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arXiv · 1207.0732

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

Jacob Farinholt
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Abstract

Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner product requirements of quantum stabilizer codes force four-cycles and eliminate the possibility of randomly generated quantum LDPC codes. Moreover, the classes of quantum LDPC codes discovered thus far generally have unknown or small minimum distance, or a fixed rate. This paper presents several new classes of quantum LDPC codes constructed from finite projective planes. These codes have rates that increase with the block length $n$ and minimum weights proportional to $n^{1/2}$.

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Jacob Farinholt. 2012-07-03. Quantum LDPC Codes Constructed from Point-Line Subsets of the Finite Projective Plane. https://arxiv.org/abs/1207.0732

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