Deterministic Generation of Multidimensional Microwave Photonic Cluster States with a Single Quantum Emitter - Part 2

Multidimensional photonic graph states, such as cluster states, have prospective applications in quantum metrology, secure quantum communication, and measurement-based quantum computation. We report on the results of an experimental implementation of a resource-efficient scheme for the deterministic generation of 2D microwave photonic cluster states utilizing a slow-light waveguide with round-trip delay ??_d = 240 ns, a flux-tunable transmon qubit as a quantum emitter, and a second auxiliary transmon as a switchable mirror. Strong decay rates of the qubits into the waveguide, in excess of 150??_d^-1 when resonant with the passband, allow for rapid emission of photons, while negligible decay rates when detuned from the passband allow for coherent qubit control. Using only single qubit gates and fast flux control of the transmon qubits we generate a state of four photons with entanglement structure consistent with that of a two-by-two cluster state, as verified by heterodyne tomographic techniques. We comment on how future design strategies could allow for generation of even larger cluster states and single-shot measurement of emitted photons, enabling the integration of quantum information processing techniques previously confined to optics into the microwave domain.