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arXiv:1604.07193 · Quantum Information Processing

Quantum error-correcting codes from algebraic geometry codes of Castle type

Carlos Munuera, Wanderson Tenório, Fernando Torres

Published Jul 2, 2016• 29 citations
arXivHTMLPDF
DOI
10.1007/s11128-016-1378-9

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Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct three families of QUENTA codes, where one of them has maximal entanglement and is maximal distance separable. At the end, we show that for any asymptotically good tower of algebraic function fields there is an asymptotically good family of maximal entanglement QUENTA codes with nonzero rate, relative minimal distance, and relative amount of entanglement