def METHOD_NAME(circuit):
    class NoiseOnLastQubitOnly(cirq.NoiseModel):
        def __init__(self):
            self.qubit_noise_gate = cirq.amplitude_damp(1.0)
        def noisy_moment(self, moment, system_qubits):
            return [
                moment,
                cirq.Moment(
                    [
                        self.qubit_noise_gate(q).with_tags(cirq.ops.VirtualTag())
                        for q in system_qubits[-1:]
                    ]
                ),
            ]
    noise = NoiseOnLastQubitOnly()
    noisy_simulator = cirq.DensityMatrixSimulator(noise=noise)
    _, intermediate_results = dfe.direct_fidelity_estimation(
        circuit, qubits, noisy_simulator, n_measured_operators=None, samples_per_term=1
    )
    return intermediate_results.pauli_traces, intermediate_results.clifford_tableau is not None