Generation of three-dimensional cluster entangled state

Measurement-based quantum computing is a promising paradigm of quantum computation, in which universal computing is achieved through a sequence of local measurements. The backbone of this approach is the preparation of multipartite entanglement, known as cluster states. Although a cluster state with two-dimensional connectivity is required for universality, a three-dimensional cluster state is necessary for additionally achieving fault tolerance. However, the challenge of making three-dimensional connectivity has limited cluster state generation capability up to two dimensions. Here we demonstrate the deterministic generation of a three-dimensional cluster state based on the photonic continuous-variable platform. To realize three-dimensional connectivity, we harness a crucial advantage of time–frequency modes of ultrafast quantum light: an arbitrary complex mode basis can be accessed directly, enabling connectivity as desired. We demonstrate the versatility of our method by generating cluster states with one-, two- and three-dimensional connectivities. For their complete characterization, we develop a quantum state tomography method for multimode Gaussian states. Moreover, we verify the cluster state generation by nullifier measurements as well as full inseparability tests. Our work paves the way towards fault-tolerant and universal-measurement-based quantum computing.