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arXiv:quant-ph/0606212 · Journal of the Optical Society of America B

Examples of Gaussian cluster computation

Peter van Loock

Published Jan 26, 2007• 43 citations
arXivHTMLPDF

Abstract

Simple examples that illustrate the principles of one-way quantum computation using Gaussian continuous-variable cluster states are given. In these examples, only single-mode evolutions, realizable via linear clusters, are considered. In particular, one can focus on Gaussian single-mode transformations performed through the cluster state. These examples highlight the differences between cluster-based schemes and protocols in which special quantum states are prepared off-line and then used as a resource for the on-line computation.

DOI
10.1364/josab.24.000340

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Simple examples that illustrate the principles of one-way quantum computation using Gaussian continuous-variable cluster states are given. In these examples, only single-mode evolutions, realizable via linear clusters, are considered. In particular, one can focus on Gaussian single-mode transformations performed through the cluster state. These examples highlight the differences between cluster-based schemes and protocols in which special quantum states are prepared off-line and then used as a resource for the on-line computation.
The linear optical creation of Gaussian cluster states, a potential resource for universal quantum computation, is investigated. First, using Bloch-Messiah reduction, we show how to achieve canonical cluster-state generation, otherwise based on pairwise acting quantum nondemolition gates, by off-line squeezers and beam splitters. Moreover, we find that, in terms of squeezing resources, the canonical states are rather wasteful. Hence we propose a systematic way to create a whole family of cluster-type states, including potentially cheaper states. Any given cluster (or graph) state can be realized this way. As an example, we consider a protocol in which a single-mode quantum state propagates through a multiple-rail cluster. Such a redundant encoding may reduce errors due to finite squeezing.
We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.