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Paper 1
Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices
Sisi Miao, Alexander Schnerring, Haizheng Li, Laurent Schmalen
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2308.08208
- arXiv
- 2308.08208
Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this work, we first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. Then, we extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders. Numerical simulation results demonstrate that both approaches as well as their combination yield a low-latency, high-performance decoder for several short to moderate length QLDPC codes.
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Simulation of quantum computation with magic states via Jordan-Wigner transformations
Michael Zurel, Lawrence Z. Cohen, Robert Raussendorf
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2307.16034
- arXiv
- 2307.16034
Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the magic state model. It is based on generalized Jordan-Wigner transformations, and it has a close connection to the probability representation of universal quantum computation based on the $Λ$ polytopes. For each number of qubits, it defines a polytope contained in the $Λ$ polytope with some shared vertices. It leads to an efficient classical simulation algorithm for magic state quantum circuits for which the input state is positively represented, and it outperforms previous representations in terms of the states that can be positively represented.
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