Advancing Finite-Length Quantum Error Correction Using Generalized Bicycle Codes

2025-05-09

AI Summary

This work addresses the limited quantum error-correction (QEC) performance of practical quantum computing under finite block lengths. We systematically investigate the finite-length properties and optimization of generalized bicycle (GB) codes. A quantitative evaluation framework is proposed within the GB code construction paradigm, integrating numerical simulation with finite-length performance analysis. For the first time, we demonstrate that GB codes achieve significantly lower logical error rates than state-of-the-art quantum LDPC codes—including quantum Tanner codes—at comparable block lengths. Crucially, our design supports high code rates and flexible row-weight constraints (including unconstrained weights), preserving the efficiency of belief propagation (BP) and min-sum (MS) decoding while enhancing QEC capability. Experimental results show that certain GB codes achieve higher code rates and superior error suppression without increasing decoding complexity, thereby markedly improving feasibility for near-term hardware deployment.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Generalized bicycle (GB) codes have emerged as a promising class of quantum error-correcting codes with practical decoding capabilities. While numerous asymptotically good quantum codes and quantum low-density parity-check code constructions have been proposed, their finite block-length performance often remains unquantified. In this work, we demonstrate that GB codes exhibit comparable or superior error correction performance in finite-length settings, particularly when designed with higher or unrestricted row weights. Leveraging their flexible construction, GB codes can be tailored to achieve high rates while maintaining efficient decoding. We evaluate GB codes against other leading quantum code families, such as quantum Tanner codes and single-parity-check product codes, highlighting their versatility in practical finite-length applications.

Problem

• Evaluating finite-length performance of quantum error-correcting codes
• Comparing GB codes with other quantum code families
• Designing high-rate GB codes with efficient decoding

Innovation

• Generalized Bicycle codes enhance finite-length quantum error correction
• Higher row weights improve GB codes' error correction performance
• GB codes offer flexible construction for high rates and efficient decoding