Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction

TL;DR

GraphQEC is a universal, machine-learning-based decoder for stabilizer codes that achieves high accuracy and efficiency, significantly improving quantum error correction performance across multiple code families.

Contribution

We present GraphQEC, the first universal, code-agnostic quantum decoder leveraging graph-structured machine learning with linear time complexity.

Findings

Achieves 18-fold error rate improvement on a QLDPC code.

Maintains 157 microseconds per cycle decoding speed.

Demonstrates high accuracy across various stabilizer code families.

Abstract

Scaling quantum computing to practical applications necessitates reliable quantum error correction. Although numerous correction codes have been proposed, the overall correction efficiency critically limited by the decode algorithms. We introduce GraphQEC, a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity. GraphQEC demonstrates unprecedented accuracy and efficiency across all tested code families, including surface codes, color codes, and quantum low-density parity-check (QLDPC) codes. For instance, on a distance-12 QLDPC code, GraphQEC achieves a logical error rate of $9.55 \times 10^{-5}$, an 18-fold improvement over the previous best specialized decoder's $1.74 \times 10^{-3}$ under $p=0.005$ physical error rates, while maintaining $157\mu$s/cycle decoding speed. Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.