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Paper 1
Layered Decoding of Quantum LDPC Codes
Julien Du Crest, Francisco Garcia-Herrero, Mehdi Mhalla, Valentin Savin, Javier Valls
- Year
- 2023
- Journal
- arXiv preprint
- DOI
- arXiv:2308.13377
- arXiv
- 2308.13377
We address the problem of performing message-passing-based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling, the usual scheduling on parallel architectures. A generic construction is given to construct layers of hypergraph product codes. In the process, we introduce two new notions, t-covering layers which is a generalization of the usual layer decomposition, and a new scheduling called random order scheduling. Numerical simulations show that the random ordering is of independent interest as it helps relieve the high error floor typical of message-passing decoders on quantum codes for both layered and serial decoding without the need for post-processing.
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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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