Characterizing the Burst Error Correction Ability of Quantum Cyclic Codes

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.

💡 Research Summary

The paper addresses a fundamental problem in quantum error correction: determining how many consecutive qubits (a burst) a given quantum code can reliably protect against. While classical burst‑error correcting codes have been studied extensively, their quantum counterparts—quantum burst error correcting codes (QBECCs)—have received far less attention, especially regarding systematic methods for evaluating burst‑error capability. The authors focus on the most prominent family of QBECCs, quantum cyclic codes (QCCs), which can be implemented efficiently with quantum shift registers, and on quantum Reed‑Solomon (RS) codes, which are known for strong random‑error performance.

Main contributions

1. Polynomial‑time burst‑error analysis for QCCs
   The authors extend a classical algorithm (originally presented in