def _parity_interaction(q0: ops.Qid,
                        q1: ops.Qid,
                        rads: float,
                        atol: float,
                        gate: Optional[ops.Gate] = None):
    """Yields a ZZ interaction framed by the given operation."""
    if abs(rads) < atol:
        return

    h = rads * -2 / np.pi
    if gate is not None:
        g = cast(ops.Gate, gate)
        yield g.on(q0), g.on(q1)

    # If rads is ±pi/4 radians within tolerance, single full-CZ suffices.
    if _is_trivial_angle(rads, atol):
        yield ops.CZ.on(q0, q1)
    else:
        yield ops.CZ(q0, q1) ** (-2 * h)

    yield ops.Z(q0)**h
    yield ops.Z(q1)**h
    if gate is not None:
        g = protocols.inverse(gate)
        yield g.on(q0), g.on(q1)