2007/12/31 by Shiang Yong Looi, Li Yu, Vlad Gheorghiu +1 · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #quant-ph
paper · pdf · doi:10.1103/physreva.78.042303
published as Phys. Rev. A 78, 042303 (2008) · Version 4 is almost exactly the same as the published version in Phys. Rev. A
openalex publication_date 2008/10/07 · arxiv created 2008/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Graph states are generalized from qubits to collections of n qudits of arbitrary dimension D, and simple graphical methods are used to construct both additive and nonadditive, as well as degenerate and nondegenerate, quantum-error-correcting codes. Codes of distance 2 saturating the quantum Singleton bound for arbitrarily large n and D are constructed using simple graphs, except when n is odd and D is even. Computer searches have produced a number of codes with distances 3 and 4, some previously known and some new. The concept of a stabilizer is extended to general D, and shown to provide a dual representation of an additive graph code.