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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 _single_cross_over_cz(moment_index: int, op: ops.Operation, qubit_with_w: ops.Qid, state: _OptimizerState) -> None: """Crosses exactly one W flip over a partial CZ. [Where W(a) is shorthand for PhasedX(phase_exponent=a).] Uses the following identity: ──────────@───── │ ───W(a)───@^t─── ≡ ───@──────O──────@──────────────────── | | │ (split into on/off cases) ───W(a)───W(a)───@^t────────────────── ≡ ───@─────────────@─────────────O────── | │ | (off doesn't interact with on) ───W(a)──────────@^t───────────W(a)─── ≡ ───────────Z^t───@──────@──────O────── │ | | (crossing causes kickback) ─────────────────@^-t───W(a)───W(a)─── (X Z^t X Z^-t = exp(pi t) I) ≡ ───────────Z^t───@──────────────────── │ (merge on/off cases) ─────────────────@^-t───W(a)────────── ≡ ───Z^t───@────────────── │ ─────────@^-t───W(a)──── """

    t = cast(float, _try_get_known_cz_half_turns(op))
    other_qubit = op.qubits[0] if qubit_with_w == op.qubits[1] else op.qubits[1]
    negated_cz = ops.CZ(*op.qubits)**-t
    kickback = ops.Z(other_qubit)**t

    state.deletions.append((moment_index, op))
    state.inline_intos.append((moment_index, negated_cz))
    state.insertions.append((moment_index, kickback))