Error Threshold in Active Steering Protocols for Few-Qubit Systems

We study active steering protocols for weakly measured qubits in the presence of error channels due to amplitude and phase noise. If the error rate is sufficiently small, the protocol approaches and stabilizes a predesignated pure target state with high fidelity and high purity, and thus implements autonomous state stabilization. We present numerical simulation results for one and two qubits, taking Andreev qubit circuits as an example. As a function of the error rate, a sharp threshold separates an error-correcting weak-damping regime from a strong-damping regime where the target state cannot be reached anymore. At the threshold, the purity gap closes.