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Journal Articles International Journal of Unconventional Computing Year : 2013

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

Mehdi Mhalla
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  • PersonId : 951154
Simon Perdrix

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.

Dates and versions

hal-00934104 , version 1 (21-01-2014)

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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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