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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_qubit_matrix_to_phased_x_z( mat: np.ndarray, atol: float = 0 ) -> List[ops.SingleQubitGate]: """Implements a single-qubit operation with a PhasedX and Z gate. If one of the gates isn't needed, it will be omitted. Args: mat: The 2x2 unitary matrix of the operation to implement. atol: A limit on the amount of error introduced by the construction. Returns: A list of gates that, when applied in order, perform the desired operation. """


    xy_turn, xy_phase_turn, total_z_turn = (
        _deconstruct_single_qubit_matrix_into_gate_turns(mat))

    # Build the intended operation out of non-negligible XY and Z rotations.
    result = [
        ops.PhasedXPowGate(exponent=2 * xy_turn,
                           phase_exponent=2 * xy_phase_turn),
        ops.Z**(2 * total_z_turn)
    ]
    result = [
        g for g in result
        if protocols.trace_distance_bound(g) > atol
    ]

    # Special case: XY half-turns can absorb Z rotations.
    if len(result) == 2 and abs(xy_turn) >= 0.5 - atol:
        return [
            ops.PhasedXPowGate(phase_exponent=2 * xy_phase_turn + total_z_turn)
        ]

    return result