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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _potential_cross_whole_w(moment_index: int, op: ops.Operation, tolerance: float, state: _OptimizerState) -> None: """Grabs or cancels a held W gate against an existing W gate. [Where W(a) is shorthand for PhasedX(phase_exponent=a).] Uses the following identity: ───W(a)───W(b)─── ≡ ───Z^-a───X───Z^a───Z^-b───X───Z^b─── ≡ ───Z^-a───Z^-a───Z^b───X───X───Z^b─── ≡ ───Z^-a───Z^-a───Z^b───Z^b─── ≡ ───Z^2(b-a)─── """

    state.deletions.append((moment_index, op))

    _, phase_exponent = cast(Tuple[float, float],
                             _try_get_known_phased_pauli(op))
    q = op.qubits[0]
    a = state.held_w_phases.get(q)
    b = phase_exponent

    if a is None:
        # Collect the gate.
        state.held_w_phases[q] = b
    else:
        # Cancel the gate.
        state.held_w_phases[q] = None
        t = 2*(b - a)
        if not decompositions.is_negligible_turn(t / 2, tolerance):
            leftover_phase = ops.Z(q)**t
            state.inline_intos.append((moment_index, leftover_phase))