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An efficient algorithm to recognize local Clifford equivalence of graph states

Maarten Van den Nest·Jeroen Dehaene·Bart De Moor
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Abstract

In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as \emph{local complementation}. It was shown that two graph states are equivalent under the local Clifford group if and only if there exists a sequence of local complementations which relates their associated graphs. In this short note we report the existence of a polynomial time algorithm, published in [Combinatorica 11 (4), 315 (1991)], which decides whether two given graphs are related by a sequence of local complementations. Hence an efficient algorithm to detect local Clifford equivalence of graph states is obtained.

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Maarten Van den Nest, Jeroen Dehaene, Bart De Moor. 2004-09-15. An efficient algorithm to recognize local Clifford equivalence of graph states. https://doi.org/10.1103/physreva.70.034302

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