code: def _potential_cross_whole_w(moment_index: int,
                               op: ops.Operation,
                               tolerance: float,
                               state: _OptimizerState) -> None:
      
      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))
docs: 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)───