# Practical Black Box Hamiltonian Learning

arXiv: https://arxiv.org/abs/2206.15464 · HTML: https://mlsanity.com/paper/2206.15464/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 45 references that are in the map.
- First posted on arXiv 30 Jun 2022.

## Builds on (most cited first, 3 of 3)

- [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)
- [Provably efficient variational generative modeling of quantum many-body systems via quantum-probabilistic information geometry](https://mlsanity.com/paper/2206.04663/) (2022)

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

- [Learning many-body Hamiltonians with Heisenberg-limited scaling](https://mlsanity.com/paper/2210.03030/) (2022)
- [Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix](https://mlsanity.com/paper/2212.04471/) (2022)
- [Learning quantum Hamiltonians at any temperature in polynomial time](https://mlsanity.com/paper/2310.02243/) (2023)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Learning k-body Hamiltonians via compressed sensing](https://mlsanity.com/paper/2410.18928/) (2024)
- [Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows](https://mlsanity.com/paper/2402.17911/) (2024)
- [Hamiltonian Property Testing](https://mlsanity.com/paper/2403.02968/) (2024)
- [Learning the structure of any Hamiltonian from minimal assumptions](https://mlsanity.com/paper/2410.21635/) (2024)
- [Ansatz-free Hamiltonian learning with Heisenberg-limited scaling](https://mlsanity.com/paper/2502.11900/) (2025)
- [Simple algorithms to test and learn local Hamiltonians](https://mlsanity.com/paper/2404.06282/) (2024)
- [Optimal certification of constant-local Hamiltonians](https://mlsanity.com/paper/2512.09778/) (2025)
- [Characterizing Arbitrary Lindbladian Dynamics with a Few Pauli Measurements](https://mlsanity.com/paper/2607.23044/) (2026)
- [Optical Quantum Sensing for Agnostic Environments via Deep Learning](https://mlsanity.com/paper/2311.07203/) (2023)
- [Quantum Scrambling Born Machine](https://mlsanity.com/paper/2602.17281/) (2026)
- [Hamiltonian locality testing and certification do not achieve the Heisenberg limit](https://mlsanity.com/paper/2610.03205/) (2026)

## Abstract (arXiv)

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality k). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol is practical for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.