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arXiv · 1311.1533

General quantum error-correcting code with entanglement based on codeword stabilized quantum code

Jeonghwan Shin·Jun Heo·Todd A. Brun
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Abstract

In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes, including additive and nonadditive codes, based on the codeword stabilized framework on subsystems. The codeword stabilized (CWS) framework is a scheme to construct quantum error-correcting codes (QECCs) including both additive and nonadditive codes, and gives a method to construct a QECC from a classical error-correcting code in standard form. Entangled pairs of qubits (ebits) can be used to improve capacity of quantum error correction. In addition, it gives a method to overcome the dual-containing constraint. Operator quantum error correction (OQEC) gives a general framework to construct quantum error-correcting codes. We construct OQEC codes with ebits based on the CWS framework. This new scheme, entanglement-assisted operator codeword stabilized (EAOCWS) quantum codes, is the most general framework we know of to construct both additive and nonadditive codes from classical error-correcting codes. We describe the formalism of our scheme, demonstrate the construction with examples, and give several EAOCWS codes.

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Jeonghwan Shin, Jun Heo, Todd A. Brun. 2013-11-06. General quantum error-correcting code with entanglement based on codeword stabilized quantum code. https://arxiv.org/abs/1311.1533

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