Learning Gaussian Boson Sampling for Integrated Quantum Photonics

Gaussian boson sampling (GBS) is a leading platform for probing the boundary between quantum and classical computation. Given its impact on practical quantum advantage, emulating GBS is crucial, but exact calculation of its output probabilities is computationally expensive and #P-hard in general. Practical GBS workflows repeatedly query related photonic circuits and detection patterns, creating an opportunity to accelerate this computation through machine learning. We formulate GBS probability evaluation as a supervised learning task and introduce PhOracle, a physics-informed recurrent model that adapts its matrix computations to the requested detection pattern. We also introduce GBSBench, a circuit-disjoint benchmark that evaluates generalization to unseen circuits and unseen detection patterns. PhOracle achieves a median absolute percentage error of 4.56% on held-out circuit-pattern queries, while matched runtime tests show that PhOracle evaluates probabilities up to 79.8$\times$ faster than the reference solver. We further apply PhOracle to closed-loop quantum circuit optimization. Without task-specific retraining, PhOracle accelerates single-pair and multipair Bell-state circuit discovery by 17.3$\times$ and 36.2$\times$, respectively, reaching fidelities close to those achieved by reference-solver search. Together, this work provides an empirical basis for future studies of learned probability models across broader quantum-photonic systems and applications.