# Scalably learning quantum many-body Hamiltonians from dynamical data

arXiv: https://arxiv.org/abs/2209.14328 · HTML: https://mlsanity.com/paper/2209.14328/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 69 references that are in the map.
- First posted on arXiv 28 Sep 2022.

## Builds on (most cited first, 4 of 4)

- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [Tensor network approaches for learning non-linear dynamical laws](https://mlsanity.com/paper/2002.12388/) (2020)
- [Automatic Differentiation for Complex Valued SVD](https://mlsanity.com/paper/1909.02659/) (2019)

## Built on by (most cited first, 8 of 8)

- [Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix](https://mlsanity.com/paper/2212.04471/) (2022)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [The power and limitations of learning quantum dynamics incoherently](https://mlsanity.com/paper/2303.12834/) (2023)
- [Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations](https://mlsanity.com/paper/2408.08639/) (2024)
- [Learning topological states from randomized measurements using variational tensor network tomography](https://mlsanity.com/paper/2406.00193/) (2024)
- [Optimal Ansatz-free Hamiltonian Learning In Situ](https://mlsanity.com/paper/2606.19486/) (2026)
- [Simple algorithms to test and learn local Hamiltonians](https://mlsanity.com/paper/2404.06282/) (2024)
- [Lindbladian Learning with Neural Differential Equations](https://mlsanity.com/paper/2603.07778/) (2026)

## Abstract (arXiv)

The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system. In this work, we introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data, by bringing together techniques from gradient-based optimization from machine learning with efficient quantum state representations in terms of tensor networks. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins. In particular, we demonstrate on synthetic data that the algorithm works even if one is restricted to one simple initial state, a small number of single-qubit observables, and time evolution up to relatively short times. For the concrete example of the one-dimensional Heisenberg model our algorithm exhibits an error constant in the system size and scaling as the inverse square root of the size of the data set.