Linear programming decoder for hypergraph product quantum codes
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.
Domains
Quantum Physics [quant-ph]Origin | Files produced by the author(s) |
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