Quantum Hypergraph States in Continuous Variables

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.

arXiv comment7 pages, 2 figures

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• Efficient verification of continuous-variable quantum states and devices without assuming identical and independent operations
• Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
• Nonlinear Phase Gates as Airy Transforms of the Wigner Function
• Graphical Framework for Non-Gaussian Quantum States
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• Nonlinear stochastic and quantum motion from Coulomb forces