# Learning models of quantum systems from experiments

arXiv: https://arxiv.org/abs/2002.06169 · HTML: https://mlsanity.com/paper/2002.06169/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2020.

## Built on by (most cited first, 16 of 16)

- [On scientific understanding with artificial intelligence](https://mlsanity.com/paper/2204.01467/) (2022)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Fundamental limits to learning closed-form mathematical models from data](https://mlsanity.com/paper/2204.02704/) (2022)
- [The power and limitations of learning quantum dynamics incoherently](https://mlsanity.com/paper/2303.12834/) (2023)
- [Structure learning of Hamiltonians from real-time evolution](https://mlsanity.com/paper/2405.00082/) (2024)
- [Deep reinforcement learning for quantum multiparameter estimation](https://mlsanity.com/paper/2209.00671/) (2022)
- [Quantum Model Learning Agent: characterisation of quantum systems through machine learning](https://mlsanity.com/paper/2112.08409/) (2021)
- [Photonic Quantum Computers](https://mlsanity.com/paper/2409.08229/) (2024)
- [Harmonic (Quantum) Neural Networks](https://mlsanity.com/paper/2212.07462/) (2022)
- [Tomography of time-dependent quantum spin networks with machine learning](https://mlsanity.com/paper/2103.08645/) (2021)
- [SPDCinv: Inverse Quantum-Optical Design of High-Dimensional Qudits](https://mlsanity.com/paper/2112.05934/) (2021)
- [AQMLator -- An Auto Quantum Machine Learning E-Platform](https://mlsanity.com/paper/2409.18338/) (2024)
- [Bayesian quantum sensing using graybox machine learning](https://mlsanity.com/paper/2601.17465/) (2026)
- [A Hybrid Quantum Neural Network to Analyse Big Experimental Powder X-ray Diffraction Data](https://mlsanity.com/paper/2609.22376/) (2026)
- [Simulation-Based Quantum System Inference with Neural Posterior Estimation](https://mlsanity.com/paper/2609.34995/) (2026)

## Abstract (arXiv)

An isolated system of interacting quantum particles is described by a Hamiltonian operator. Hamiltonian models underpin the study and analysis of physical and chemical processes throughout science and industry, so it is crucial they are faithful to the system they represent. However, formulating and testing Hamiltonian models of quantum systems from experimental data is difficult because it is impossible to directly observe which interactions the quantum system is subject to. Here, we propose and demonstrate an approach to retrieving a Hamiltonian model from experiments, using unsupervised machine learning. We test our methods experimentally on an electron spin in a nitrogen-vacancy interacting with its spin bath environment, and numerically, finding success rates up to 86%. By building agents capable of learning science, which recover meaningful representations, we can gain further insight on the physics of quantum systems.