# 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()`](qiskit_fermions.operators.OperatorTrait.html.md#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()`](qiskit_fermions.operators.terms.groups_have_uniform_coeffs.html.md#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`](qiskit_fermions.operators.OperatorTrait.html.md#qiskit_fermions.operators.OperatorTrait)).