +755,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -752,7 +792,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -780,7 +820,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, "metadata": { "scrolled": false }, @@ -788,7 +828,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+8a52d88
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed Jun 07 16:59:56 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+8a52d88
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed Sep 06 22:41:18 2023 JST
" ], "text/plain": [ "" diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 19d7761f1..13ff23e44 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -17,7 +17,7 @@ import numpy as np from qiskit import QuantumCircuit -from qiskit.algorithms.exceptions import AlgorithmError +from qiskit_algorithms.exceptions import AlgorithmError from qiskit.primitives import BaseSampler from qiskit.quantum_info import SparsePauliOp @@ -307,7 +307,7 @@ def _sample_bases_uniform( return bases, basis_shots def _sample_bases_weighted( - self, q2vars: list[list[int]], expectation_values: list[float], vars_per_qubit: int + self, q2vars: list[list[int]], expectation_values: list[complex] | None, vars_per_qubit: int ) -> tuple[np.ndarray, np.ndarray]: """ Perform weighted sampling from the expectation values. The goal is to make smarter choices diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 970e724f9..bb007cac5 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -13,16 +13,15 @@ """Quantum Random Access Optimizer class.""" from __future__ import annotations -import timeit from typing import cast import numpy as np from qiskit import QuantumCircuit -from qiskit_algorithms import VariationalResult -from qiskit_algorithms.minimum_eigensolvers import ( +from qiskit_algorithms import ( MinimumEigensolver, MinimumEigensolverResult, - NumPyMinimumEigensolver, + NumPyMinimumEigensolverResult, + VariationalResult, ) from qiskit_optimization.algorithms import ( @@ -217,23 +216,22 @@ def solve_relaxed( # Get the list of operators that correspond to each decision variable. variable_ops = [encoding._term2op(i) for i in range(encoding.num_vars)] - # Solve the relaxed problem - start_time_relaxed = timeit.default_timer() + # Solve the relaxed problem. relaxed_result = self.min_eigen_solver.compute_minimum_eigenvalue( encoding.qubit_op, aux_operators=variable_ops ) - relaxed_result.time_taken = timeit.default_timer() - start_time_relaxed # Get auxiliary expectation values for rounding. + expectation_values: list[complex] | None = None if relaxed_result.aux_operators_evaluated is not None: - expectation_values = [v[0] for v in relaxed_result.aux_operators_evaluated] - else: - expectation_values = None + expectation_values = [ + v[0] for v in relaxed_result.aux_operators_evaluated # type: ignore + ] # Get the circuit corresponding to the relaxed solution. if isinstance(relaxed_result, VariationalResult): circuit = relaxed_result.optimal_circuit.bind_parameters(relaxed_result.optimal_point) - elif isinstance(self.min_eigen_solver, NumPyMinimumEigensolver): + elif isinstance(relaxed_result, NumPyMinimumEigensolverResult): statevector = relaxed_result.eigenstate circuit = QuantumCircuit(encoding.num_qubits) circuit.initialize(statevector) diff --git a/qiskit_optimization/algorithms/qrao/rounding_common.py b/qiskit_optimization/algorithms/qrao/rounding_common.py index 0aae64120..9516dd92b 100644 --- a/qiskit_optimization/algorithms/qrao/rounding_common.py +++ b/qiskit_optimization/algorithms/qrao/rounding_common.py @@ -27,7 +27,7 @@ class RoundingResult: """Result of rounding""" - expectation_values: list[float] + expectation_values: list[complex] | None """Expectation values""" samples: list[SolutionSample] """List of samples after rounding""" @@ -46,7 +46,7 @@ class RoundingContext: encoding: QuantumRandomAccessEncoding """Encoding containing the problem information.""" - expectation_values: list[float] | None = None + expectation_values: list[complex] | None """Expectation values for the relaxed Hamiltonian.""" circuit: QuantumCircuit | None = None """Circuit corresponding to the encoding and expectation values.""" diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 685bc2c69..11ba24b47 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -16,7 +16,7 @@ import numpy as np from qiskit.circuit import QuantumCircuit -from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver +from qiskit_algorithms.minimum_eigensolvers import NumPyMinimumEigensolver from qiskit.primitives import Sampler from qiskit_optimization.algorithms.qrao import ( diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py index 00fd08cf7..91c379b87 100644 --- a/test/algorithms/qrao/test_quantum_random_access_optimizer.py +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -15,13 +15,13 @@ from test.optimization_test_case import QiskitOptimizationTestCase import numpy as np -from qiskit.algorithms.minimum_eigensolvers import ( +from qiskit_algorithms.minimum_eigensolvers import ( NumPyMinimumEigensolver, NumPyMinimumEigensolverResult, VQE, VQEResult, ) -from qiskit.algorithms.optimizers import COBYLA +from qiskit_algorithms.optimizers import COBYLA from qiskit.circuit.library import RealAmplitudes from qiskit.primitives import Estimator from qiskit.utils import algorithm_globals From 0fa002583200f7826fa8a7c6464314e992370b57 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 7 Sep 2023 00:13:39 +0900 Subject: [PATCH 55/67] fix lint --- qiskit_optimization/algorithms/qrao/magic_rounding.py | 2 +- .../algorithms/qrao/quantum_random_access_optimizer.py | 2 +- test/algorithms/qrao/test_magic_rounding.py | 6 +++--- 3 files changed, 5 insertions(+), 5 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/magic_rounding.py b/qiskit_optimization/algorithms/qrao/magic_rounding.py index 13ff23e44..02261d16b 100644 --- a/qiskit_optimization/algorithms/qrao/magic_rounding.py +++ b/qiskit_optimization/algorithms/qrao/magic_rounding.py @@ -17,9 +17,9 @@ import numpy as np from qiskit import QuantumCircuit -from qiskit_algorithms.exceptions import AlgorithmError from qiskit.primitives import BaseSampler from qiskit.quantum_info import SparsePauliOp +from qiskit_algorithms.exceptions import AlgorithmError from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.exceptions import QiskitOptimizationError diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index bb007cac5..3b1b918a5 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -225,7 +225,7 @@ def solve_relaxed( expectation_values: list[complex] | None = None if relaxed_result.aux_operators_evaluated is not None: expectation_values = [ - v[0] for v in relaxed_result.aux_operators_evaluated # type: ignore + v[0] for v in relaxed_result.aux_operators_evaluated # type: ignore ] # Get the circuit corresponding to the relaxed solution. diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index 11ba24b47..e5fd86ee4 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -16,17 +16,17 @@ import numpy as np from qiskit.circuit import QuantumCircuit -from qiskit_algorithms.minimum_eigensolvers import NumPyMinimumEigensolver from qiskit.primitives import Sampler +from qiskit_algorithms.minimum_eigensolvers import NumPyMinimumEigensolver +from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.algorithms.qrao import ( MagicRounding, QuantumRandomAccessEncoding, QuantumRandomAccessOptimizer, - RoundingResult, RoundingContext, + RoundingResult, ) -from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.problems import QuadraticProgram From 8e0cb426ca368663f68a030b4c0e16ad9bbf5483 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 7 Sep 2023 17:20:48 +0900 Subject: [PATCH 56/67] fix --- .../13_quantum_random_access_optimizer.ipynb | 42 +++++++++---------- 1 file changed, 21 insertions(+), 21 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 53361c76c..482bb0255 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -36,7 +36,7 @@ " QuantumRandomAccessEncoding,\n", " SemideterministicRounding,\n", " QuantumRandomAccessOptimizer,\n", - ")" + ")\n" ] }, { @@ -101,7 +101,7 @@ "\n", "maxcut = Maxcut(graph)\n", "problem = maxcut.to_quadratic_program()\n", - "print(problem.prettyprint())" + "print(problem.prettyprint())\n" ] }, { @@ -153,7 +153,7 @@ " \"We achieve a compression ratio of \"\n", " f\"({encoding.num_vars} binary variables : {encoding.num_qubits} qubits) \"\n", " f\"≈ {encoding.compression_ratio}.\\n\"\n", - ")" + ")\n" ] }, { @@ -177,8 +177,8 @@ "metadata": {}, "outputs": [], "source": [ + "from qiskit_algorithms import VQE\n", "from qiskit_algorithms.optimizers import COBYLA\n", - "from qiskit_algorithms.minimum_eigensolvers import VQE\n", "from qiskit.circuit.library import RealAmplitudes\n", "from qiskit.primitives import Estimator\n", "\n", @@ -202,7 +202,7 @@ "semidterministic_rounding = SemideterministicRounding()\n", "\n", "# Construct the optimizer\n", - "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=semidterministic_rounding)" + "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=semidterministic_rounding)\n" ] }, { @@ -242,7 +242,7 @@ " f\"The objective function value: {results.fval}\\n\"\n", " f\"x: {results.x}\\n\"\n", " f\"relaxed function value: {-1 * results.relaxed_fval}\\n\"\n", - ")" + ")\n" ] }, { @@ -288,7 +288,7 @@ " f\"The obtained solution places a partition between nodes {maxcut_partition[0]} \"\n", " f\"and nodes {maxcut_partition[1]}.\"\n", ")\n", - "maxcut.draw(results, pos=nx.spring_layout(graph, seed=seed))" + "maxcut.draw(results, pos=nx.spring_layout(graph, seed=seed))\n" ] }, { @@ -323,7 +323,7 @@ } ], "source": [ - "results.relaxed_result" + "results.relaxed_result\n" ] }, { @@ -353,7 +353,7 @@ } ], "source": [ - "results.samples" + "results.samples\n" ] }, { @@ -389,7 +389,7 @@ "exact_mes = NumPyMinimumEigensolver()\n", "exact = MinimumEigenOptimizer(exact_mes)\n", "exact_result = exact.solve(problem)\n", - "print(exact_result.prettyprint())" + "print(exact_result.prettyprint())\n" ] }, { @@ -418,7 +418,7 @@ "source": [ "print(\"QRAO Approximate Optimal Function Value:\", results.fval)\n", "print(\"Exact Optimal Function Value:\", exact_result.fval)\n", - "print(f\"Approximation Ratio: {results.fval / exact_result.fval :.2f}\")" + "print(f\"Approximation Ratio: {results.fval / exact_result.fval :.2f}\")\n" ] }, { @@ -466,7 +466,7 @@ "# Construct the optimizer\n", "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=magic_rounding)\n", "\n", - "results = qrao.solve(problem)" + "results = qrao.solve(problem)\n" ] }, { @@ -490,7 +490,7 @@ " f\"The objective function value: {results.fval}\\n\"\n", " f\"x: {results.x}\\n\"\n", " f\"relaxed function value: {-1 * results.relaxed_fval}\\n\"\n", - ")" + ")\n" ] }, { @@ -531,7 +531,7 @@ "print(f\"The number of distinct samples is {len(results.samples)}.\")\n", "print(\"Top 10 samples with the largest fval:\")\n", "for sample in results.samples[:10]:\n", - " print(sample)" + " print(sample)\n" ] }, { @@ -567,7 +567,7 @@ "encoding.encode(problem)\n", "\n", "# Solve the relaxed problem\n", - "relaxed_results, rounding_context = qrao.solve_relaxed(encoding)" + "relaxed_results, rounding_context = qrao.solve_relaxed(encoding)\n" ] }, { @@ -607,7 +607,7 @@ "source": [ "for k in dir(relaxed_results):\n", " if not k.startswith(\"_\"):\n", - " print(f\"{k}: {getattr(relaxed_results, k)}\")" + " print(f\"{k}: {getattr(relaxed_results, k)}\")\n" ] }, { @@ -651,7 +651,7 @@ " f\"x: {qrao_results_sdr.x}\\n\"\n", " f\"relaxed function value: {-1 * qrao_results_sdr.relaxed_fval}\\n\"\n", " f\"The number of distinct samples is {len(qrao_results_sdr.samples)}.\"\n", - ")" + ")\n" ] }, { @@ -682,7 +682,7 @@ " f\"x: {qrao_results_mr.x}\\n\"\n", " f\"relaxed function value: {-1 * qrao_results_mr.relaxed_fval}\\n\"\n", " f\"The number of distinct samples is {len(qrao_results_mr.samples)}.\"\n", - ")" + ")\n" ] }, { @@ -742,7 +742,7 @@ "\n", "maxcut = Maxcut(graph)\n", "problem = maxcut.to_quadratic_program()\n", - "print(problem.prettyprint())" + "print(problem.prettyprint())\n" ] }, { @@ -779,7 +779,7 @@ "print(\"Encoded Problem:\\n=================\")\n", "print(encoding.qubit_op) # The Hamiltonian without the offset\n", "print(\"Offset = \", encoding.offset)\n", - "print(\"Variables encoded on each qubit: \", encoding.q2vars)" + "print(\"Variables encoded on each qubit: \", encoding.q2vars)\n" ] }, { @@ -807,7 +807,7 @@ " print(\n", " f\"Violation identified: {str_dvars} evaluates to {obj_val} \"\n", " f\"but the encoded problem evaluates to {encoded_obj_val}.\"\n", - " )" + " )\n" ] }, { From 74dec95a3f2cd74697ecd3822e74fc69e4649dd6 Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Thu, 7 Sep 2023 18:34:49 +0900 Subject: [PATCH 57/67] Update docs/tutorials/13_quantum_random_access_optimizer.ipynb Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 482bb0255..dd026fe7f 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -303,7 +303,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The `MinimumEigensolverResult` ([details](https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html)) that results from performing VQE on the relaxed Hamiltonian is available:" + "The [MinimumEigensolverResult](https://qiskit.org/ecosystem/algorithms/stubs/qiskit_algorithms.MinimumEigensolverResult.html) that results from performing VQE on the relaxed Hamiltonian is available:" ] }, { From a5ec6431c5b0f5fc90e230952c47d615486c7dbe Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Thu, 7 Sep 2023 21:44:25 +0900 Subject: [PATCH 58/67] Update docs/tutorials/13_quantum_random_access_optimizer.ipynb Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- docs/tutorials/13_quantum_random_access_optimizer.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index dd026fe7f..b9c202acc 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -382,7 +382,7 @@ } ], "source": [ - "from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver\n", + "from qiskit_algorithms import NumPyMinimumEigensolver\n", "\n", "from qiskit_optimization.algorithms import MinimumEigenOptimizer\n", "\n", From c1c329de6edd1183ada58dc642e26570ce5ac43b Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 7 Sep 2023 21:51:17 +0900 Subject: [PATCH 59/67] fix --- .../13_quantum_random_access_optimizer.ipynb | 70 +++++++++---------- 1 file changed, 35 insertions(+), 35 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index b9c202acc..22ec2ccfd 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -227,9 +227,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "The objective function value: 6.0\n", - "x: [1 0 1 1 0 1]\n", - "relaxed function value: 8.999999989370085\n", + "The objective function value: 9.0\n", + "x: [1 0 1 0 0 1]\n", + "relaxed function value: 8.999999987496103\n", "\n" ] } @@ -268,12 +268,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [1, 4] and nodes [0, 2, 3, 5].\n" + "The obtained solution places a partition between nodes [1, 3, 4] and nodes [0, 2, 5].\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -314,7 +314,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -344,7 +344,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([1, 0, 1, 1, 0, 1]), fval=6.0, probability=1.0, status=)]" + "[SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -409,9 +409,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "QRAO Approximate Optimal Function Value: 6.0\n", + "QRAO Approximate Optimal Function Value: 9.0\n", "Exact Optimal Function Value: 9.0\n", - "Approximation Ratio: 0.67\n" + "Approximation Ratio: 1.00\n" ] } ], @@ -480,7 +480,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999996668583572\n", + "relaxed function value: 8.999995210512584\n", "\n" ] } @@ -514,16 +514,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.009, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0107, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0202, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0212, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.020799999999999996, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.022, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0095, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0112, status=)\n", + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0207, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0218, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0208, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0219, status=)\n", "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0211, status=)\n", "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0223, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0213, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0214, status=)\n" + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0201, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0211, status=)\n" ] } ], @@ -552,7 +552,7 @@ "\n", "By invoking `qrao.solve_relaxed()`, we obtain two essential outputs:\n", "\n", - "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the ground state, eigenvalues, and other relevant details. You can refer to the Qiskit [documentation](https://qiskit.org/documentation/stubs/qiskit.algorithms.eigensolvers.EigensolverResult.html#qiskit.algorithms.eigensolvers.EigensolverResult) for a comprehensive explanation of the entries within this object.\n", + "- `MinimumEigensolverResult`: This object contains the results of running the minimum eigen optimizer such as the VQE on the relaxed problem. It provides information about the eigenvalue, and other relevant details. You can refer to the Qiskit Algorithms [documentation](https://qiskit.org/documentation/stubs/qiskit.algorithms.MinimumEigensolverResult.html) for a comprehensive explanation of the entries within this object.\n", "- `RoundingContext`: This object encapsulates essential information about the encoding and the solution of the relaxed problem in a form that is ready for consumption by the rounding schemes." ] }, @@ -579,28 +579,28 @@ "name": "stdout", "output_type": "stream", "text": [ - "aux_operators_evaluated: [(0.010980469912106938, {'variance': 0.9999999972816058, 'shots': 1000}), (0.02592971014759554, {'variance': 0.9999999972817522, 'shots': 1000}), (0.010449337841060821, {'variance': 1.0000000000000002, 'shots': 1000}), (-0.04120945001189342, {'variance': 1.0000000000000002, 'shots': 1000}), (0.028653133992095906, {'variance': 0.9999999994586152, 'shots': 1000}), (0.014092338840393742, {'variance': 0.9999999994587615, 'shots': 1000})]\n", - "combine: >\n", - "cost_function_evals: 118\n", - "eigenvalue: -4.499996371675237\n", + "aux_operators_evaluated: [(0.01092058304023368, {'variance': 0.9999999999399583, 'shots': 1000}), (0.025989603303204444, {'variance': 0.9999999999398398, 'shots': 1000}), (0.01044933784106082, {'variance': 1.0, 'shots': 1000}), (-0.04120945001189341, {'variance': 1.0, 'shots': 1000}), (0.02853685521557189, {'variance': 0.9999999913489581, 'shots': 1000}), (0.014208614935522862, {'variance': 0.9999999913488397, 'shots': 1000})]\n", + "combine: >\n", + "cost_function_evals: 106\n", + "eigenvalue: -4.499994868883425\n", "optimal_circuit: ┌──────────────────────────────────────────────────────────┐\n", "q_0: ┤0 ├\n", " │ RealAmplitudes(θ[0],θ[1],θ[2],θ[3],θ[4],θ[5],θ[6],θ[7]) │\n", "q_1: ┤1 ├\n", " └──────────────────────────────────────────────────────────┘\n", - "optimal_parameters: {ParameterVectorElement(θ[0]): 0.3532646937914269, ParameterVectorElement(θ[1]): 2.4273161830112815, ParameterVectorElement(θ[2]): -0.8428005493659728, ParameterVectorElement(θ[3]): -0.4310546814880949, ParameterVectorElement(θ[4]): 2.0803783002882614, ParameterVectorElement(θ[5]): -1.767912211852171, ParameterVectorElement(θ[6]): 0.6592719674949016, ParameterVectorElement(θ[7]): 4.230855465332269}\n", - "optimal_point: [ 0.35326469 2.42731618 -0.84280055 -0.43105468 2.0803783 -1.76791221\n", - " 0.65927197 4.23085547]\n", - "optimal_value: -4.499996371675237\n", + "optimal_parameters: {ParameterVectorElement(θ[0]): -1.395652360544842, ParameterVectorElement(θ[1]): 3.8439883152556567, ParameterVectorElement(θ[2]): 4.177081165651515, ParameterVectorElement(θ[3]): -0.5726083236276287, ParameterVectorElement(θ[4]): -1.882944923220605, ParameterVectorElement(θ[5]): -1.3604773864196114, ParameterVectorElement(θ[6]): 0.9908319483567548, ParameterVectorElement(θ[7]): -0.07746769477257553}\n", + "optimal_point: [-1.39565236 3.84398832 4.17708117 -0.57260832 -1.88294492 -1.36047739\n", + " 0.99083195 -0.07746769]\n", + "optimal_value: -4.499994868883425\n", "optimizer_evals: None\n", - "optimizer_result: { 'fun': -4.499996371675237,\n", + "optimizer_result: { 'fun': -4.499994868883425,\n", " 'jac': None,\n", - " 'nfev': 118,\n", + " 'nfev': 106,\n", " 'nit': None,\n", " 'njev': None,\n", - " 'x': array([ 0.35326469, 2.42731618, -0.84280055, -0.43105468, 2.0803783 ,\n", - " -1.76791221, 0.65927197, 4.23085547])}\n", - "optimizer_time: 0.22208309173583984\n" + " 'x': array([-1.39565236, 3.84398832, 4.17708117, -0.57260832, -1.88294492,\n", + " -1.36047739, 0.99083195, -0.07746769])}\n", + "optimizer_time: 0.17730474472045898\n" ] } ], @@ -633,7 +633,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.999996371675238\n", + "relaxed function value: -8.999994868883425\n", "The number of distinct samples is 1.\n" ] } @@ -665,7 +665,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.999996371675238\n", + "relaxed function value: -8.999994868883425\n", "The number of distinct samples is 56.\n" ] } @@ -828,7 +828,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+8a52d88
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Wed Sep 06 22:41:18 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+8a52d88
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Thu Sep 07 21:45:37 2023 JST
" ], "text/plain": [ "" From cbba4f89485057ae7984c2bc2110a9dd663f882a Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Thu, 7 Sep 2023 21:51:52 +0900 Subject: [PATCH 60/67] Update qiskit_optimization/algorithms/qrao/__init__.py Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- qiskit_optimization/algorithms/qrao/__init__.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/__init__.py b/qiskit_optimization/algorithms/qrao/__init__.py index 85f758534..0e54689e3 100644 --- a/qiskit_optimization/algorithms/qrao/__init__.py +++ b/qiskit_optimization/algorithms/qrao/__init__.py @@ -48,8 +48,8 @@ .. code-block:: python - from qiskit.algorithms.optimizers import COBYLA - from qiskit.algorithms.minimum_eigensolvers import VQE + from qiskit_algorithms.optimizers import COBYLA + from qiskit_algorithms import VQE from qiskit.circuit.library import RealAmplitudes from qiskit.primitives import Estimator From 4b2ea88953c114154a9f764581416ce7fdfa669d Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Thu, 7 Sep 2023 21:52:53 +0900 Subject: [PATCH 61/67] Update releasenotes/notes/qrao-89d5ff1d2927de64.yaml Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- releasenotes/notes/qrao-89d5ff1d2927de64.yaml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml index 7ea21ff9b..863addd3d 100644 --- a/releasenotes/notes/qrao-89d5ff1d2927de64.yaml +++ b/releasenotes/notes/qrao-89d5ff1d2927de64.yaml @@ -22,8 +22,8 @@ features: .. code-block:: python - from qiskit.algorithms.optimizers import COBYLA - from qiskit.algorithms.minimum_eigensolvers import VQE + from qiskit_algorithms.optimizers import COBYLA + from qiskit_algorithms import VQE from qiskit.circuit.library import RealAmplitudes from qiskit.primitives import Estimator From 9f61f4cd0fed2c42b862b7d5d4bb82e5e4a9b0f3 Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Thu, 7 Sep 2023 21:53:09 +0900 Subject: [PATCH 62/67] Update test/algorithms/qrao/test_magic_rounding.py Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- test/algorithms/qrao/test_magic_rounding.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/algorithms/qrao/test_magic_rounding.py b/test/algorithms/qrao/test_magic_rounding.py index e5fd86ee4..8a7e77f74 100644 --- a/test/algorithms/qrao/test_magic_rounding.py +++ b/test/algorithms/qrao/test_magic_rounding.py @@ -17,7 +17,7 @@ import numpy as np from qiskit.circuit import QuantumCircuit from qiskit.primitives import Sampler -from qiskit_algorithms.minimum_eigensolvers import NumPyMinimumEigensolver +from qiskit_algorithms import NumPyMinimumEigensolver from qiskit_optimization.algorithms import OptimizationResultStatus, SolutionSample from qiskit_optimization.algorithms.qrao import ( From bf16e259321a772b173843e47c0651c1355039dd Mon Sep 17 00:00:00 2001 From: a-matsuo <47442626+a-matsuo@users.noreply.github.com> Date: Thu, 7 Sep 2023 21:53:21 +0900 Subject: [PATCH 63/67] Update test/algorithms/qrao/test_quantum_random_access_optimizer.py Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com> --- test/algorithms/qrao/test_quantum_random_access_optimizer.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test/algorithms/qrao/test_quantum_random_access_optimizer.py b/test/algorithms/qrao/test_quantum_random_access_optimizer.py index 91c379b87..ae797e2fe 100644 --- a/test/algorithms/qrao/test_quantum_random_access_optimizer.py +++ b/test/algorithms/qrao/test_quantum_random_access_optimizer.py @@ -15,7 +15,7 @@ from test.optimization_test_case import QiskitOptimizationTestCase import numpy as np -from qiskit_algorithms.minimum_eigensolvers import ( +from qiskit_algorithms import ( NumPyMinimumEigensolver, NumPyMinimumEigensolverResult, VQE, From 3b4570e529aaee24cb751e4046e09cb98a0dfafd Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 7 Sep 2023 21:57:49 +0900 Subject: [PATCH 64/67] fix mypy --- .../algorithms/qrao/quantum_random_access_optimizer.py | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index 3b1b918a5..a4559a1fc 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -224,9 +224,7 @@ def solve_relaxed( # Get auxiliary expectation values for rounding. expectation_values: list[complex] | None = None if relaxed_result.aux_operators_evaluated is not None: - expectation_values = [ - v[0] for v in relaxed_result.aux_operators_evaluated # type: ignore - ] + expectation_values = [v[0] for v in relaxed_result.aux_operators_evaluated] # Get the circuit corresponding to the relaxed solution. if isinstance(relaxed_result, VariationalResult): From 6e1f1c3bd198277c80f0af0f069454ec41fe5955 Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 7 Sep 2023 22:26:38 +0900 Subject: [PATCH 65/67] fix --- .../13_quantum_random_access_optimizer.ipynb | 110 +++++++++--------- 1 file changed, 55 insertions(+), 55 deletions(-) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/13_quantum_random_access_optimizer.ipynb index 22ec2ccfd..93daf59f2 100644 --- a/docs/tutorials/13_quantum_random_access_optimizer.ipynb +++ b/docs/tutorials/13_quantum_random_access_optimizer.ipynb @@ -36,7 +36,7 @@ " QuantumRandomAccessEncoding,\n", " SemideterministicRounding,\n", " QuantumRandomAccessOptimizer,\n", - ")\n" + ")" ] }, { @@ -101,7 +101,7 @@ "\n", "maxcut = Maxcut(graph)\n", "problem = maxcut.to_quadratic_program()\n", - "print(problem.prettyprint())\n" + "print(problem.prettyprint())" ] }, { @@ -153,7 +153,7 @@ " \"We achieve a compression ratio of \"\n", " f\"({encoding.num_vars} binary variables : {encoding.num_qubits} qubits) \"\n", " f\"≈ {encoding.compression_ratio}.\\n\"\n", - ")\n" + ")" ] }, { @@ -202,7 +202,7 @@ "semidterministic_rounding = SemideterministicRounding()\n", "\n", "# Construct the optimizer\n", - "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=semidterministic_rounding)\n" + "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=semidterministic_rounding)" ] }, { @@ -227,9 +227,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "The objective function value: 9.0\n", - "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999999987496103\n", + "The objective function value: 6.0\n", + "x: [1 0 1 1 0 1]\n", + "relaxed function value: 8.999999989772657\n", "\n" ] } @@ -242,7 +242,7 @@ " f\"The objective function value: {results.fval}\\n\"\n", " f\"x: {results.x}\\n\"\n", " f\"relaxed function value: {-1 * results.relaxed_fval}\\n\"\n", - ")\n" + ")" ] }, { @@ -268,12 +268,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "The obtained solution places a partition between nodes [1, 3, 4] and nodes [0, 2, 5].\n" + "The obtained solution places a partition between nodes [1, 4] and nodes [0, 2, 3, 5].\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -288,7 +288,7 @@ " f\"The obtained solution places a partition between nodes {maxcut_partition[0]} \"\n", " f\"and nodes {maxcut_partition[1]}.\"\n", ")\n", - "maxcut.draw(results, pos=nx.spring_layout(graph, seed=seed))\n" + "maxcut.draw(results, pos=nx.spring_layout(graph, seed=seed))" ] }, { @@ -314,7 +314,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 7, @@ -323,7 +323,7 @@ } ], "source": [ - "results.relaxed_result\n" + "results.relaxed_result" ] }, { @@ -344,7 +344,7 @@ { "data": { "text/plain": [ - "[SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=1.0, status=)]" + "[SolutionSample(x=array([1, 0, 1, 1, 0, 1]), fval=6.0, probability=1.0, status=)]" ] }, "execution_count": 8, @@ -353,7 +353,7 @@ } ], "source": [ - "results.samples\n" + "results.samples" ] }, { @@ -389,7 +389,7 @@ "exact_mes = NumPyMinimumEigensolver()\n", "exact = MinimumEigenOptimizer(exact_mes)\n", "exact_result = exact.solve(problem)\n", - "print(exact_result.prettyprint())\n" + "print(exact_result.prettyprint())" ] }, { @@ -409,16 +409,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "QRAO Approximate Optimal Function Value: 9.0\n", + "QRAO Approximate Optimal Function Value: 6.0\n", "Exact Optimal Function Value: 9.0\n", - "Approximation Ratio: 1.00\n" + "Approximation Ratio: 0.67\n" ] } ], "source": [ "print(\"QRAO Approximate Optimal Function Value:\", results.fval)\n", "print(\"Exact Optimal Function Value:\", exact_result.fval)\n", - "print(f\"Approximation Ratio: {results.fval / exact_result.fval :.2f}\")\n" + "print(f\"Approximation Ratio: {results.fval / exact_result.fval :.2f}\")" ] }, { @@ -466,7 +466,7 @@ "# Construct the optimizer\n", "qrao = QuantumRandomAccessOptimizer(min_eigen_solver=vqe, rounding_scheme=magic_rounding)\n", "\n", - "results = qrao.solve(problem)\n" + "results = qrao.solve(problem)" ] }, { @@ -480,7 +480,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: 8.999995210512584\n", + "relaxed function value: 8.999996519407159\n", "\n" ] } @@ -490,7 +490,7 @@ " f\"The objective function value: {results.fval}\\n\"\n", " f\"x: {results.x}\\n\"\n", " f\"relaxed function value: {-1 * results.relaxed_fval}\\n\"\n", - ")\n" + ")" ] }, { @@ -514,16 +514,16 @@ "text": [ "The number of distinct samples is 56.\n", "Top 10 samples with the largest fval:\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0095, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 1]), fval=9.0, probability=0.0094, status=)\n", "SolutionSample(x=array([0, 1, 0, 1, 1, 0]), fval=9.0, probability=0.0112, status=)\n", - "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0207, status=)\n", - "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0218, status=)\n", - "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0208, status=)\n", - "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0219, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0211, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.0223, status=)\n", - "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.0201, status=)\n", - "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.0211, status=)\n" + "SolutionSample(x=array([0, 0, 0, 1, 1, 0]), fval=6.0, probability=0.0195, status=)\n", + "SolutionSample(x=array([1, 1, 1, 0, 0, 1]), fval=6.0, probability=0.0205, status=)\n", + "SolutionSample(x=array([0, 1, 1, 1, 1, 0]), fval=6.0, probability=0.0214, status=)\n", + "SolutionSample(x=array([1, 0, 0, 0, 0, 1]), fval=6.0, probability=0.0194, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 0, 0]), fval=6.0, probability=0.0204, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 1, 1]), fval=6.0, probability=0.021599999999999998, status=)\n", + "SolutionSample(x=array([1, 0, 1, 0, 1, 1]), fval=6.0, probability=0.02, status=)\n", + "SolutionSample(x=array([0, 1, 0, 1, 0, 0]), fval=6.0, probability=0.021, status=)\n" ] } ], @@ -531,7 +531,7 @@ "print(f\"The number of distinct samples is {len(results.samples)}.\")\n", "print(\"Top 10 samples with the largest fval:\")\n", "for sample in results.samples[:10]:\n", - " print(sample)\n" + " print(sample)" ] }, { @@ -567,7 +567,7 @@ "encoding.encode(problem)\n", "\n", "# Solve the relaxed problem\n", - "relaxed_results, rounding_context = qrao.solve_relaxed(encoding)\n" + "relaxed_results, rounding_context = qrao.solve_relaxed(encoding)" ] }, { @@ -579,35 +579,35 @@ "name": "stdout", "output_type": "stream", "text": [ - "aux_operators_evaluated: [(0.01092058304023368, {'variance': 0.9999999999399583, 'shots': 1000}), (0.025989603303204444, {'variance': 0.9999999999398398, 'shots': 1000}), (0.01044933784106082, {'variance': 1.0, 'shots': 1000}), (-0.04120945001189341, {'variance': 1.0, 'shots': 1000}), (0.02853685521557189, {'variance': 0.9999999913489581, 'shots': 1000}), (0.014208614935522862, {'variance': 0.9999999913488397, 'shots': 1000})]\n", - "combine: >\n", - "cost_function_evals: 106\n", - "eigenvalue: -4.499994868883425\n", + "aux_operators_evaluated: [(0.010835872623325702, {'variance': 0.9999999914513272, 'shots': 1000}), (0.026074300411246972, {'variance': 0.999999991452347, 'shots': 1000}), (0.01044933784106082, {'variance': 1.0, 'shots': 1000}), (-0.04120945001189341, {'variance': 1.0, 'shots': 1000}), (0.02868127134978543, {'variance': 0.9999999973575187, 'shots': 1000}), (0.014064208211884945, {'variance': 0.9999999973585384, 'shots': 1000})]\n", + "combine: >\n", + "cost_function_evals: 114\n", + "eigenvalue: -4.499994593889271\n", "optimal_circuit: ┌──────────────────────────────────────────────────────────┐\n", "q_0: ┤0 ├\n", " │ RealAmplitudes(θ[0],θ[1],θ[2],θ[3],θ[4],θ[5],θ[6],θ[7]) │\n", "q_1: ┤1 ├\n", " └──────────────────────────────────────────────────────────┘\n", - "optimal_parameters: {ParameterVectorElement(θ[0]): -1.395652360544842, ParameterVectorElement(θ[1]): 3.8439883152556567, ParameterVectorElement(θ[2]): 4.177081165651515, ParameterVectorElement(θ[3]): -0.5726083236276287, ParameterVectorElement(θ[4]): -1.882944923220605, ParameterVectorElement(θ[5]): -1.3604773864196114, ParameterVectorElement(θ[6]): 0.9908319483567548, ParameterVectorElement(θ[7]): -0.07746769477257553}\n", - "optimal_point: [-1.39565236 3.84398832 4.17708117 -0.57260832 -1.88294492 -1.36047739\n", - " 0.99083195 -0.07746769]\n", - "optimal_value: -4.499994868883425\n", + "optimal_parameters: {ParameterVectorElement(θ[0]): 0.3782657558818425, ParameterVectorElement(θ[1]): 2.6307309944567154, ParameterVectorElement(θ[2]): -1.872906908815765, ParameterVectorElement(θ[3]): 0.1989998525444124, ParameterVectorElement(θ[4]): -2.8660234975739094, ParameterVectorElement(θ[5]): -0.9853046968649906, ParameterVectorElement(θ[6]): -0.7699284547923341, ParameterVectorElement(θ[7]): 3.5498132912316986}\n", + "optimal_point: [ 0.37826576 2.63073099 -1.87290691 0.19899985 -2.8660235 -0.9853047\n", + " -0.76992845 3.54981329]\n", + "optimal_value: -4.499994593889271\n", "optimizer_evals: None\n", - "optimizer_result: { 'fun': -4.499994868883425,\n", + "optimizer_result: { 'fun': -4.499994593889271,\n", " 'jac': None,\n", - " 'nfev': 106,\n", + " 'nfev': 114,\n", " 'nit': None,\n", " 'njev': None,\n", - " 'x': array([-1.39565236, 3.84398832, 4.17708117, -0.57260832, -1.88294492,\n", - " -1.36047739, 0.99083195, -0.07746769])}\n", - "optimizer_time: 0.17730474472045898\n" + " 'x': array([ 0.37826576, 2.63073099, -1.87290691, 0.19899985, -2.8660235 ,\n", + " -0.9853047 , -0.76992845, 3.54981329])}\n", + "optimizer_time: 0.19381928443908691\n" ] } ], "source": [ "for k in dir(relaxed_results):\n", " if not k.startswith(\"_\"):\n", - " print(f\"{k}: {getattr(relaxed_results, k)}\")\n" + " print(f\"{k}: {getattr(relaxed_results, k)}\")" ] }, { @@ -633,7 +633,7 @@ "text": [ "The objective function value: 3.0\n", "x: [0 0 0 1 0 0]\n", - "relaxed function value: -8.999994868883425\n", + "relaxed function value: -8.999994593889271\n", "The number of distinct samples is 1.\n" ] } @@ -651,7 +651,7 @@ " f\"x: {qrao_results_sdr.x}\\n\"\n", " f\"relaxed function value: {-1 * qrao_results_sdr.relaxed_fval}\\n\"\n", " f\"The number of distinct samples is {len(qrao_results_sdr.samples)}.\"\n", - ")\n" + ")" ] }, { @@ -665,7 +665,7 @@ "text": [ "The objective function value: 9.0\n", "x: [1 0 1 0 0 1]\n", - "relaxed function value: -8.999994868883425\n", + "relaxed function value: -8.999994593889271\n", "The number of distinct samples is 56.\n" ] } @@ -682,7 +682,7 @@ " f\"x: {qrao_results_mr.x}\\n\"\n", " f\"relaxed function value: {-1 * qrao_results_mr.relaxed_fval}\\n\"\n", " f\"The number of distinct samples is {len(qrao_results_mr.samples)}.\"\n", - ")\n" + ")" ] }, { @@ -742,7 +742,7 @@ "\n", "maxcut = Maxcut(graph)\n", "problem = maxcut.to_quadratic_program()\n", - "print(problem.prettyprint())\n" + "print(problem.prettyprint())" ] }, { @@ -779,7 +779,7 @@ "print(\"Encoded Problem:\\n=================\")\n", "print(encoding.qubit_op) # The Hamiltonian without the offset\n", "print(\"Offset = \", encoding.offset)\n", - "print(\"Variables encoded on each qubit: \", encoding.q2vars)\n" + "print(\"Variables encoded on each qubit: \", encoding.q2vars)" ] }, { @@ -807,7 +807,7 @@ " print(\n", " f\"Violation identified: {str_dvars} evaluates to {obj_val} \"\n", " f\"but the encoded problem evaluates to {encoded_obj_val}.\"\n", - " )\n" + " )" ] }, { @@ -828,7 +828,7 @@ { "data": { "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+8a52d88
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Thu Sep 07 21:45:37 2023 JST
" + "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.24.0.dev0+8a52d88
qiskit-aer0.12.0
qiskit-optimization0.6.0
System information
Python version3.9.10
Python compilerClang 13.1.6 (clang-1316.0.21.2.5)
Python buildmain, Aug 9 2022 18:26:17
OSDarwin
CPUs10
Memory (Gb)64.0
Thu Sep 07 21:53:47 2023 JST
" ], "text/plain": [ "" From d5ffb28247cac097900d468042d2eeabaf9864af Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Thu, 7 Sep 2023 22:32:09 +0900 Subject: [PATCH 66/67] fix --- .../algorithms/qrao/quantum_random_access_optimizer.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py index a4559a1fc..9d41ab4f5 100644 --- a/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py +++ b/qiskit_optimization/algorithms/qrao/quantum_random_access_optimizer.py @@ -224,7 +224,7 @@ def solve_relaxed( # Get auxiliary expectation values for rounding. expectation_values: list[complex] | None = None if relaxed_result.aux_operators_evaluated is not None: - expectation_values = [v[0] for v in relaxed_result.aux_operators_evaluated] + expectation_values = [v[0] for v in relaxed_result.aux_operators_evaluated] # type: ignore # Get the circuit corresponding to the relaxed solution. if isinstance(relaxed_result, VariationalResult): From 208daad03b9d37341694eecfe26f182e90ef703b Mon Sep 17 00:00:00 2001 From: a-matsuo Date: Fri, 8 Sep 2023 17:16:43 +0900 Subject: [PATCH 67/67] change the index number --- ...s_optimizer.ipynb => 12_quantum_random_access_optimizer.ipynb} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/tutorials/{13_quantum_random_access_optimizer.ipynb => 12_quantum_random_access_optimizer.ipynb} (100%) diff --git a/docs/tutorials/13_quantum_random_access_optimizer.ipynb b/docs/tutorials/12_quantum_random_access_optimizer.ipynb similarity index 100% rename from docs/tutorials/13_quantum_random_access_optimizer.ipynb rename to docs/tutorials/12_quantum_random_access_optimizer.ipynb