Quantum LDPC Codes with Almost Linear Minimum Distance

12/07/2020

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by   Pavel Panteleev, et al.

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We give a construction of quantum LDPC codes of dimension Θ(log N) and distance Θ(N/log N) as the code length N→∞. Using a product of chain complexes this construction also provides a family of quantum LDPC codes of distance Ω(N^1-α/2/log N) and dimension Ω(N^αlog N), where 0 ≤α < 1. We also introduce and study a new operation called lifted product, which naturally generalizes the product operations for quantum codes and chain complexes.