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Efficient decoding of random errors for quantum expander codes

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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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Dates and versions

hal-01656427 , version 1 (11-12-2017)

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  • HAL Id : hal-01656427 , version 1

Cite

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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