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Add Slater determinant and fermionic Gaussian state initial states (#483
) * add QuadraticHamiltonian class * preparation of Slater determinants and fermionic Gaussian states * validate input * expose _fermionic_op as to_fermionic_op * use tuple labels and merge loops * update docs * add num_modes argument * document new errors * add num_modes property * update doc * spelling * mypy * from __future__ import annotations * add release note * trigger CI * fix spelling * update terra * split so each class has own file * fix comments and error messages, don't name registers * revert library init description * run copyright check * add release note * spelling * spelling and docs * make private functions hidden again * mypy * improve docs and error messages * split test file * add input validation * mypy * lint * add slater determinants test file * create utils module * test unsupported mappers fail gracefully * fix imports * raise NotImplementedError for unsupported mapper * improve docs * rewrite documentation * improve docs and error messages * factor out validation function * improve slater determinant docs * add tutorial notebook * typo * fix warning in notebook * edit notebook * comma * spelling and format * add note to QuadraticHamiltonian class * Update docs/tutorials/11_quadratic_hamiltonian_and_slater_determinants.ipynb Co-authored-by: Max Rossmannek <[email protected]> * add hyperlinks * update print output in notebook * Update releasenotes/notes/slater-53415163fff84313.yaml Co-authored-by: Steve Wood <[email protected]> * format * edit notebook kernel to satisfy CI * edit notebook * edit notebook to say creation instead of annihilation Co-authored-by: Panagiotis Barkoutsos <[email protected]> Co-authored-by: Manoel Marques <[email protected]> Co-authored-by: Max Rossmannek <[email protected]> Co-authored-by: Steve Wood <[email protected]> Co-authored-by: Max Rossmannek <[email protected]> Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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docs/tutorials/11_quadratic_hamiltonian_and_slater_determinants.ipynb
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qiskit_nature/circuit/library/initial_states/fermionic_gaussian_state.py
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| # 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. | ||
|
|
||
| """Fermionic Gaussian states.""" | ||
|
|
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| from typing import Optional, Sequence | ||
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| import numpy as np | ||
| from qiskit import QuantumCircuit, QuantumRegister | ||
| from qiskit_nature.converters.second_quantization import QubitConverter | ||
| from qiskit_nature.mappers.second_quantization import JordanWignerMapper | ||
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| from .utils.givens_rotations import _prepare_fermionic_gaussian_state_jordan_wigner | ||
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| def _validate_transformation_matrix( | ||
| mat: np.ndarray, rtol: float = 1e-5, atol: float = 1e-8 | ||
| ) -> None: | ||
| if not len(mat.shape) == 2: | ||
| raise ValueError( | ||
| "transformation_matrix must be a 2-dimensional array. " | ||
| f"Instead, got shape {mat.shape}." | ||
| ) | ||
|
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| n, p = mat.shape # pylint: disable=invalid-name | ||
| if p != n * 2: | ||
| raise ValueError( | ||
| "transformation_matrix must have shape (n_orbitals, 2 * n_orbitals). " | ||
| f"Instead, got shape {mat.shape}." | ||
| ) | ||
|
|
||
| left = mat[:, :n] | ||
| right = mat[:, n:] | ||
| comm1 = left @ left.T.conj() + right @ right.T.conj() | ||
| comm2 = left @ right.T + right @ left.T | ||
| one = np.eye(n) | ||
| zero = np.zeros((n, n)) | ||
| if not np.allclose(comm1, one, rtol=rtol, atol=atol) or not np.allclose(comm2, zero): | ||
| raise ValueError( | ||
| "transformation_matrix does not describe a valid transformation " | ||
| "of fermionic ladder operators. A valid matrix should have the block form " | ||
| "[W1 W2] where W1 @ W1.T.conj() + W2 @ W2.T.conj() = I and " | ||
| "W1 @ W2.T + W2 @ W1.T = 0." | ||
| ) | ||
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| class FermionicGaussianState(QuantumCircuit): | ||
| r"""A circuit that prepares a fermionic Gaussian state. | ||
| A fermionic Gaussian state is a state of the form | ||
| .. math:: | ||
| b^\dagger_1 \cdots b^\dagger_{N_p} \lvert \overline{\text{vac}} \rangle | ||
| where | ||
| .. math:: | ||
| \begin{pmatrix} | ||
| b^\dagger_1 \\ | ||
| \vdots \\ | ||
| b^\dagger_N \\ | ||
| \end{pmatrix} | ||
| = W | ||
| \begin{pmatrix} | ||
| a^\dagger_1 \\ | ||
| \vdots \\ | ||
| a^\dagger_N \\ | ||
| a_1 \\ | ||
| \vdots \\ | ||
| a_N | ||
| \end{pmatrix}, | ||
| - :math:`a^\dagger_1, \ldots, a^\dagger_{N}` are the fermionic creation operators | ||
| - :math:`W` is an :math:`N \times 2N` matrix such that | ||
| :math:`b^\dagger_1, \ldots, b^\dagger_{N}` also satisfy the | ||
| fermionic anticommutation relations | ||
| - :math:`\lvert \overline{\text{vac}} \rangle` is the mutual 0-eigenvector of | ||
| the operators :math:`\{b_j^\dagger b_j\}` | ||
| The matrix :math:`W` has the block form | ||
| .. math:: | ||
| \begin{pmatrix} | ||
| W_1 & W_2 | ||
| \end{pmatrix} | ||
| where :math:`W_1` and :math:`W_2` must satisfy | ||
| .. math:: | ||
| W_1 W_1^\dagger + W_2 W_2^\dagger = I \\ | ||
| W_1 W_2^T + W_2 W_1^T = 0 | ||
| The matrix :math:`W` is commonly obtained by calling the | ||
| :meth:`~.QuadraticHamiltonian.diagonalizing_bogoliubov_transform` | ||
| method of the :class:`~.QuadraticHamiltonian` class. | ||
| This matrix is used to create circuits that prepare eigenstates of the | ||
| quadratic Hamiltonian. | ||
| Currently, only the Jordan-Wigner Transformation is supported. | ||
| Reference: `arXiv:1711.05395`_ | ||
| .. _arXiv:1711.05395: https://arxiv.org/abs/1711.05395 | ||
| """ | ||
|
|
||
| def __init__( | ||
| self, | ||
| transformation_matrix: np.ndarray, | ||
| occupied_orbitals: Optional[Sequence[int]] = None, | ||
| qubit_converter: QubitConverter = None, | ||
| validate: bool = True, | ||
| rtol: float = 1e-5, | ||
| atol: float = 1e-8, | ||
| **circuit_kwargs, | ||
| ) -> None: | ||
| r""" | ||
| Args: | ||
| transformation_matrix: The matrix :math:`W` that specifies the coefficients of the | ||
| new creation operators in terms of the original creation and annihilation operators. | ||
| This matrix must satisfy special constraints; see the main body of the docstring | ||
| of this class. | ||
| occupied_orbitals: The pseudo-particle orbitals to fill. These refer to the indices | ||
| of the operators :math:`\{b^\dagger_j\}` from the main body of the docstring | ||
| of this function. The default behavior is to use the empty set of orbitals, | ||
| which corresponds to a state with zero pseudo-particles. | ||
| qubit_converter: a QubitConverter instance. | ||
| validate: Whether to validate the inputs. | ||
| rtol: Relative numerical tolerance for input validation. | ||
| atol: Absolute numerical tolerance for input validation. | ||
| circuit_kwargs: Keyword arguments to pass to the QuantumCircuit initializer. | ||
| Raises: | ||
| ValueError: transformation_matrix must be a 2-dimensional array. | ||
| ValueError: transformation_matrix must have shape (n_orbitals, 2 * n_orbitals). | ||
| NotImplementedError: Currently, only the Jordan-Wigner Transform is supported. | ||
| Please use | ||
| :class:`qiskit_nature.mappers.second_quantization.JordanWignerMapper` | ||
| to construct the qubit mapper used to construct `qubit_converter`. | ||
| """ | ||
| if validate: | ||
| _validate_transformation_matrix(transformation_matrix, rtol=rtol, atol=atol) | ||
|
|
||
| if occupied_orbitals is None: | ||
| occupied_orbitals = [] | ||
| if qubit_converter is None: | ||
| qubit_converter = QubitConverter(JordanWignerMapper()) | ||
|
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| n, _ = transformation_matrix.shape | ||
| register = QuantumRegister(n) | ||
| super().__init__(register, **circuit_kwargs) | ||
|
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| if isinstance(qubit_converter.mapper, JordanWignerMapper): | ||
| operations = _prepare_fermionic_gaussian_state_jordan_wigner( | ||
| register, transformation_matrix, occupied_orbitals | ||
| ) | ||
| for gate, qubits in operations: | ||
| self.append(gate, qubits) | ||
| else: | ||
| raise NotImplementedError( | ||
| "Currently, only the Jordan-Wigner Transform is supported. " | ||
| "Please use " | ||
| "qiskit_nature.mappers.second_quantization.JordanWignerMapper " | ||
| "to construct the qubit mapper used to construct qubit_converter." | ||
| ) |
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