Deterministic generation of two-dimensional multi-photon cluster states

Here, we present a device capable of emitting large-scale entangled microwave photonic states in a two dimensional ladder structure. The device consists of a pair of coupled superconducting transmon qubits which are each tuneably coupled to a common output waveguide.

This architecture permits entanglement between each transmon and a deterministically emitted photonic qubit. By interleaving two-qubit gates with controlled photon emission, we generate $2 \times n$ grids of time- and frequency-multiplexed cluster states of itinerant microwave photons. We generate states with fidelities above 0.50 for up to eight qubits and, in addition, observe nonzero localizable entanglement for states of up to 16 qubits.