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.

本研究探讨了学习和利用孤立量子力学系统的哈密顿量及其变分热态估计进行数据分析技术的可能性，并使用量子哈密顿基模型的方法进行产生建模，证明可以用混合态表示这样的大型强子对撞机数据。在进一步步骤中，我们将学习到的哈密顿量用于异常检测，表明不同样本类型一旦被视为量子多体系统，就可以形成不同的动力行为。利用这些特征来量化样本类型之间的差异。我们的研究结果表明，设计用于场论计算的方法可以在机器学习应用中加以利用，以将理论方法应用于数据分析技术。