Efficient Approximate Degenerate Ordered Statistics Decoding for Quantum Codes via Reliable Subset Reduction

2024-12-30

AI Summary

Ordered Statistics Decoding (OSD) for quantum error correction suffers from high computational complexity, hindering practical deployment. Method: This paper proposes Approximate Degenerate OSD (ADOSD), the first framework to incorporate approximate degeneracy into OSD. It introduces a hybrid hard/soft-decision reliability metric to efficiently identify critical variables and theoretically identifies a class of degeneracy conditions under which high-order OSD can be rigorously reduced to zeroth-order. Results: Experiments on mainstream quantum codes—including surface codes—demonstrate that ADOSD achieves a higher error threshold and lower logical error rate than standard OSD under 1% depolarizing noise, while its decoding latency is comparable to only 2–3 belief propagation (BP) iterations. Implemented on a single-threaded CPU, ADOSD delivers stable, efficient performance, substantially enhancing the practical feasibility of OSD in real-world quantum error correction systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Efficient decoding of quantum codes is crucial for achieving high-performance quantum error correction. In this paper, we introduce the concept of approximate degenerate decoding and integrate it with ordered statistics decoding (OSD). Previously, we proposed a reliability metric that leverages both hard and soft decisions from the output of belief propagation (BP), which is particularly useful for identifying highly reliable subsets of variables. Using the approach of reliable subset reduction, we reduce the effective problem size. Additionally, we identify a degeneracy condition that allows high-order OSD to be simplified to order-0 OSD. By integrating these techniques, we present an ADOSD algorithm that significantly improves OSD efficiency in the code capacity noise model. We demonstrate the effectiveness of our BP+ADOSD approach through extensive simulations on a varity of quantum codes, including generalized hypergraph-product codes, topological codes, lift-connected surface codes, and bivariate bicycle codes. The results indicate that the BP+ADOSD decoder outperforms existing methods, achieving higher error thresholds and enhanced performance at low error rates. Additionally, we validate the efficiency of our approach in terms of computational time, demonstrating that ADOSD requires, on average, the same amount of time as two to three BP iterations on surface codes at a depolarizing error rate of around $1%$. All the proposed algorithms are compared using single-threaded CPU implementations.

Problem

• Quantum Code Decoding
• Efficiency
• Accuracy

Innovation

• Approximate Decorrelation Decoding
• Quantum Error Correction
• Ordered Statistics Decoding