Simple Sets of Measurements for Universal Quantum Computation and Graph State Preparation

Abstract

We show that the set of observables $\{Z\otimes X, (\cos\theta) X + (\sin\theta) Y \ {\rm all} \ \theta \in [0,2\pi)\}$ with one ancillary qubit is universal for quantum computation. The set is simpler than a previous one in the sense that one-qubit projective measurements described by the observables in the set are ones only in the (X,Y) plane of the Bloch sphere. The proof of the universality implies a simple set of observables that is approximately universal for quantum computation. Moreover, it implies a simple set of observables for efficient graph state preparation.