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Graph States, Pivot Minor, and Universality of (X,Z)-measurements

Mehdi Mhalla 1 Simon Perdrix 1 
1 CAPP - Calculs algorithmes programmes et preuves
LIG - Laboratoire d'Informatique de Grenoble
Abstract : The graph state formalism offers strong connections between quantum information processing and graph theory. Exploring these connections, first we show that any graph is a pivot-minor of a planar graph, and even a pivot minor of a triangular grid. Then, we prove that the application of measurements in the (X,Z) plane over graph states represented by triangular grids is a universal measurement-based model of quantum computation. These two results are in fact two sides of the same coin, the proof of which is a combination of graph theoretical and quantum information techniques.
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Contributor : Mehdi Mhalla Connect in order to contact the contributor
Submitted on : Tuesday, January 21, 2014 - 3:34:20 PM
Last modification on : Wednesday, July 6, 2022 - 4:17:00 AM

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  • HAL Id : hal-00934104, version 1
  • ARXIV : 1202.6551



Mehdi Mhalla, Simon Perdrix. Graph States, Pivot Minor, and Universality of (X,Z)-measurements. International Journal of Unconventional Computing, 2013, 9 (1-2), pp.153-171. ⟨hal-00934104⟩



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