2020/12/31 by Nikolas P. Breuckmann, Jens N. Eberhardt · 134 citations
Computer Science · Physics and Astronomy · #Block code #Complexity and Algorithms in Graphs #Concatenated error correction code #Expander code #Hamming code #Linear code #Low-density parity-check code #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum convolutional code #Qubit #Turbo code #quant-ph
paper · pdf · open access · doi:10.1109/tit.2021.3097347
published in IEEE Transactions on Information Theory 67(10), 6653-6674 (Institute of Electrical and Electronics Engineers) · 23 pages, 11 figures
openalex created_date 2020/12/21 · arxiv created 2021/07/28 · arxiv updated 2021/07/29 · openalex publication_date 2021/08/10 · openalex updated_date 2026/08/05
This work provides the first explicit and non-random family of [[N,K,D]] LDPC quantum codes which encode K ∈ Θ(N^(4)/(5)) logical qubits with distance D ∈ Ω(N^(3)/(5)). The family is constructed by amalgamating classical codes and Ramanujan graphs via an operation called balanced product. Recently, Hastings-Haah-O'Donnell and Panteleev-Kalachev were the first to show that there exist families of LDPC quantum codes which break the polylog(N)√(N) distance barrier. However, their constructions are based on probabilistic arguments which only guarantee the code parameters with high probability whereas our bounds hold unconditionally. Further, balanced products allow for non-abelian twisting of the check matrices, leading to a construction of LDPC quantum codes that can be shown to have K∈ Θ(N) and that we conjecture to have linear distance D∈ Θ(N).