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qiskit.quantum_info.double_commutator

double_commutator(a, b, c, *, commutator=True)[source]

Compute symmetric double commutator of a, b and c.

See also Equation (13.6.18) in [1].

If commutator is True, it returns

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

If commutator is False, it returns

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