Golden codes: quantum LDPC codes built from regular tessellations of hyperbolic 4-manifolds

2017/12/31 by Vivien Londe, Anthony Leverrier
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.IT #math.IT

paper · pdf · doi:10.26421/qic19.5-6

published as QIC Vol.19 No.5&6 (2019) · 30 pages, 4 figures

arxiv created 2019/06/18 · arxiv updated 2019/06/20

Abstract

We adapt a construction of Guth and Lubotzky [arXiv:1310.5555] to obtain a family of quantum LDPC codes with non-vanishing rate and minimum distance scaling like n^0.1 where n is the number of physical qubits. Similarly as in [arXiv:1310.5555], our homological code family stems from hyperbolic 4-manifolds equipped with tessellations. The main novelty of this work is that we consider a regular tessellation consisting of hypercubes. We exploit this strong local structure to design and analyze an efficient decoding algorithm.

Citations

• Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds