Enhancing Decoding Performance using Efficient Error Learning

TL;DR

This paper introduces a method to improve quantum error correction by using efficient error learning from partial error data, significantly enhancing decoding performance with minimal additional resource overhead.

Contribution

It demonstrates how adapting maximum likelihood decoders with error information from Cycle Error Reconstruction improves quantum code decoding efficiency and performance.

Findings

Achieves 10x performance gain using only 1% of error data

Significant improvements across various error models

Utilizes heuristic to complete error distribution from limited data

Abstract

Lowering the resource overhead needed to achieve fault-tolerant quantum computation is crucial to building scalable quantum computers. We show that adapting conventional maximum likelihood (ML) decoders to a small subset of efficiently learnable physical error characteristics can significantly improve the logical performance of a quantum error-correcting code. Specifically, we leverage error information obtained from efficient characterization methods based on Cycle Error Reconstruction (CER), which yields Pauli error rates on the $n$ qubits of an error-correcting code. Although the total number of Pauli error rates needed to describe a general noise process is exponentially large in $n$, we show that only a few of the largest few Pauli error rates are needed and that a heuristic technique can complete the Pauli error distribution for ML decoding from this restricted dataset. Using these techniques, we demonstrate significant performance improvements for decoding quantum codes under a variety of physically relevant error models. For instance, with CER data that constitute merely $1\%$ of the Pauli error rates in the system, we achieve a $10X$ gain in performance compared to the case where decoding is based solely on the fidelity of the underlying noise process. Our conclusions underscore the promise of recent error characterization methods for improving quantum error correction and lowering overheads.