Journal
PHYSICAL REVIEW A
Volume 78, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.78.042303
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Funding
- National Science Foundation [PHY0456951]
- Division Of Physics
- Direct For Mathematical & Physical Scien [0757251, GRANTS:13712866] Funding Source: National Science Foundation
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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.
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