def _commutes_(self, other: Any, *, atol: float) -> None | bool | NotImplementedType:
        r"""Determines if this object commutes with the other object.

        Can return None to indicate the commutation relationship is
        indeterminate (e.g. incompatible matrix sizes). Can return
        NotImplemented to indicate to the caller that they should try some other
        way of determining the commutation relationship.

        Args:
            other: The other object that may or may not commute with the
                receiving object.
            atol: Absolute error tolerance. Some objects that commute may appear
                to not quite commute, due to rounding error from floating point
                computations. This parameter indicates an acceptable level of
                deviation from exact commutativity. The exact meaning of what
                error is being tolerated is not specified. It could be the
                maximum angle between rotation axes in the Bloch sphere, or the
                maximum trace of the absolute value of the commutator, or
                some other value convenient to the implementor of the method.

        Returns:
            Whether or not the values commute.

            True: `self` commutes with `other` within absolute tolerance `atol`.

            False: `self` does not commute with `other`.

            None: There is not a well defined commutation result. For example,
            whether or not parameterized operations will commute may depend
            on the parameter values and so is indeterminate.

            NotImplemented: Unable to determine anything about commutativity.
            Consider falling back to other strategies, such as asking
            `other` if it commutes with `self` or computing the unitary
            matrices of both values.
        """
Determines if this object commutes with the other object.

        Can return None to indicate the commutation relationship is
        indeterminate (e.g. incompatible matrix sizes). Can return
        NotImplemented to indicate to the caller that they should try some other
        way of determining the commutation relationship.

        Args:
            other: The other object that may or may not commute with the
                receiving object.
            atol: Absolute error tolerance. Some objects that commute may appear
                to not quite commute, due to rounding error from floating point
                computations. This parameter indicates an acceptable level of
                deviation from exact commutativity. The exact meaning of what
                error is being tolerated is not specified. It could be the
                maximum angle between rotation axes in the Bloch sphere, or the
                maximum trace of the absolute value of the commutator, or
                some other value convenient to the implementor of the method.

        Returns:
            Whether or not the values commute.

            True: `self` commutes with `other` within absolute tolerance `atol`.

            False: `self` does not commute with `other`.

            None: There is not a well defined commutation result. For example,
            whether or not parameterized operations will commute may depend
            on the parameter values and so is indeterminate.

            NotImplemented: Unable to determine anything about commutativity.
            Consider falling back to other strategies, such as asking
            `other` if it commutes with `self` or computing the unitary
            matrices of both values.
        
cirq-core/cirq/protocols/commutes_protocol.py