Quantum Error Correction beyond the Bounded Distance Decoding Limit

TL;DR

This paper introduces quantum error-correcting codes based on non-binary LDPC codes over Galois fields that outperform existing codes and exceed the bounded distance decoding limit, especially with larger Galois fields.

Contribution

It presents a novel quantum error correction scheme using non-binary LDPC codes over Galois fields that surpasses traditional performance limits.

Findings

Codes outperform existing quantum codes

Error floors are significantly reduced with larger Galois fields

Surpass the bounded distance decoding limit

Abstract

In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., $2^p$, the error floors are considerably improved.