Deterministic generation of multidimensional photonic cluster states with a single quantum emitter

Entanglement is a key resource in quantum computing and other prospective technologies. Multidimensional photonic graph states, such as cluster states, have a special entanglement structure that makes them a valuable resource for quantum metrology, secure quantum communication and measurement-based quantum computation. However, to date, the generation of multidimensional photonic cluster states has relied on probabilistic methods that limit the scalability of typical optical generation methods. Here we present an experimental implementation in the microwave domain of a resource-efficient scheme for the deterministic generation of two-dimensional photonic cluster states. Using a coupled resonator array as a slow-light waveguide, a single flux-tunable transmon qubit as a quantum emitter and a second auxiliary transmon as a switchable mirror, we achieve rapid, shaped emission of entangled photon wavepackets, and selective time-delayed feedback of photon wavepackets to the emitter qubit. We use these capabilities to generate a two-dimensional cluster state of four photons with 70% fidelity, as verified by the tomographic reconstruction of the quantum state.