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qiskit.quantum_info.double_commutator

double_commutator(a, b, c, *, commutator=True)

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Compute symmetric double commutator of a, b and c.

See also Equation (13.6.18) in [1].

If commutator is True, it returns

[[A,B],C]/2+[A,[B,C]]/2=(2ABC+2CBA−BAC−CAB−ACB−BCA)/2.[[A, B], C]/2 + [A, [B, C]]/2 = (2ABC + 2CBA - BAC - CAB - ACB - BCA)/2.

If commutator is False, it returns

{[A,B],C}/2+{A,[B,C]}/2=(2ABC−2CBA−BAC+CAB−ACB+BCA)/2.\lbrace[A, B], C\rbrace/2 + \lbrace A, [B, C]\rbrace/2 = (2ABC - 2CBA - BAC + CAB - ACB + BCA)/2.

Parameters

  • a (OperatorTypeT) – Operator a.
  • b (OperatorTypeT) – Operator b.
  • c (OperatorTypeT) – Operator c.
  • commutator (bool) – If True compute the double commutator, if False the double anti-commutator.

Returns

The double commutator

Return type

OperatorTypeT

References

[1]: R. McWeeny.

Methods of Molecular Quantum Mechanics. 2nd Edition, Academic Press, 1992. ISBN 0-12-486552-6.

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