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arXiv:1002.4094 · Physical Review Letters

Arbitrarily Large Continuous-Variable Cluster States from a Single Quantum Nondemolition Gate

Nicolas C. Menicucci, Xian Ma, Timothy C. Ralph

Published Jun 23, 2010• 75 citations
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Abstract

We present a compact experimental design for producing an arbitrarily large optical continuous-variable cluster state using just one single-mode vacuum squeezer and one quantum nondemolition gate. Generating the cluster state and computing with it happen simultaneously: more entangled modes become available as previous modes are measured, thereby making finite the requirements for coherence and stability even as the computation length increases indefinitely.

DOI
10.1103/physrevlett.104.250503

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•Oct 18, 2012•1 citation
We present a compact experimental design for producing an arbitrarily large optical continuous-variable cluster state using just one single-mode vacuum squeezer and one quantum nondemolition gate. Generating the cluster state and computing with it happen simultaneously: more entangled modes become available as previous modes are measured, thereby making finite the requirements for coherence and stability even as the computation length increases indefinitely.
An extensible experimental design for optical continuous-variable cluster states of arbitrary size using four offline (vacuum) squeezers and six beam splitters is presented. This method has all the advantages of a temporal-mode encoding [Phys. Rev. Lett. 104, 250503 (2010)], including finite requirements for coherence and stability even as the computation length increases indefinitely, with none of the difficulty of inline squeezing. The extensibility stems from a construction based on Gaussian projected entangled pair states. The potential for use of this design within a fully fault-tolerant model is discussed.
We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum, using a multifrequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO.
One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but nonuniversal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to ($3\ifmmode\times\else\texttimes\fi{}{10}^{3}$ frequencies) $\ifmmode\times\else\texttimes\fi{}$ (unlimited number of temporal modes) into a computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on this entanglement resource.
We experimentally demonstrate a controlled-phase gate for continuous variables using a cluster-state resource of four optical modes. The two independent input states of the gate are coupled with the cluster in a teleportation-based fashion. As a result, one of the entanglement links present in the initial cluster state appears in the two unmeasured output modes as the corresponding entangling gate acting on the input states. The genuine quantum character of this gate becomes manifest and is verified through the presence of entanglement at the output for a product two-mode coherent input state. By combining our gate with the recently reported module for single-mode Gaussian operations [R. Ukai et al., Phys. Rev. Lett. 106, 240504 (2011)], it is possible to implement any multimode Gaussian operation as a fully measurement-based one-way quantum computation.
Cluster states are an essential component in one-way quantum computation protocols. We present novel schemes to generate addressable and scalable cluster states. Specifically, we exploit the entanglement contained in quadrature squeezed cylindrically polarized modes as the resource for our cluster state production. We carefully examine the properties of the obtained cluster states and quantify these. It is shown that these cluster states can be built through very compact designs. All modes are directly addressable, as needed for one-way quantum computation. Furthermore, we experimentally implement one of the proposed schemes and verify its feasibility by measuring the quantum correlations between the different nodes of the cluster state.