feature: adding TwoQubitPauliChannel (#300)

src/braket/circuits/noise.py

@@ -11,7 +11,7 @@
 # ANY KIND, either express or implied. See the License for the specific
 # language governing permissions and limitations under the License.
 
-from typing import Any, Optional, Sequence
+from typing import Any, Dict, Optional, Sequence
 
 from braket.circuits.quantum_operator import QuantumOperator
 from braket.circuits.qubit_set import QubitSet
@@ -121,7 +121,7 @@ def __init__(
     def probability(self) -> float:
         """
         Returns:
-            probability (float): The probability that parameterizes the noise channel.
+            probability (float): The probability that parametrizes the noise channel.
         """
         return self._probability
 
@@ -163,7 +163,7 @@ def __init__(
     def probability(self) -> float:
         """
         Returns:
-            probability (float): The probability that parameterizes the noise channel.
+            probability (float): The probability that parametrizes the noise channel.
         """
         return self._probability
 
@@ -205,18 +205,110 @@ def __init__(
     def probability(self) -> float:
         """
         Returns:
-            probability (float): The probability that parameterizes the noise channel.
+            probability (float): The probability that parametrizes the noise channel.
         """
         return self._probability
 
     def __repr__(self):
         return f"{self.name}('probability': {self.probability}, 'qubit_count': {self.qubit_count})"
 
 
+class MultiQubitPauliNoise(Noise):
+    """
+    Class `MultiQubitPauliNoise` represents a general multi-qubit Pauli channel,
+    parameterized by up to 4**N - 1 probabilities.
+    """
+
+    _allowed_substrings = {"I", "X", "Y", "Z"}
+
+    def __init__(
+        self,
+        probabilities: Dict[str, float],
+        qubit_count: Optional[int],
+        ascii_symbols: Sequence[str],
+    ):
+        """[summary]
+
+        Args:
+            probabilities (Dict[str, float]): A dictionary with Pauli string as the keys,
+            and the probabilities as values, i.e. {"XX": 0.1. "IZ": 0.2}.
+            qubit_count (Optional[int]): The number of qubits the Pauli noise acts on.
+            ascii_symbols (Sequence[str]): ASCII string symbols for the noise. These are used when
+                printing a diagram of a circuit. The length must be the same as `qubit_count`, and
+                index ordering is expected to correlate with the target ordering on the instruction.
+
+        Raises:
+            ValueError: If the `qubit_count` is less than 1, `ascii_symbols` are `None`, or
+                `ascii_symbols` length != `qubit_count`. Also if `probabilities` are not `float`s,
+                any `probabilities` > 1, or `probabilities` < 0, or if the sum of all
+                probabilities is > 1,
+                or if "II" is specified as a Pauli string.
+                Also if any Pauli string contains invalid strings.
+                Also if the length of probabilities is greater than 4**qubit_count.
+            TypeError: If the type of the dictionary keys are not strings.
+                If the probabilities are not floats.
+        """
+
+        super().__init__(qubit_count=qubit_count, ascii_symbols=ascii_symbols)
+        self.probabilities = probabilities
+
+        if not probabilities:
+            raise ValueError("Pauli dictionary must not be empty.")
+
+        identity = self.qubit_count * "I"
+        if identity in probabilities:
+            raise ValueError(
+                f"{identity} is not allowed as a key. Please enter only non-identity Pauli strings."
+            )
+
+        for pauli_string, prob in probabilities.items():
+            if not isinstance(pauli_string, str):
+                raise TypeError(f"Type of {pauli_string} was not a string.")
+            if len(pauli_string) != self.qubit_count:
+                raise ValueError(
+                    (
+                        "Length of each Pauli string must be equal to number of qubits. "
+                        f"{pauli_string} had length {len(pauli_string)} instead of length {self.qubit_count}."  # noqa
+                    )
+                )
+            if not isinstance(prob, float):
+                raise TypeError(
+                    (
+                        "Probabilities must be a float type. "
+                        f"The probability for {pauli_string} was of type {type(prob)}."
+                    )
+                )
+            if not set(pauli_string) <= self._allowed_substrings:
+                raise ValueError(
+                    (
+                        "Strings must be Pauli strings consisting of only [I, X, Y, Z]. "
+                        f"Received {pauli_string}."
+                    )
+                )
+            if prob < 0.0 or prob > 1.0:
+                raise ValueError(
+                    (
+                        "Individual probabilities must be real numbers in the interval [0, 1]. "
+                        f"Probability for {pauli_string} was {prob}."
+                    )
+                )
+        total_prob = sum(probabilities.values())
+        if total_prob > 1.0 or total_prob < 0.0:
+            raise ValueError(
+                (
+                    "Total probability must be a real number in the interval [0, 1]. "
+                    f"Total probability was {total_prob}."
+                )
+            )
+
+    def __repr__(self):
+        return f"{self.name}('probabilities' : {self.probabilities}, 'qubit_count': {self.qubit_count})"  # noqa
+
+
 class PauliNoise(Noise):
     """
-    Class `PauliNoise` represents the general Pauli noise channel on N qubits
-    parameterized by three probabilities.
+    Class `PauliNoise` represents the a single-qubit Pauli noise channel
+    acting on one qubit. It is parameterized by three probabilities.
     """
 
     def __init__(

src/braket/circuits/noises.py

@@ -11,7 +11,8 @@
 # ANY KIND, either express or implied. See the License for the specific
 # language governing permissions and limitations under the License.
 
-from typing import Iterable
+import itertools
+from typing import Dict, Iterable
 
 import numpy as np
 
@@ -21,6 +22,7 @@
 from braket.circuits.noise import (
     DampingNoise,
     GeneralizedAmplitudeDampingNoise,
+    MultiQubitPauliNoise,
     Noise,
     PauliNoise,
     SingleProbabilisticNoise,
@@ -552,6 +554,135 @@ def two_qubit_dephasing(
 Noise.register_noise(TwoQubitDephasing)
 
 
+class TwoQubitPauliChannel(MultiQubitPauliNoise):
+    """Two-Qubit Pauli noise channel which transforms a
+        density matrix :math:`\\rho` according to:
+
+    .. math::
+        \\rho \\Rightarrow (1-p) \\rho +
+            p_{IX} IX \\rho IX^{\\dagger} +
+            p_{IY} IY \\rho IY^{\\dagger} +
+            p_{IZ} IZ \\rho IZ^{\\dagger} +
+            p_{XI} XI \\rho XI^{\\dagger} +
+            p_{XX} XX \\rho XX^{\\dagger} +
+            p_{XY} XY \\rho XY^{\\dagger} +
+            p_{XZ} XZ \\rho XZ^{\\dagger} +
+            p_{YI} YI \\rho YI^{\\dagger} +
+            p_{YX} YX \\rho YX^{\\dagger} +
+            p_{YY} YY \\rho YY^{\\dagger} +
+            p_{YZ} YZ \\rho YZ^{\\dagger} +
+            p_{ZI} ZI \\rho ZI^{\\dagger} +
+            p_{ZX} ZX \\rho ZX^{\\dagger} +
+            p_{ZY} ZY \\rho ZY^{\\dagger} +
+            p_{ZZ} ZZ \\rho ZZ^{\\dagger})
+    where
+
+    .. math::
+        I = \\left(
+                \\begin{matrix}
+                    1 & 0 \\\\
+                    0 & 1
+                \\end{matrix}
+            \\right)
+
+        X = \\left(
+                \\begin{matrix}
+                    0 & 1 \\\\
+                    1 & 0
+                \\end{matrix}
+            \\right)
+
+        Y = \\left(
+                \\begin{matrix}
+                    0 & -i \\\\
+                    i &  0
+                \\end{matrix}
+            \\right)
+
+        Z = \\left(
+                \\begin{matrix}
+                    1 & 0 \\\\
+                    0 & -1
+                \\end{matrix}
+            \\right)
+
+        p = \\text{sum of all probabilities}
+
+    This noise channel is shown as `PC_2({"pauli_string": probability})` in circuit diagrams.
+    """
+
+    _paulis = {
+        "I": np.array([[1.0, 0.0], [0.0, 1.0]], dtype=complex),
+        "X": np.array([[0.0, 1.0], [1.0, 0.0]], dtype=complex),
+        "Y": np.array([[0.0, -1.0j], [1.0j, 0.0]], dtype=complex),
+        "Z": np.array([[1.0, 0.0], [0.0, -1.0]], dtype=complex),
+    }
+    _tensor_products_strings = itertools.product(_paulis.keys(), repeat=2)
+    _names_list = ["".join(x) for x in _tensor_products_strings]
+
+    def __init__(self, probabilities: Dict[str, float]):
+        super().__init__(
+            probabilities=probabilities,
+            qubit_count=None,
+            ascii_symbols=[
+                f"PC2({probabilities})",
+                f"PC2({probabilities})",
+            ],
+        )
+
+        total_prob = sum(self.probabilities.values())
+
+        K_list = [np.sqrt(1 - total_prob) * np.identity(4)]  # "II" element
+        for pstring in self._names_list[1:]:  # ignore "II"
+            if pstring in self.probabilities:
+                mat = np.sqrt(self.probabilities[pstring]) * np.kron(
+                    self._paulis[pstring[0]], self._paulis[pstring[1]]
+                )
+                K_list.append(mat)
+            else:
+                K_list.append(np.zeros((4, 4)))
+        self._matrix = K_list
+
+    def to_ir(self, target: QubitSet):
+        return ir.MultiQubitPauliChannel.construct(
+            targets=[target[0], target[1]], probabilities=self.probabilities
+        )
+
+    def to_matrix(self) -> Iterable[np.ndarray]:
+        return self._matrix
+
+    @staticmethod
+    def fixed_qubit_count() -> int:
+        return 2
+
+    @staticmethod
+    @circuit.subroutine(register=True)
+    def two_qubit_pauli_channel(
+        target1: QubitInput, target2: QubitInput, probabilities: Dict[str, float]
+    ) -> Iterable[Instruction]:
+        """Registers this function into the circuit class.
+
+        Args:
+            target (Qubit, int, or iterable of Qubit / int): Target qubits
+            probability (float): Probability of two-qubit Pauli channel.
+
+        Returns:
+            Iterable[Instruction]: `Iterable` of Depolarizing instructions.
+
+        Examples:
+            >>> circ = Circuit().two_qubit_pauli_channel(0, 1, {"XX": 0.1})
+        """
+        return [
+            Instruction(
+                Noise.TwoQubitPauliChannel(probabilities=probabilities),
+                target=[target1, target2],
+            )
+        ]
+
+
+Noise.register_noise(TwoQubitPauliChannel)
+
+
 class AmplitudeDamping(DampingNoise):
     """AmplitudeDamping noise channel which transforms a density matrix :math:`\\rho` according to:
 
@@ -789,15 +920,15 @@ class Kraus(Noise):
 
     Args:
         matrices (Iterable[np.array]): A list of matrices that define a noise
-            channel. These matrices need to satisify the requirement of CPTP map.
+            channel. These matrices need to satisfy the requirement of CPTP map.
         display_name (str): Name to be used for an instance of this general noise
             channel for circuit diagrams. Defaults to `KR`.
 
     Raises:
         ValueError: If any matrix in `matrices` is not a two-dimensional square
             matrix,
             or has a dimension length which is not a positive exponent of 2,
-            or the `matrices` do not satisify CPTP condition.
+            or the `matrices` do not satisfy CPTP condition.
     """
 
     def __init__(self, matrices: Iterable[np.ndarray], display_name: str = "KR"):

src/braket/circuits/observables.py

@@ -230,7 +230,7 @@ def eigenvalues(self):
     def eigenvalue(self, index: int) -> float:
         if index in self._eigenvalue_indices:
             return self._eigenvalue_indices[index]
-        dimension = 2 ** self.qubit_count
+        dimension = 2**self.qubit_count
         if index >= dimension:
             raise ValueError(
                 f"Index {index} requested but observable has at most {dimension} eigenvalues"

src/braket/circuits/quantum_operator_helpers.py

@@ -35,7 +35,7 @@ def verify_quantum_operator_matrix_dimensions(matrix: np.array) -> None:
     matrix = np.array(matrix, dtype=complex)
     qubit_count = int(np.log2(matrix.shape[0]))
 
-    if 2 ** qubit_count != matrix.shape[0] or qubit_count < 1:
+    if 2**qubit_count != matrix.shape[0] or qubit_count < 1:
         raise ValueError(f"`matrix` dimension {matrix.shape[0]} is not a positive power of 2")
 
 

src/braket/circuits/unitary_calculation.py

@@ -60,7 +60,7 @@ def calculate_unitary(qubit_count: int, instructions: Iterable[Instruction]) ->
         TypeError: If `instructions` is not composed only of `Gate` instances,
             i.e. a circuit with `Noise` operators will raise this error.
     """
-    unitary = np.eye(2 ** qubit_count, dtype=complex)
+    unitary = np.eye(2**qubit_count, dtype=complex)
     un_tensor = np.reshape(unitary, qubit_count * [2, 2])
 
     for instr in instructions:
@@ -83,4 +83,4 @@ def calculate_unitary(qubit_count: int, instructions: Iterable[Instruction]) ->
             casting="no",
         )
 
-    return np.reshape(un_tensor, 2 * [2 ** qubit_count])
+    return np.reshape(un_tensor, 2 * [2**qubit_count])

src/braket/tasks/gate_model_quantum_task_result.py

@@ -424,7 +424,7 @@ def _probability_from_measurements(
 
         # count the basis state occurrences, and construct the probability vector
         basis_states, counts = np.unique(indices, return_counts=True)
-        probabilities = np.zeros([2 ** num_measured_qubits], dtype=np.float64)
+        probabilities = np.zeros([2**num_measured_qubits], dtype=np.float64)
         probabilities[basis_states] = counts / shots
         return probabilities
 

test/integ_tests/test_tensor_network_simulator.py

@@ -64,7 +64,7 @@ def _qft(circuit, num_qubits):
     for i in range(num_qubits):
         circuit.h(i)
         for j in range(1, num_qubits - i):
-            circuit.cphaseshift(i + j, i, math.pi / (2 ** j))
+            circuit.cphaseshift(i + j, i, math.pi / (2**j))
 
     for qubit in range(math.floor(num_qubits / 2)):
         circuit.swap(qubit, num_qubits - qubit - 1)
@@ -78,7 +78,7 @@ def _inverse_qft(circuit, num_qubits):
 
     for i in reversed(range(num_qubits)):
         for j in reversed(range(1, num_qubits - i)):
-            circuit.cphaseshift(i + j, i, -math.pi / (2 ** j))
+            circuit.cphaseshift(i + j, i, -math.pi / (2**j))
         circuit.h(i)
 
     return circuit