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arXiv:2410.07897 · Lecture notes in computer science

Minimal Trellises for Non-degenerate and Degenerate Decoding of Quantum Stabilizer Codes

Evagoras Stylianou, Vladimir R. Sidorenko, Christian Deppe, Holger Boche

Published Jan 1, 2025• 2 citations
arXivHTMLPDF
DOI
10.1007/978-3-031-82014-4_16

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This paper introduces several techniques for minimal trellis construction for degenerate decoding of quantum stabilizer codes, specifically the minimal multi-goal trellis for the cosets of the stabilizer group S in the normalizer group N. The methods include a merging algorithm, a Shannon-product approach, and the BCJR-Wolf method. The study establishes the necessary properties of multi-goal trellises and bounds on the decoding complexity of the minimal multi-goal trellis using the sum-product Viterbi algorithm. The proposed multi-goal trellises decrease the decoding complexity by a factor O(n), where n is the code length.
The size of vertex set of quantum trellises affects the efficiency of decoding algorithms,which can be improved by reducing the number of vertices.Based on the standard check matrix of stabilizer codes,an algorithm to construct trellis-oriented generators for quantum stabilizer codes is presented.By using this algorithm,the trellises with minimal vertex set can be constructed.In addition,an algorithm to construct trellises iteratively for quantum stabilizer codes is also introduced.The algorithm proposed in this paper is more efficient and less complex than the one proposed by Olliver,and so is more suitable for the applications of larger scale and stricter timeliness.