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In practical communication and computation systems, errors occurpredominantly in adjacent positions rather than in a random manner. In thispaper, we develop a stabilizer formalism for quantum burst error correctioncodes (QBECC) to combat such error patterns in the quantum regime. Ourcontributions are as follows. Firstly, we derive an upper bound for thecorrectable burst errors of QBECCs, the quantum Reiger bound (QRB). This boundgeneralizes the quantum Singleton bound for standard quantum error correctioncodes (QECCs). Secondly, we propose two constructions of QBECCs: one byheuristic computer search and the other by concatenating two quantum tensorproduct codes (QTPCs). We obtain several new QBECCs with better parameters thanexisting codes with the same coding length. Moreover, some of the constructedcodes can saturate the quantum Reiger bounds. Finally, we perform numericalexperiments for our constructed codes over Markovian correlated depolarizingquantum memory channels, and show that QBECCs indeed outperform standard QECCsin this scenario.

Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors