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

2012/07/03 by Jacob Farinholt, Farinholt, Jacob · 1 citation
Computer Science · #Error Correcting Code Techniques #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.1207.0732

openalex publication_date 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Fermion-to-Fermion Low-Density Parity-Check Codes

Related

• List Decodable Quantum LDPC Codes
• Constructions and performance of classes of quantum LDPC codes
• A Joint Code and Belief Propagation Decoder Design for Quantum LDPC Codes
• Decoding Quasi-Cyclic Quantum LDPC Codes
• Good Quantum LDPC Codes with Linear Time Decoders