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 multi-mode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.
@article{arxiv.quant-ph/0605198,
title = {Universal Quantum Computation with Continuous-Variable Cluster States},
author = {Nicolas C. Menicucci and Peter van Loock and Mile Gu and Christian Weedbrook and Timothy C. Ralph and Michael A. Nielsen},
journal= {arXiv preprint arXiv:quant-ph/0605198},
year = {2007}
}