Source code for

# This code is part of a Qiskit project.
# (C) Copyright IBM 2021, 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
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"""The AngularMomentum property."""

from __future__ import annotations

import logging
from typing import Mapping

import numpy as np

import qiskit_nature  # pylint: disable=unused-import
from qiskit_nature.second_q.operators import FermionicOp

from .s_operators import s_minus_operator, s_plus_operator, s_z_operator

LOGGER = logging.getLogger(__name__)

[docs]class AngularMomentum: r"""The AngularMomentum property. The operator constructed by this property is the $S^2$ operator which is computed as: .. math:: S^2 = (S^+ S^- + S^- S^+) / 2 + S^z S^z .. warning:: If you are working with a non-orthogonal basis, you _must_ provide the ``overlap`` attribute in order to obtain the correct expectation value of this observable. Refer to the more extensive documentation of the :mod:`.s_operators` module for more details. See also: - the $S^z$ operator: :func:`.s_z_operator` - the $S^+$ operator: :func:`.s_plus_operator` - the $S^-$ operator: :func:`.s_minus_operator` The following attributes can be set via the initializer but can also be read and updated once the ``AngularMomentum`` object has been constructed. Attributes: num_spatial_orbitals (int): the number of spatial orbitals. """ def __init__(self, num_spatial_orbitals: int, overlap: np.ndarray | None = None) -> None: r""" Args: num_spatial_orbitals: the number of spatial orbitals in the system. overlap: the overlap-matrix between the $\alpha$- and $\beta$-spin orbitals. When this is ``None``, the overlap-matrix is assumed to be identity. """ self.num_spatial_orbitals = num_spatial_orbitals self._overlap: np.ndarray | None = None self.overlap = overlap @property def overlap(self) -> np.ndarray | None: r"""The overlap-matrix between the $\alpha$- and $\beta$-spin orbitals. When this is ``None``, the overlap-matrix is assumed to be identity. """ return self._overlap @overlap.setter def overlap(self, overlap: np.ndarray | None) -> None: self._overlap = overlap if overlap is not None: norb = self.num_spatial_orbitals delta = np.eye(2 * norb) delta[:norb, :norb] -= overlap.T @ overlap delta[norb:, norb:] -= overlap @ overlap.T summed = np.einsum("ij->", np.abs(delta)) if not np.isclose(summed, 0.0, atol=1e-6): LOGGER.warning( "The provided alpha-beta overlap matrix is NOT unitary! This can happen when " "the alpha- and beta-spin orbitals do not span the same space. To provide an " "example of what this means, consider an active space chosen from unrestricted-" "spin orbitals. Computing <S^2> within this active space may not result in the " "same <S^2> value as obtained on the single-reference starting point. More " "importantly, this implies that the inactive subspace will account for the " "difference between these two <S^2> values, possibly resulting in significant " "spin contamination in both subspaces. You should verify whether this is " "intentional/acceptable or whether your choice of active space can be improved." " As a reference, here is the summed-absolute deviation of `S^T @ S` from the " "identity: %s", str(summed), )
[docs] def second_q_ops(self) -> Mapping[str, FermionicOp]: """Returns the second quantized angular momentum operator. Returns: A mapping of strings to `FermionicOp` objects. """ s_z = s_z_operator(self.num_spatial_orbitals) overlap_ab = self.overlap s_p = s_plus_operator(self.num_spatial_orbitals, overlap=overlap_ab) overlap_ba = overlap_ab.T if overlap_ab is not None else None s_m = s_minus_operator(self.num_spatial_orbitals, overlap=overlap_ba) spm_smp = (s_p @ s_m + s_m @ s_p).normal_order() op = 0.5 * spm_smp + s_z @ s_z return {self.__class__.__name__: op}
[docs] def interpret( self, result: "qiskit_nature.second_q.problems.EigenstateResult" # type: ignore[name-defined] ) -> None: """Interprets an :class:`~qiskit_nature.second_q.problems.EigenstateResult` in this property's context. Args: result: the result to add meaning to. """ result.total_angular_momentum = [] if result.aux_operators_evaluated is None: return for aux_op_eigenvalues in result.aux_operators_evaluated: if not isinstance(aux_op_eigenvalues, dict): continue _key = self.__class__.__name__ if aux_op_eigenvalues[_key] is not None: result.total_angular_momentum.append(aux_op_eigenvalues[_key].real) else: result.total_angular_momentum.append(None)