Affine Subcode Ensemble Decoding for Degeneracy-Aware Quantum Error Correction

2026-05-07

AI Summary

This work addresses the challenge of poor convergence in belief propagation (BP) decoding of quantum low-density parity-check (QLDPC) codes, which arises from degeneracy and limits error-correction performance. The authors propose the first extension of classical affine subcode-integrated decoding to the quantum setting, explicitly handling degeneracy by augmenting the stabilizer code’s parity-check matrix with linearly independent rows to form a hypergraph-cover representation. This approach effectively reduces the search space of viable error corrections, thereby significantly improving BP decoder convergence. Monte Carlo simulations on toric codes and generalized bicycle codes demonstrate a marked reduction in logical error rates, confirming the efficacy and superiority of the proposed method.

Abstract

Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show that appending linearly independent rows to a check matrix of a stabilizer code can reduce the search space for a valid degenerate solution. Motivated by this, we extend the recently proposed affine subcode ensemble decoding technique from the classical to the quantum setting. Moreover, we employ overcomplete matrices for each decoding path. Monte-Carlo simulations on toric and generalized bicycle codes demonstrate improved convergence and reduced logical error rate.

Problem

• quantum error correction
• degeneracy
• belief-propagation decoding
• LDPC codes
• stabilizer codes

Innovation

• affine subcode ensemble decoding
• degeneracy-aware decoding
• quantum LDPC codes
• overcomplete check matrices
• belief propagation