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

2025-01-23

AI Summary

Non-binary LDPC codes for quantum error correction suffer from error floors induced by short cycles in their parity-check matrices, degrading decoding performance. Method: This work systematically identifies and classifies three critical cycle types (Type-I, Type-II, Type-III) in the Tanner graph and analyzes their distinct impacts on belief propagation (BP) decoding. We propose two novel decoding strategies: (i) an adaptive processing mechanism for Type-I cycles leveraging degeneracy-induced noise asymmetry, and (ii) a collaborative parity-check scheme exploiting Type-III non-codeword cycles. We further prove that Type-II cycles are fundamentally uncorrectable under standard BP. Contribution/Results: Integrating non-binary coding theory, graphical cycle analysis, and algebraic decoding optimization, our approach substantially suppresses the error floor and surpasses conventional BP performance limits in the high-SNR regime, establishing a new paradigm for practical quantum error correction.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Quantum Error Correction
• Traditional Encoding Methods
• Error Rate Reduction

Innovation

• Non-binary LDPC Codes
• Quantum Error Correction
• Matrix Structural Analysis