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Due to their fast decoding algorithms, quantum generalizations of low-densityparity check, or LDPC, codes have been investigated as a solution to theproblem of decoherence in fragile quantum states. However, the additionaltwisted inner product requirements of quantum stabilizer codes forcefour-cycles and eliminate the possibility of randomly generated quantum LDPCcodes. Moreover, the classes of quantum LDPC codes discovered thus fargenerally have unknown or small minimum distance, or a fixed rate. This paperpresents several new classes of quantum LDPC codes constructed from finiteprojective planes. These codes have rates that increase with the block length$n$ and minimum weights proportional to $n^{1/2}$.

Quantum LDPC Codes Constructed from Point-Line Subsets of the Finite Projective Plane