---
title: groups_are_hermitian (latest version)
description: API reference for qiskit_fermions.operators.terms.groups_are_hermitian in the latest version of qiskit-fermions
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit-fermions/operators-terms-groups-are-hermitian
---

# 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()`](/docs/api/qiskit-fermions/operators-operator-trait#is_hermitian "qiskit_fermions.operators.OperatorTrait.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()`](/docs/api/qiskit-fermions/operators-terms-groups-have-uniform-coeffs "qiskit_fermions.operators.terms.groups_have_uniform_coeffs"). Uniform coefficients do not make a group Hermitian, and a Hermitian group may mix magnitudes.

```pycon
>>> 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**](https://docs.python.org/3/builtins/exceptions.html#TypeError) – if `op` is not a supported operator type (see [`OperatorTrait`](/docs/api/qiskit-fermions/operators-operator-trait "qiskit_fermions.operators.OperatorTrait")).