Monitoring the generation of photonic linear cluster states with partial measurements

Quantum states of light with many entangled photons are key resources for photonic quantum computing and quantum communication. In this work, we exploit a highly resource-efficient generation scheme based on a linear optical circuit embedding a fibered delay loop acting as a quantum memory. The single photons are generated with a bright single-photon source based on a semiconductor quantum dot, allowing to perform the entangling scheme up to 6 photons. We demonstrate 2, 3, 4 and 6-photon entanglement generation at respective rates of 6kHz, 120Hz, 2.2Hz, and 2mHz, corresponding to an average scaling ratio of 46. We introduce a method for real-time control of entanglement generation based on partially post-selected measurements. The visibility of such measurements enables discrimination and correcting for experimental phase drifts or entangling gate fidelity variations, and thus carries faithful information to monitor the entanglement process, an important feature for the practical implementation of photonic measurement-based quantum computation.