  In practical communication and computation systems, errors occur
predominantly in adjacent positions rather than in a random manner. In this
paper, we develop a stabilizer formalism for quantum burst error correction
codes (QBECC) to combat such error patterns in the quantum regime. Our
contributions are as follows. Firstly, we derive an upper bound for the
correctable burst errors of QBECCs, the quantum Reiger bound (QRB). This bound
generalizes the quantum Singleton bound for standard quantum error correction
codes (QECCs). Secondly, we propose two constructions of QBECCs: one by
heuristic computer search and the other by concatenating two quantum tensor
product codes (QTPCs). We obtain several new QBECCs with better parameters than
existing codes with the same coding length. Moreover, some of the constructed
codes can saturate the quantum Reiger bounds. Finally, we perform numerical
experiments for our constructed codes over Markovian correlated depolarizing
quantum memory channels, and show that QBECCs indeed outperform standard QECCs
in this scenario.
