Universal Quantum Computation with Continuous-Variable Cluster States

TLDR

Universal quantum computation requires a nonlinear element. The authors generalize the cluster‑state model to continuous‑variable systems and propose an optical implementation with squeezed‑light sources, linear optics, and homodyne detection, including an experiment to demonstrate cluster‑based error reduction for Gaussian operations. The scheme uses Gaussian cluster states prepared with squeezed‑light sources and linear optics, performs arbitrary multimode Gaussian transformations via homodyne detection, and requires only a single‑mode non‑Gaussian measurement to provide the necessary nonlinearity. Homodyne detection alone enables arbitrary multimode Gaussian transformations using the cluster state.

Abstract

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.