A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices
arXiv:0712.0103 · doi:10.1109/TIT.2011.2165812
Abstract
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in the literature. In this paper, a new but simple construction of stabilizer codes is proposed based on syndrome assignment by classical parity-check matrices. This method reduces the construction of quantum stabilizer codes to the construction of classical parity-check matrices that satisfy a specific commutative condition. The quantum stabilizer codes from this construction have a larger set of correctable error operators than expected. Its (asymptotic) coding efficiency is comparable to that of CSS codes. A class of quantum Reed-Muller codes is constructed, which have a larger set of correctable error operators than that of the quantum Reed-Muller codes developed previously in the literature. Quantum stabilizer codes inspired by classical quadratic residue codes are also constructed and some of which are optimal in terms of their coding parameters.
arXiv comment34 pages, 3 figures, 5 tables, index terms add, abstract and conclusion slightly modified
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Cited by in corpus (5)
- Linear Programming Bounds for Entanglement-Assisted Quantum Error-Correcting Codes by Split Weight Enumerators
- Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes
- Fault-tolerant Preparation of Stabilizer States for Quantum CSS Codes by Classical Error-Correcting Codes
- Transversal Clifford and T-gate codes of short length and high distance
- Design of Quantum Stabilizer Codes From Quadratic Residues Sets