Compact Toffoli gate using weighted graph states

TL;DR

This paper presents three compact measurement-based graph states for implementing a Toffoli gate with high success probabilities, making it feasible for current quantum experiments across various platforms.

Contribution

The authors introduce three minimal graph states for measurement-based Toffoli gates, achieving success probabilities up to 1/2, and demonstrate their experimental feasibility.

Findings

Success probabilities of 1/4, 1/2, and 1 for the three graph states.

Graph states are setup-independent, suitable for different quantum systems.

The approach enables practical implementation of Toffoli gates in current experiments.

Abstract

We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven or eight qubits, we show that success probabilities of 1/4, 1/2 and 1 respectively can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup-independent, they could be realized in a variety of systems, including linear optics and ion-traps.