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We adapt a construction of Guth and Lubotzky [arXiv:1310.5555] to obtain afamily of quantum LDPC codes with non-vanishing rate and minimum distancescaling like $n^{0.1}$ where $n$ is the number of physical qubits. Similarly asin [arXiv:1310.5555], our homological code family stems from hyperbolic4-manifolds equipped with tessellations. The main novelty of this work is thatwe consider a regular tessellation consisting of hypercubes. We exploit thisstrong local structure to design and analyze an efficient decoding algorithm.

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