Deterministic generation of two-dimensional cluster states of itinerant microwave photonic qubits, part 1: generation.

Multidimensional cluster states are a key resource for quantum communication, measurement-based quantum computing and quantum metrology. Cluster states consisting of a few photonic qubits entangled in two dimensions have been generated using deterministic protocols and discrete variable encoding, but for useful applications the scale of such states must be greatly increased. Here we present a device capable of emitting large-scale entangled microwave photonic states in two dimensions. The device consists of a pair of coupled superconducting transmon qubits which are each tuneably coupled to a common output waveguide. This architecture permits on-demand entanglement between each transmon and a deterministically emitted photonic qubit. By interleaving two-qubit gates with controlled photon emission, we generate 2xN grids of time- and frequency-multiplexed many-body states of microwave radiation fields. We demonstrate the generation of two-dimensional cluster states and measure a signature of localisable entanglement across up to 18 photonic qubits. In addition to cluster states, we expect the device architecture to be capable of generating a wide range of other tensor network states such as tree graph states, repeater states or the ground state of the toric code, and to be readily scalable to generate larger and higher-dimensional states.