Quantum Error Correction Exploiting Degeneracy to Approach the Hashing Bound

2025-06-18

AI Summary

Quantum error correction faces the fundamental challenge of leveraging error degeneracy to approach the quantum Hashing bound. This paper proposes a degeneracy-aware LDPC code iterative decoding framework that, for the first time, explicitly models and jointly optimizes the degenerate structure of quantum errors alongside high-order Galois-field LDPC code design. Extensive Monte Carlo simulations are conducted under the depolarizing channel. Compared to conventional decoders, our method achieves a threshold of 9.45% physical error rate at code rate 1/3 and logical size 104k qubits (312k physical qubits), with a frame error rate of 10⁻⁴—significantly closing the gap to the quantum Hashing bound. The core innovation lies in embedding degeneracy into the belief propagation process, enabling simultaneous breakthroughs in decoding performance and theoretical limit attainment at high code rates.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and compatibility with iterative decoding algorithms whose computational complexity scales linearly with the number of physical qubits. In this work, we demonstrate that explicitly exploiting the degeneracy of quantum errors can significantly enhance the decoding performance. Simulation results over the depolarizing channel indicate that the proposed method, at a coding rate of 1/3, achieves a frame error rate as low as $10^{-4}$ at a physical error rate of 9.45% for a code with 104,000 logical qubits and 312,000 physical qubits, approaching the quantum hashing bound. These findings highlight the critical role of degeneracy in closing the gap to the fundamental limits of quantum error correction.

Problem

• Enhancing quantum error correction by exploiting degeneracy
• Approaching the quantum hashing bound with improved decoding
• Scaling quantum computation with low-density parity-check codes

Innovation

• Exploits quantum error degeneracy for enhancement
• Uses low-density parity-check Galois field codes
• Approaches quantum hashing bound performance