We adapt a construction of Guth and Lubotzky {GL14} to obtain a family of quantum LDPC codes with non-vanishing rate and minimum distance scaling like n0.1 where n is the number of physical qubits. Similarly as in Ref.~{GL14}, 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.
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Londe et al. (2019) studied this question.