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

12/22/2017

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by   Vivien Londe, et al.

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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^0.2 where n is the number of physical qubits. Similarly as in [arXiv:1310.5555], our homological code family stems from tessellated hyperbolic 4-manifolds. 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.