2013/11/19 by Hussain Anwar, Benjamin J. Brown, Earl T. Campbell +1 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Code (set theory) #Combinatorics #Computer science #Decoding methods #Error detection and correction #Generalization #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum mechanics #Quantum-Dot Cellular Automata #Topology (electrical circuits) #Toric code #quant-ph
paper · pdf · doi:10.1088/1367-2630/16/6/063038
published as New J. Phys. 16 (2014) 063038 · 20 pages, 21 figures, comments are welcome
arxiv created 2013/11/19 · openalex publication_date 2014/06/17 · arxiv updated 2014/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Qudit toric codes are a natural higher-dimensional generalization of the well- studied qubit toric code. However, standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this paper we introduce two renormalization group decoders for qudit codes and analyse their error correction thresholds and efficiency. The first decoder is a generalization of a 'hard-decisions' decoder due to Bravyi and Haah (arXiv:1112.3252). We modify this decoder to overcome a percolation effect which limits its threshold performance for many-level quantum systems. The second decoder is a generalization of a 'soft-decisions' decoder due to Poulin and Duclos-Cianci (2010 Phys. Rev. Lett. 104 050504), with a small cell size to optimize the efficiency of implementation in the high dimensional case. In each case, we estimate thresholds for the uncorrelated bit-flip error model and provide a comparative analysis of the performance of both these approaches to error correction of qudit toric codes.