54 lines
1.4 KiB
Plaintext
54 lines
1.4 KiB
Plaintext
---
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title: double_commutator
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description: API reference for qiskit.quantum_info.double_commutator
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in_page_toc_min_heading_level: 1
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python_api_type: function
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python_api_name: qiskit.quantum_info.double_commutator
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---
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<span id="qiskit-quantum-info-double-commutator" />
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# qiskit.quantum\_info.double\_commutator
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<Function id="qiskit.quantum_info.double_commutator" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.24/qiskit/quantum_info/operators/utils/double_commutator.py" signature="double_commutator(a, b, c, *, commutator=True)">
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Compute symmetric double commutator of a, b and c.
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See also Equation (13.6.18) in \[1].
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If commutator is True, it returns
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$$
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[[A, B], C]/2 + [A, [B, C]]/2
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= (2ABC + 2CBA - BAC - CAB - ACB - BCA)/2.
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$$
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If commutator is False, it returns
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$$
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\lbrace[A, B], C\rbrace/2 + \lbrace A, [B, C]\rbrace/2
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= (2ABC - 2CBA - BAC + CAB - ACB + BCA)/2.
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$$
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**Parameters**
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* **a** (*OperatorTypeT*) – Operator a.
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* **b** (*OperatorTypeT*) – Operator b.
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* **c** (*OperatorTypeT*) – Operator c.
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* **commutator** (*bool*) – If `True` compute the double commutator, if `False` the double anti-commutator.
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**Returns**
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The double commutator
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**Return type**
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*OperatorTypeT*
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**References**
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## \[1]: R. McWeeny.
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Methods of Molecular Quantum Mechanics. 2nd Edition, Academic Press, 1992. ISBN 0-12-486552-6.
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</Function>
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