Good Quantum LDPC Codes with Linear Time Decoders
Irit Dinur, Min-Hsiu Hsieh, Ting-Chun Lin, Thomas Vidick
Abstract
We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain (2m× m)V →δ0 (2m)E →δ1 2F where V (X-checks) are the vertices, E (qubits) are the edges, and F (Z-checks) are the squares of a left-right Cayley complex, and where the maps are defined based on a pair of constant-size random codes CA,CB:2m→2Δ where Δ is the regularity of the underlying Cayley graphs.
Topics & Concepts
Low-density parity-check codeMathematicsDiscrete mathematicsQubitCombinatoricsDecoding methodsQuantumConstruct (python library)Computer scienceAlgorithmPhysicsQuantum mechanicsProgramming languageQuantum Computing Algorithms and ArchitectureError Correcting Code TechniquesQuantum-Dot Cellular Automata