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Efficient decoding of random errors for quantum expander codes

Abstract : We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Z\'emor can correct a constant fraction of random errors with very high probability. This is the first construction of a constant-rate quantum LDPC code with an efficient decoding algorithm that can correct a linear number of random errors with a negligible failure probability. Finding codes with these properties is also motivated by Gottesman's construction of fault tolerant schemes with constant space overhead. In order to obtain this result, we study a notion of α-percolation: for a random subset W of vertices of a given graph, we consider the size of the largest connected α-subset of W, where X is an α-subset of W if |X∩W|≥α|X|.
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Contributor : Anthony Leverrier <>
Submitted on : Monday, December 11, 2017 - 2:54:12 PM
Last modification on : Tuesday, December 24, 2019 - 3:26:01 PM


  • HAL Id : hal-01656427, version 1



Anthony Leverrier. Efficient decoding of random errors for quantum expander codes. Conference on ”Quantum Information Theory”, Dec 2017, Paris, France. pp.1-33. ⟨hal-01656427⟩



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