期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 67, 期 10, 页码 6653-6674出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2021.3097347
关键词
Quantum codes; quantum error-correction; quantum fault-tolerance
资金
- University College London Quantum Science and Technology Institute (UCLQ) Fellowship
- Engineering and Physical Sciences Research Council (EPSRC) Prosperity Partnership in Quantum Software for Simulation and Modelling [EP/S005021/1]
- EPSRC [EP/S005021/1] Funding Source: UKRI
This work introduces a novel family of LDPC quantum codes that encode a large number of logical qubits with significant distance. In comparison to previous research, our proposed family offers stronger guarantees and utilizes balanced products for construction.
This work provides the first explicit and non-random family of [[N, K, D]] LDPC quantum codes which encode K is an element of Theta(N-4/5) logical qubits with distance D is an element of Omega(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)root 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 is an element of Theta(N) and that we conjecture to have linear distance D is an element of Theta(N).
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