# A Hybrid Quantum-Classical Hamiltonian Learning Algorithm

arXiv: https://arxiv.org/abs/2103.01061 · HTML: https://mlsanity.com/paper/2103.01061/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 93 references that are in the map.
- First posted on arXiv 1 Mar 2021.

## Builds on (most cited first, 11 of 11)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [An Improved Cutting Plane Method for Convex Optimization, Convex-Concave Games and its Applications](https://mlsanity.com/paper/2004.04250/) (2020)
- [A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization](https://mlsanity.com/paper/1508.04874/) (2015)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [Efficient Convex Optimization with Membership Oracles](https://mlsanity.com/paper/1706.07357/) (2017)
- [A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver](https://mlsanity.com/paper/1910.09694/) (2019)
- [Variational Quantum Singular Value Decomposition](https://mlsanity.com/paper/2006.02336/) (2020)
- [Variational quantum Gibbs state preparation with a truncated Taylor series](https://mlsanity.com/paper/2005.08797/) (2020)

## Built on by (most cited first, 1 of 1)

- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)

## Abstract (arXiv)

Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators. In this paper, we propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator components of the Hamiltonian. Its main subroutine is the practical log-partition function estimation algorithm, which is based on the minimization of the free energy of the system. Concretely, we devise a stochastic variational quantum eigensolver (SVQE) to diagonalize the Hamiltonians and then exploit the obtained eigenvalues to compute the free energy's global minimum using convex optimization. Our approach not only avoids the challenge of estimating von Neumann entropy in free energy minimization, but also reduces the quantum resources via importance sampling in Hamiltonian diagonalization, facilitating the implementation of our method on near-term quantum devices. Finally, we demonstrate our approach's validity by conducting numerical experiments with Hamiltonians of interest in quantum many-body physics.