2012/12/31 by Alexey A. Kovalev, Leonid P. Pryadko · 4 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.88.012311
published as Phys. Rev. A 88, 012311 (2013) · 13 pages, 4 figures
arxiv created 2013/01/02 · arxiv updated 2013/07/12
We introduce a "hyperbicycle" ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay et al. as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many of thus defined codes have finite rate and a limited-weight stabilizer generators, an analog of classical low-density parity check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have wider range of parameters; in particular, they can have higher rate while preserving the (estimated) error threshold.