Compare Papers
Paper 1
Efficient decoding of random errors for quantum expander codes
Omar Fawzi, Antoine Grospellier, Anthony Leverrier
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1711.08351
- arXiv
- 1711.08351
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 Zémor 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 $|X \cap W| \geq α|X|$.
Open paperPaper 2
Clustered error correction of codeword-stabilized quantum codes.
Li Y, Dumer I, Pryadko LP.
- Year
- 2010
- Journal
- Phys Rev Lett
- DOI
- 10.1103/physrevlett.104.190501
- arXiv
- -
No abstract.
Open paper