2008/01/06 by Dan Hu, Weidong Tang, Meisheng Zhao +3 · 1 citation
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.78.012306
12 pages, 5 figures (pdf)
arxiv created 2008/01/06 · openalex publication_date 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In this paper, we present a systematic way based on the nonbinary graph state of constructing good nonbinary quantum codes, both additive and nonadditive, for systems with integer dimensions. With a computer search, which results in many interesting codes including some nonadditive codes meeting the Singleton bounds, we are able to construct explicitly four families of optimal codes, namely, [[6,2,3]]p, [[7,3,3]]p, [[8,2,4]]p, and [[8,4,3]]p for any odd dimension p and a family of nonadditive codes ((5,p,3))p for arbitrary p>3. In the case of composite numbers as dimensions, we also construct a family of stabilizer codes ((6,2p2,3))2p for odd p, whose coding subspace is not of a dimension that is a power of the dimension of the physical subsystem.