Quantum Computing with Continuous-Variable Clusters

TL;DR

This paper advances the theoretical and experimental framework for continuous-variable quantum computing using cluster states, introducing new protocols and resource characterizations for universal quantum computation.

Contribution

It provides a novel implementation of the cubic phase gate via photon detection and characterizes resource requirements, showing universal states with scalable offline squeezing.

Findings

Implementation of cubic phase gate via photon detection

Characterization of offline squeezed resources for arbitrary graph states

Existence of universal states with non-increasing offline squeezing per mode

Abstract

Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.