Quantum-probabilistic Hamiltonian learning for generative modeling and anomaly detection

The Hamiltonian of an isolated quantum -mechanical system determines its dynamics and physical behavior. This study investigates the possibility of learning and utilizing a system's Hamiltonian and its variational thermal state estimation for data analysis techniques. For this purpose, we employ the method of quantum Hamiltonian -based models for the generative modeling of simulated Large Hadron Collider data and demonstrate the representability of such data as a mixed state. In a further step, we use the learned Hamiltonian for anomaly detection, showing that different sample types can form distinct dynamical behaviors once treated as a quantum many -body system. We exploit these characteristics to quantify the difference between sample types. Our findings show that the methodologies designed for field theory computations can be utilized in machine learning applications to employ theoretical approaches in data analysis techniques.