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On the construction of stabilizer codes with an arbitrary binary matrix

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Abstract

This paper proposes a simple framework for constructing a stabilizer code with an arbitrary binary matrix. We define a relation between A 1 and A 2 of a binary check matrix A = (A 1|A 2) associated with stabilizer generators of a quantum error-correcting code. Given an arbitrary binary matrix, we can derive a pair of A 1 and A 2 by the relation. As examples, we illustrate two kinds of stabilizer codes: quantum LDPC codes and quantum convolutional codes. By the nature of the proposed framework, the stabilizer codes covered in this paper belong to general stabilizer (non-CSS) codes.

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Authors and Affiliations

  1. Department of Information and Communications, Gwangju Institute of Science and Technology, Gwangju, Republic of Korea

    Yongsoo Hwang & Moongu Jeon

  2. Electrical and Computer Engineering Department, Duke University, Durham, NC, USA

    Byung-Soo Choi

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  1. Yongsoo Hwang
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  2. Byung-Soo Choi
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  3. Moongu Jeon
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Correspondence to Moongu Jeon.

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Hwang, Y., Choi, BS. & Jeon, M. On the construction of stabilizer codes with an arbitrary binary matrix. Quantum Inf Process 12, 467–479 (2013). https://doi.org/10.1007/s11128-012-0394-7

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  • DOI: https://doi.org/10.1007/s11128-012-0394-7

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