Continuous generation of an indistinguishable all-photonic cluster state

Cluster states are key resources for measurement-based quantum information processing. We use a semiconductor quantum dot to continuously and deterministically generate an indistinguishable all-photonic cluster state at a sub-GHz generation rate. Our demonstration uses a quantum-dot heavy hole spin as the photon's entangler [1-2], where the spin precession rate is tuned to match one-quarter of the excitation laser repetition rate. Consequently, a single cycle of the protocol repeats itself indefinitely. The generated state is characterized by polarization tomography. Projecting the first and last photon on a circular polarization basis disentangled the remaining photons from the hole. By measuring 4 sequential photons, we demonstrate the concept of an all-photonic cluster. In addition, we demonstrate that the photon generation is deterministic by performing tomography of sequential photons in which one photon was not detected. [1] I. Schwartz et al., Science 354, 434(2016) [2] Z.-E. Su et al., Rep. Prog. Phys. 87, 077601(2024)