Efficient Mitigation of Error Floors in Quantum Error Correction using Non-Binary Low-Density Parity-Check Codes

Abstract

In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated noise becomes trapped, and develop tailored decoding methods for each cycle type. For Type-I cycles, we propose a method to make the difference between estimated and true noise degenerate. Type-II cycles are shown to be uncorrectable, while for Type-III cycles, we utilize the fact that cycles in non-binary LDPC codes do not necessarily correspond to codewords, allowing us to estimate the true noise. Our method significantly improves decoding performance and reduces error floors.