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arXiv · 1108.5490

Low-complexity quantum codes designed via codeword-stabilized framework

Alexey A. Kovalev·Ilya Dumer·Leonid P. Pryadko
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Abstract

We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code. For codes that can be obtained from a given graph, we give several upper bounds on the distance of a generic (additive or non-additive) CWS code, and the lower Gilbert-Varshamov bound for the existence of additive CWS codes. We also consider additive cyclic CWS codes and show that these codes correspond to a previously unexplored class of single-generator cyclic stabilizer codes. We present several families of simple stabilizer codes with relatively good parameters.

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Alexey A. Kovalev, Ilya Dumer, Leonid P. Pryadko. 2011-08-28. Low-complexity quantum codes designed via codeword-stabilized framework. https://doi.org/10.1103/physreva.84.062319

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