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

TL;DR

This paper demonstrates that weighted graph states with arbitrarily small weights on planar graphs can serve as universal resources for measurement-based quantum computation, expanding the possibilities for weakly entangling systems.

Contribution

It introduces a new class of universal resource states generated by non-maximally entangling gates, broadening the scope of measurement-based quantum computation.

Findings

Weighted graph states with small weights are universal for quantum computation.

First example of universal resources using only non-maximally entangling gates.

Potential applications in weakly interacting quantum systems like photonics.

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.