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

Mehdi Mhalla; Simon Perdrix

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arXiv · 1202.6551

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

Mehdi Mhalla·Simon Perdrix

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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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Mehdi Mhalla, Simon Perdrix. 2012-02-29. Graph States, Pivot Minor, and Universality of (X,Z)-measurements. https://arxiv.org/abs/1202.6551

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