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Quantum error-correcting codes associated with graphs
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Quantum error-correcting codes associated with graphs
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We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any dimension. As new examples we construct a large class of codes saturating the singleton bound, as well as a tenfold code detecting 3 errors.
Forward citations
Cited by 2 Pith papers
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Fun with Graph States: Nonlocal Bell Pairs and the Arf Invariant
Graph-state inner products are governed by the F2-rank of the adjacency matrix and the Arf invariant, yielding a nonlocal Bell-pair factorization of the Hilbert space.
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The Structure of Circle Graph States
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
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