Statistical Mechanics-Inspired Quantum Generative Models for Rare-Event Simulation and Anomaly Detection

Reliable estimation of tail risk and detection of low-prevalence anomalies remain challenging under distribution shift and limited simulation budgets. This paper introduces a statistical mechanics-inspired hybrid quantum generative model that learns an energy-shaped proposal for rare-event simulation while producing a calibrated anomaly score for deployment. Across simulation budgets from 200 to 6400 samples, relative error decreased from 0.31 to 0.08, outperforming normalizing flows (0.44 to 0.12), diffusion sampling (0.48 to 0.14), and a classical energy model (0.46 to 0.13). At a fixed evaluation budget, the proposed estimator achieved relative error 0.10 with effective sample size 1120 and tail hit rate 6.8%, compared with 0.16, 760, and 4.1% for flows. For anomaly detection, AUROC reached 0.962 and AUPRC reached 0.714, with precision 0.61 at 80% recall, exceeding flow scoring (AUROC 0.935, AUPRC 0.624, precision 0.49) and VAE reconstruction (AUROC 0.928, AUPRC 0.598, precision 0.46). Under temporal drift after a single calibration, realized false positive rate stayed within 0.0004 of a 0.5% target, whereas baselines drifted by up to 0.0084. Ablations showed peak AUPRC near moderate circuit depth and mid-scale qubits, while monotone annealing reduced rare-event error from 0.12 to 0.10 and improved stability. Under increasing noise, mitigation preserved AUPRC from 0.74 at low noise to 0.69 at moderate noise, supporting feasibility for NISQ-constrained monitoring and tail estimation.