• DOI:10.1103/PhysRevA.70.034302
• Corpus ID: 35190821

Efficient algorithm to recognize the local Clifford equivalence of graph states

@article{Nest2004EfficientAT,
  title={Efficient algorithm to recognize the local Clifford equivalence of graph states},
  author={Maarten Van den Nest and Jeroen Dehaene and Bart De Moor},
  journal={Physical Review A},
  year={2004},
  volume={70},
  pages={034302}
}

• M. V. D. Nest, J. Dehaene, B. Moor
• Published 5 May 2004
• Mathematics
• Physical Review A

In Van den Nest et al. [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 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 Brief Report we report the existence of a polynomial time algorithm, published in A. Bouchet [Combinatorica 11, 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.