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

TL;DR

This paper demonstrates that a simplified set of projective measurements and a single ancillary qubit are sufficient for universal quantum computation and efficient graph state preparation, reducing resource complexity.

Contribution

It introduces a simpler, more practical set of observables for universal quantum computation using only measurements in the (X,Y) plane with one ancillary qubit.

Findings

Set of observables {Z⊗X, (cosθ)X + (sinθ)Y} is universal for quantum computation.

The set is simpler than previous sets, involving only measurements in the (X,Y) plane.

The proof provides a method for efficient graph state preparation.

Abstract

We consider the problem of minimizing resources required for universal quantum computation using only projective measurements. The resources we focus on are observables, which describe projective measurements, and ancillary qubits. We show that the set of observables {Z \otimes X, (cos\theta)X + (sin\theta)Y 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 immediately implies a simple set of observables that is approximately universal for quantum computation. Moreover, the proof implies a simple set of observables for preparing graph states efficiently.