Quantum Hypergraph States in Continuous Variables

TL;DR

This paper introduces a new class of non-Gaussian continuous-variable quantum states based on hypergraphs, enabling universal quantum computation with Gaussian measurements alone, thus overcoming experimental challenges.

Contribution

It defines hypergraph-based non-Gaussian states that satisfy universality criteria using only Gaussian measurements, leveraging intrinsic multimode nonlinearity.

Findings

Hypergraph states enable three-mode operations.

A hypergraph can implement the cubic phase gate.

States satisfy Lloyd-Braunstein criteria for universality.

Abstract

The measurement based, or one-way, model of quantum computation for continuous variables uses a highly entangled state called a cluster state to accomplish the task of computing. Cluster states that are universal for computation are a subset of a class of states called graph states. These states are Gaussian states and therefore require that the homodyne detection (Gaussian measurement) scheme is supplemented with a non-Gaussian measurement for universal computation, a significant experimental challenge. Here we define a new non-Gaussian class of states based on hypergraphs which satisfy the requirements of the Lloyd-Braunstein criteria while restricted to a Gaussian measurement strategy. Our main result is to show that, taking advantage of the intrinsic multimode nonlinearity, a hypergraph consisting of 3-edges can be used to apply a three-mode operation to an input three-mode state. As a special case, this technique can be used to apply the cubic phase gate to a single mode.