# This code is part of a Qiskit project.
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# (C) Copyright IBM 2022, 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.
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"""
Commutator Utilities (:mod:`qiskit_nature.second_q.operators.commutators`)
==========================================================================
.. currentmodule:: qiskit_nature.second_q.operators.commutators
Utility functions to compute commutators of
:class:`qiskit_nature.second_q.operators.SparseLabelOp` instances.
.. autosummary::
:toctree: ../stubs/
commutator
anti_commutator
double_commutator
"""
from .sparse_label_op import SparseLabelOp
[ドキュメント]def commutator(op_a: SparseLabelOp, op_b: SparseLabelOp) -> SparseLabelOp:
r"""Compute commutator of `op_a` and `op_b`.
.. math::
AB - BA.
Args:
op_a: Operator A.
op_b: Operator B.
Returns:
The computed commutator. If available for your kind of operator, you may want to
``normal_order()`` it.
"""
return (op_a @ op_b - op_b @ op_a).simplify(atol=0)
[ドキュメント]def anti_commutator(op_a: SparseLabelOp, op_b: SparseLabelOp) -> SparseLabelOp:
r"""Compute anti-commutator of `op_a` and `op_b`.
.. math::
AB + BA.
Args:
op_a: Operator A.
op_b: Operator B.
Returns:
The computed anti--commutator. If available for your kind of operator, you may want to
``normal_order()`` it.
"""
return (op_a @ op_b + op_b @ op_a).simplify(atol=0)
[ドキュメント]def double_commutator(
op_a: SparseLabelOp,
op_b: SparseLabelOp,
op_c: SparseLabelOp,
sign: bool = False,
) -> SparseLabelOp:
r"""Compute symmetric double commutator of `op_a`, `op_b` and `op_c`.
See also Equation (13.6.18) in [1].
If `sign` is `False`, it returns
.. math::
[[A, B], C]/2 + [A, [B, C]]/2
= (2ABC + 2CBA - BAC - CAB - ACB - BCA)/2.
If `sign` is `True`, it returns
.. math::
\lbrace[A, B], C\rbrace/2 + \lbrace A, [B, C]\rbrace/2
= (2ABC - 2CBA - BAC + CAB - ACB + BCA)/2.
Args:
op_a: Operator A.
op_b: Operator B.
op_c: Operator C.
sign: False anti-commutes, True commutes.
Returns:
The computed double commutator.
References:
[1]: R. McWeeny.
Methods of Molecular Quantum Mechanics.
2nd Edition, Academic Press, 1992.
ISBN 0-12-486552-6.
"""
sign_num = 1 if sign else -1
op_ab = op_a @ op_b
op_ba = op_b @ op_a
op_ac = op_a @ op_c
op_ca = op_c @ op_a
op_abc = op_ab @ op_c
op_cba = op_c @ op_ba
op_bac = op_ba @ op_c
op_cab = op_c @ op_ab
op_acb = op_ac @ op_b
op_bca = op_b @ op_ca
res = (
op_abc
- sign_num * op_cba
+ 0.5 * (-op_bac + sign_num * op_cab - op_acb + sign_num * op_bca)
)
return res.simplify(atol=0)