Asymptotically good Quantum and locally testable classical LDPC codes
Pavel Panteleev, Gleb Kalachev
Abstract
We study classical and quantum LDPC codes of constant rate obtained by the lifted product construction over non-abelian groups. We show that the obtained families of quantum LDPC codes are asymptotically good, which proves the qLDPC conjecture. Moreover, we show that the produced classical LDPC codes are also asymptotically good and locally testable with constant query and soundness parameters, which proves a well-known conjecture in the field of locally testable codes.
Topics & Concepts
Low-density parity-check codeMathematicsConjectureDiscrete mathematicsAsymptotically optimal algorithmConstant (computer programming)Abelian groupPure mathematicsComputer scienceAlgorithmDecoding methodsProgramming languageError Correcting Code TechniquesQuantum Computing Algorithms and ArchitectureAdvanced Data Storage Technologies