Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors
arXiv:1801.03861
Abstract
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.
arXiv commentAccepted by IEEE International Symposium on Information Theory (ISIT), 2018
References in corpus (11)
- Mixed State Entanglement and Quantum Error Correction
- Good Quantum Error-Correcting Codes Exist
- Quantum Error Correction and Orthogonal Geometry
- Correcting Quantum Errors with Entanglement
- Quantum channels and memory effects
- General entanglement-assisted quantum error-correcting codes
- Catalytic quantum error correction
- Entanglement-assisted quantum turbo codes
- Entanglement-Assisted Quantum Quasi-Cyclic Low-Density Parity-Check Codes
- Quantum Stabilizer Codes for Correlated and Asymmetric Depolarizing Errors
- On the MacWilliams Identity for Classical and Quantum Convolutional Codes