groups_are_hermitian

groups_are_hermitian(op, *, atol=1e-08)

Returns, for each group, whether the operator formed by that group’s terms is Hermitian.

Groups prescribe no meaning of their own; this checks one common convention, namely that each group is separately Hermitian. That is the property a randomized product formula relies on when it samples whole groups, since only a Hermitian group has a unitary time evolution. It is equally what Qiskit’s PauliEvolutionGate requires of each group once mapped: a lone hopping term b†_i b_j is not Hermitian, so it has to share a group with its adjoint. If the operator tracks no groups, this returns None.

An empty group counts as Hermitian, because the zero operator is.

Note

This is not implied by (nor does it imply) groups_have_uniform_coeffs(). Uniform coefficients do not make a group Hermitian, and a Hermitian group may mix magnitudes.

>>> from qiskit_bosons.operators import BosonOperator
>>> from qiskit_bosons.operators.terms.grouping import groups_are_hermitian
>>> # built from the sparse arrays rather than a dictionary, because only the former
>>> # fixes the term order that the group indices are paired with
>>> op = BosonOperator(
...     [1.0, 1.0, 1.0],
...     [True, False, True, False, True, False],
...     [0, 1, 1, 0, 2, 3],
...     [0, 2, 4, 6],
... )
>>> op.groups = [0, 0, 1]  # the leading hopping pair, then one unpaired term
>>> groups_are_hermitian(op)
[True, False]
Parameters:

  • op – the operator whose groups to check.

  • atol – The numerical accuracy upto which coefficients are considered equal. This value defaults to 1e-8.

Returns:

One flag per group index, or None if the operator tracks no groups.

Raises:

TypeError – if op is not a supported operator type (see OperatorTrait).