Deterministic multi-mode gates on a scalable photonic quantum computing platform

Quantum computing can be realized with numerous different hardware platforms and computational protocols. A highly promising approach to foster scalability is to apply a photonic platform combined with a measurement-induced quantum information processing protocol where gate operations are realized through optical measurements on a multipartite entangled quantum state -- a so-called cluster state. Heretofore, a few quantum gates on non-universal or non-scalable cluster states have been, but a full set of gates for universal scalable quantum computing has not been realized. We propose and demonstrate the deterministic implementation of a multi-mode set of measurement-induced quantum gates in a large two-dimensional (2D) optical cluster state using phase-controlled continuous variable quadrature measurements. Each gate is simply programmed into the phases of the high-efficiency quadrature measurements which execute the transformations by teleportation through the cluster state. Using these programmable gates, we demonstrate a small quantum circuit consisting of 10 single-mode gates and 2 two-mode gates on a three-mode input state. On this platform, fault-tolerant universal quantum computing is possible if the cluster state entanglement is improved and a supply of Gottesman-Kitaev-Preskill qubits is available. Moreover, it operates at the telecom wavelength and is therefore network connectable without quantum transducers.