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 $\alpha$-percolation: for a random subset $W$ of vertices of a given graph, we consider the size of the largest connected $\alpha$-subset of $W$, where $X$ is an $\alpha$-subset of $W$ if $|X \cap W| \geq \alpha |X|$.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.inria.fr/hal-01671348
Contributor : Anthony Leverrier <>
Submitted on : Friday, December 22, 2017 - 10:52:24 AM
Last modification on : Tuesday, December 24, 2019 - 3:26:05 PM

Identifiers

• HAL Id : hal-01671348, version 1
• ARXIV : 1711.08351

Citation

Omar Fawzi, Antoine Grospellier, Anthony Leverrier. Efficient decoding of random errors for quantum expander codes. 2017. ⟨hal-01671348⟩

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