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arXiv · 0712.1979

Quantum Error Correcting Codes Using Qudit Graph States

Shiang Yong Looi·Li Yu·Vlad Gheorghiu·Robert B. Griffiths
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Abstract

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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Shiang Yong Looi, Li Yu, Vlad Gheorghiu, Robert B. Griffiths. 2008-11-11. Quantum Error Correcting Codes Using Qudit Graph States. https://doi.org/10.1103/physreva.78.042303

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