Quantum Error Correcting Codes Using Qudit Graph States

Details Quantum Error Correcting Codes Using Qudit Graph States Quantum Error Correcting Codes Using Qudit Graph States

2007-12-12

arxiv.org/abs/0712.1979v4

Phys. Rev. A 78, 042303 (2008)

Physics

Quantum Physics

Version 4 is almost exactly the same as the published version in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.78.042303

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 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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