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International Conference on Educational and Information Technology

One kind of quantum CSS code for burst errors

Jianhong Shi, Wan‐Su Bao

Published Sep 1, 2010• 0 citations
Publisher

Abstract

Quantum error correction is an important research area of quantum information. This paper proposes one kind of quantum CSS code for burst errors. Two construction methods are given of the proposed CSS code obtaining from classical cyclic code. Using these methods, a group of CSS codes of length 15 and 30 suitable for burst errors are obtained. In conclusion, the capability of correcting burst errors of the quantum CSS codes is much larger than their capability of correcting random errors.

DOI
10.1109/iceit.2010.5607805

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Quantum error correction is an important research area of quantum information. This paper proposes one kind of quantum CSS code for burst errors. Two construction methods are given of the proposed CSS code obtaining from classical cyclic code. Using these methods, a group of CSS codes of length 15 and 30 suitable for burst errors are obtained. In conclusion, the capability of correcting burst errors of the quantum CSS codes is much larger than their capability of correcting random errors.
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.
Stabilizer codes are an important branch of quantum codes, but the existing stabilizer codes constructed from the classical binary codes almost exclusively belong to the special subclass of CSS codes. This paper develops simple and systematic constructions for two rich classes of non-CSS quantum stabilizer codes: quantum low density parity check (LDPC) codes based on classical quasi-cyclic LDPC codes and quantum convolutional codes based on classical LDPC-convolutional codes. Both classes enjoy a wide range of lengths and rates, and offer stronger error correction capability than the existing codes.
Burst errors, which involve the corruption of consecutive symbols, are a more realistic and common type of error in many communication and storage systems. While classical codes for burst correction are well-established, quantum errorcorrecting codes that handle burst errors and error localization have been less explored. In this paper, we present constructions of quantum codes designed to locate and correct burst errors. We introduce a nearly optimal quantum error-locating burst code, which can identify an interval of2b2 b2bqubits containing a burst of quantum errors of length at mostbbb, improving upon previous constructions in terms of redundancy. This code leverages a stabilizer framework that is not based on the CSS (Calderbank-Shor-Steane) construction, offering a more efficient error-locating capability. Additionally, our construction can correct a large structured set of burst errors, specifically those of lengthbbbthat do not end with aYYYPauli operator. We prove that the redundancy of this code is optimal with respect to this error set.
We prove that certain classical cyclic redundancy check codes can be used for classical error correction and not just classical error detection. We extend the idea of classical cyclic redundancy check codes to quantum cyclic redundancy check codes. This allows us to construct quantum stabilizer codes which can correct burst errors where the burst length attains the quantum Reiger bound. We then consider a certain family of quantum cyclic redundancy check codes for which we present a fast linear time decoding algorithm.