Characterizing the Burst Error Correction Ability of Quantum Cyclic Codes

TL;DR

This paper analyzes the burst error correction capabilities of quantum cyclic codes, providing algorithms to determine their limits, constructing codes that saturate bounds, and introducing an efficient decoder that handles various burst errors.

Contribution

It characterizes the burst error correction limits of quantum cyclic codes, develops polynomial-time algorithms, and proposes a linear-time decoder for practical quantum error correction.

Findings

Quantum Reed-Solomon codes outperform previous burst error correction results.

Many QBECCs saturate the quantum Reiger bound.

The proposed decoder effectively handles degenerate burst errors.

Abstract

Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst errors. In this work, we characterize the burst error correction ability of QCCs constructed from the Calderbank-Shor-Steane (CSS) and the Hermitian constructions. We determine the burst error correction limit of QCCs and quantum Reed-Solomon codes with algorithms in polynomial-time complexities. As a result, lots of QBECCs saturating the quantum Reiger bound are obtained. We show that quantum Reed-Solomon codes have better burst error correction abilities than the previous results. At last, we give the quantum error-trapping decoder (QETD) of QCCs for decoding burst errors. The decoder runs in linear time and can decode both degenerate and nondegenerate burst errors. What's more, the numerical results show that QETD can decode much more degenerate burst errors than the nondegenerate ones.