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arXiv · 1202.0928

Improved quantum hypergraph-product LDPC codes

Alexey A. Kovalev·Leonid P. Pryadko
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Abstract

We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Zémor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal single-qubit-encoding toric codes with block length $n=t^2+(t+1)^2$ and distance $d=2t+1$, $t=1,2,...$. We also suggest several related algebraic constructions which nearly quadruple the rate of the existing hypergraph-product codes.

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Alexey A. Kovalev, Leonid P. Pryadko. 2012-05-18. Improved quantum hypergraph-product LDPC codes. https://doi.org/10.1109/isit.2012.6284206

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