# Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection

arXiv: https://arxiv.org/abs/2211.03803 · HTML: https://mlsanity.com/paper/2211.03803/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 49 references that are in the map.
- First posted on arXiv 7 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm](https://mlsanity.com/paper/1910.02071/) (2019)
- [Style-based quantum generative adversarial networks for Monte Carlo events](https://mlsanity.com/paper/2110.06933/) (2021)
- [A Quantum Generative Adversarial Network for distributions](https://mlsanity.com/paper/2110.02742/) (2021)
- [Running the Dual-PQC GAN on noisy simulators and real quantum hardware](https://mlsanity.com/paper/2205.15003/) (2022)

## Built on by (most cited first, 7 of 7)

- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [Unravelling physics beyond the standard model with classical and quantum anomaly detection](https://mlsanity.com/paper/2301.10787/) (2023)
- [Generative Invertible Quantum Neural Networks](https://mlsanity.com/paper/2302.12906/) (2023)
- [Jet Discrimination with Quantum Complete Graph Neural Network](https://mlsanity.com/paper/2403.04990/) (2024)
- [MEMO-QCD: Quantum Density Estimation through Memetic Optimisation for Quantum Circuit Design](https://mlsanity.com/paper/2406.08591/) (2024)
- [TRANSIT your events into a new mass: Fast background interpolation for weakly-supervised anomaly searches](https://mlsanity.com/paper/2503.04342/) (2025)
- [Quantum-Inspired Tensor Network Autoencoders for Anomaly Detection: A MERA-Based Approach](https://mlsanity.com/paper/2604.06541/) (2026)

## Abstract (arXiv)

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.