Estimation of the second-order coherence function using quantum reservoir and ensemble methods

We propose a machine-learning-based approach enhanced by quantum reservoir computing (QRC) to estimate the zero-time second-order correlation function g⁽²⁾(0). Typically, measuring g⁽²⁾(0) requires single-photon detectors and time-correlated measurements. Machine learning may offer practical solutions by training a model to estimate g⁽²⁾(0) solely from average intensity measurements. In our method, emission from a given quantum source is first processed in QRC. During the inference phase, only intensity measurements are used, and these are then passed to a software-based decision-tree ensemble model. We evaluate this hybrid quantum-classical approach across a variety of quantum optical systems and demonstrate that it provides accurate estimates of g⁽²⁾(0). We further extend our analysis to assess the ability of a trained model to generalize beyond its training distribution, both to the same system under different physical parameters and to fundamentally different quantum sources. While the model may yield reliable estimates within specific regimes, its performance across distinct systems is generally limited.