Scaling of Computational Order Parameters in Rydberg Atom Graph States

TL;DR

This paper demonstrates how to create and analyze large-scale graph states on Rydberg atom quantum simulators, using non-local measurements to assess their computational usefulness for measurement-based quantum computing.

Contribution

It introduces a method to generate and measure graph states with an always-on Rydberg interaction, and develops finite-size scaling of order parameters to evaluate quantum computational power.

Findings

Successful construction of large graph states on Rydberg atoms

Development of non-local measurement-based order parameters

Finite-size scaling analysis of computational efficacy

Abstract

Graph states are computationally powerful quantum states with many applications including use as resource states for measurement-based quantum computing (MBQC). We demonstrate construction of graph states on a Rydberg atom quantum analogue simulator. We show how an always-on interaction can be used to simultaneously entangle all Rydberg atoms into a graph state. We construct and implement many-body computational order parameters for graph states using non-local measurement-based logic operations in the Clifford group. The order parameters measure the efficacy of entanglement to allow MBQC on graph states of any size. We parameterize finite-size scaling of these order parameters. Our results define a route to efficiently test computational power in quantum devices.