Adaptive Weight Estimator for Quantum Error Correction in a Time-Dependent Environment

Quantum error correction of a surface code or repetition code requires the pairwise matching of error events in a space-time graph of qubit measurements, such that the total weight of the matching is minimized. The input weights follow from a physical model of the error processes that affect the qubits. This approach becomes problematic if the system has sources of error that change over time. Here, it is shown that the weights can be determined from the measured data in the absence of an error model. The resulting adaptive decoder performs well in a time-dependent environment, provided that the characteristic timescale tau(env) of the variations is greater than delta t/(p) over bar, with dt the duration of one error-correction cycle and (p) over bar the typical error probability per qubit in one cycle.