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Title: Graphical nonbinary quantum error-correcting codes
Authors: Hu, D.
Tang, W.
Zhao, M.
Chen, Q.
Yu, S. 
Oh, C.H. 
Issue Date: 3-Jul-2008
Source: Hu, D., Tang, W., Zhao, M., Chen, Q., Yu, S., Oh, C.H. (2008-07-03). Graphical nonbinary quantum error-correcting codes. Physical Review A - Atomic, Molecular, and Optical Physics 78 (1) : -. ScholarBank@NUS Repository.
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 ((6,2 p2, 3)) 2p for odd p, whose coding subspace is not of a dimension that is a power of the dimension of the physical subsystem. © 2008 The American Physical Society.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
ISSN: 10502947
DOI: 10.1103/PhysRevA.78.012306
Appears in Collections:Staff Publications

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