Graphical nonbinary quantum error-correcting codes

Date: 2008-12-30
Authors Dan Hu (胡丹), Weidong Tang (汤卫东), Meisheng Zhao (赵梅生), and Qing Chen (陈清),Sixia Yu (郁司夏),C. H. Oh
Journal No. Phys. Rev. A 78, 012306 (2008)    
Abstract 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.