The Hamiltonian of an isolated quantum mechanical system determines its dynamics and physical behaviour. This study investigates the possibility of learning and utilising 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 modelling 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 behaviours 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 utilised in machine learning applications to employ theoretical approaches in data analysis techniques.

翻译：一个孤立的量子力学系统的哈密顿量决定了其动力学行为和物理性质。本研究探讨了学习并利用系统哈密顿量及其变分热态估计进行数据分析技术的可能性。为此，我们采用量子哈密顿量基模型方法对模拟的大型强子对撞机数据进行生成建模，并证明了此类数据可作为混合态进行表示。进一步，我们将学习到的哈密顿量用于异常检测，表明不同样本类型在作为量子多体系统处理时能形成独特的动力学行为。我们利用这些特性来量化样本类型之间的差异。研究结果表明，为场论计算设计的方法可被应用于机器学习领域，从而在数据分析技术中采用理论方法。