def fermi_fourier_trans_inverse_conjugate_4(qubits):
    """We will need to map the momentum states in the reversed order for
    spin-down states to the position picture. This transformation can be
    simply implemented the complex conjugate of the former one. We only
    need to change the S gate to S* = S ** 3.

    Args:
        qubits: list of four qubits
    """

    yield fswap(qubits[1], qubits[2]),
    yield fermi_fourier_trans_2(qubits[0], qubits[1])
    yield fermi_fourier_trans_2(qubits[2], qubits[3])
    yield fswap(qubits[1], qubits[2])
    yield fermi_fourier_trans_2(qubits[0], qubits[1])
    yield cirq.S(qubits[2]) ** 3
    yield fermi_fourier_trans_2(qubits[2], qubits[3])
    yield fswap(qubits[1], qubits[2])