Measurement-based quantum computation on weighted graph states with arbitrarily small weight

Abstract

Weighted graph states are a natural generalization of graph states, which are generated by applying controlled-phase gates, instead of controlled-Z gates, to a separable state. In this paper, we show that uniformly weighted graph states on a suitable planar graph constitute universal resources for measurement-based quantum computation for an arbitrary nonzero constant weight. To our knowledge, this is the first example of universal resources prepared with only non-maximally entangling gates and has potential applications to weakly interacting systems, such as photonic systems.

Figures (7)

• Figure 1: Our weighted graph state serving as a universal resource and its transformation to a 2D cluster state. A concrete example with $k=m=3$ is shown in Fig. \ref{['fig:entire_transformation']} in Note99.
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