Affine Subcode Ensemble Decoding for Degeneracy-Aware Quantum Error Correction

TL;DR

This paper extends affine subcode ensemble decoding to quantum error correction, improving convergence and reducing logical error rates in quantum LDPC codes by using overcomplete matrices and check matrix augmentation.

Contribution

It introduces a quantum adaptation of affine subcode ensemble decoding and demonstrates its effectiveness through simulations on quantum codes.

Findings

Improved convergence in quantum LDPC decoding.

Reduced logical error rates in simulations.

Effective use of overcomplete matrices for decoding paths.

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.