Time-series forecasting with multiphoton quantum states and integrated photonics

Quantum machine learning algorithms have very recently attracted significant attention in photonic platforms. In particular, reconfigurable integrated photonic circuits offer a promising route, thanks to the possibility of implementing adaptive feedback loops, which is an essential ingredient for achieving the necessary nonlinear behavior characteristic of neural networks. Here, we implement a quantum reservoir computing protocol in which information is processed through a reconfigurable linear optical integrated photonic circuit and measured using single-photon detectors. We exploit a multiphoton-based setup for time-series forecasting tasks in a variety of scenarios, where the input signal is encoded in one of the circuit's optical phases, thus modulating the quantum reservoir state. The resulting output probabilities are used to set the feedback phases and, at the end of the computation, are fed to a classical digital layer trained via linear regression to perform predictions. We then focus on the investigation of the role of input photon indistinguishability in the reservoir's capabilities of predicting time-series. We experimentally demonstrate that two-photon indistinguishable input states lead to significantly better performance compared to distinguishable ones. This enhancement arises from the quantum correlations present in indistinguishable states, which enable the system to approximate higher-order nonlinear functions when using comparable physical resources, highlighting the importance of quantum interference and indistinguishability as a resource in photonic quantum reservoir computing.