Quantum LDPC codes with Ω(√(n)log^kn) distance, for any k

08/21/2020

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by   Tali Kaufman, et al.

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In this work we construct quantum LDPC codes of distance √(n)log^k n for any k, improving a recent result of Evra et. al. <cit.>. The work of <cit.> took advantage of the high dimensional expansion notion known as cosystolic expansion, that occurs in Ramanujan complexes. Our improvement is achieved by considering tensor product of Ramanujan complexes. The main conceptual contribution of our work is the following: a tensor product of a cosystolic expander with a complex with a linear cosystole has a linear cosystole.