Adaptive weight estimator for quantum error correction

TL;DR

This paper introduces an adaptive weight estimation method for quantum error correction that dynamically adjusts to changing error environments, improving decoding performance without relying on a fixed error model.

Contribution

It presents a novel adaptive decoder that estimates weights directly from measurement data, enabling effective quantum error correction in time-varying error conditions.

Findings

The adaptive decoder performs well when environmental variations are slow compared to the error correction cycle.

The method does not require prior knowledge of the physical error model.

Performance depends on the characteristic time scale of error fluctuations.

Abstract

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 we show how 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 time scale $\tau_{\mathrm{env}}$ of the variations is greater than $\delta t/\bar{p}$, with $\delta t$ the duration of one error-correction cycle and $\bar{p}$ the typical error probability per qubit in one cycle.