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Linear programming decoder for hypergraph product quantum codes

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Abstract

We introduce a decoder for quantum CSS codes thatis based on linear programming. Our definition is a priori slightlydifferent from the one proposed by Li and Vontobel as we havea syndrome oriented approach instead of an error oriented one,but we show that the success condition is equivalent. Although weprove that this decoder fails for quantum codes that do not havegood soundness property (i.e., having large errors with syndromeof small weight) such as the toric code, we obtain good resultsfrom simulations. We run our decoder for hypergraph productsof two random LDPC codes, showing that it performs better thanbelief propagation, even combined with the small-set-flip decoderthat can provably correct a constant fraction of random errors.
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Dates and versions

hal-03135797 , version 1 (09-02-2021)

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Omar Fawzi, Lucien Grouès, Anthony Leverrier. Linear programming decoder for hypergraph product quantum codes. IEEE ITW 2020 - IEEE Information theory workshop 2020, Apr 2021, Riva del Garda / Virtual, Italy. ⟨10.1109/ITW46852.2021.9457611⟩. ⟨hal-03135797⟩
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