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. If the operator tracks no groups, this returns None.

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

Note

This inherits the one-sided guarantee of is_hermitian(): a True entry is always reliable, while a False entry is reliable only for operator types whose normal form is a genuine canonical form. For the others the check is conservative and can report False for a group that is in fact Hermitian.

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_fermions.operators import FermionOperator
>>> from qiskit_fermions.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 = FermionOperator(
...     [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 conjugate 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).