Quantum Error Correction Exploiting Degeneracy to Approach the Hashing Bound

TL;DR

This paper introduces a quantum error correction method that leverages error degeneracy to significantly improve decoding performance, nearing the theoretical quantum hashing bound with large-scale codes.

Contribution

It demonstrates that explicitly exploiting degeneracy in quantum error correction codes enhances decoding efficiency and performance, approaching fundamental quantum limits.

Findings

Achieves a frame error rate of 10^{-4} at 9.45% physical error rate

Uses codes with over 100,000 logical qubits and 300,000 physical qubits

Approaches the quantum hashing bound with the proposed method

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.