# Improved algorithms for learning quantum Hamiltonians, via flat polynomials

arXiv: https://arxiv.org/abs/2407.04540 · HTML: https://mlsanity.com/paper/2407.04540/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 10 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Builds on (most cited first, 1 of 1)

- [Learning quantum Hamiltonians at any temperature in polynomial time](https://mlsanity.com/paper/2310.02243/) (2023)

## Built on by (most cited first, 3 of 3)

- [Efficient Hamiltonian, structure and trace distance learning of Gaussian states](https://mlsanity.com/paper/2411.03163/) (2024)
- [Provable learning separation for predicting time-evolution of quantum many-body systems](https://mlsanity.com/paper/2607.06472/) (2026)
- [Computationally sufficient statistics for Ising models](https://mlsanity.com/paper/2602.12449/) (2026)

## Abstract (arXiv)

We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample complexity and runtime dependence to singly exponential in the inverse-temperature parameter, as opposed to doubly exponential. Our main technical contribution is a new flat polynomial approximation to the exponential function, with significantly lower degree than the flat polynomial approximation used in [BLMT24].