@inproceedings{
wanner2024predicting,
title={Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithms},
author={Marc Wanner and Laura Lewis and Chiranjib Bhattacharyya and Devdatt Dubhashi and Alexandru Gheorghiu},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=ybLXvqJyQA}
}
A fundamental problem in quantum many-body physics is that of finding ground states of local
Hamiltonians. A number of recent works gave provably efficient machine learning (ML) algorithms
for learning ground states. Specifically, [Huang et al. Science 2022], introduced an approach for learning
properties of the ground state of an $n$-qubit gapped local Hamiltonian $H$ from only $n^{\mathcal{O}(1)}$ data
points sampled from Hamiltonians in the same phase of matter. This was subsequently improved
by [Lewis et al. Nature Communications 2024], to $\mathcal{O}(\log 𝑛)$ samples when the geometry of the $n$-qubit system is known.
In this work, we introduce two approaches that achieve a constant sample complexity, independent
of system size $n$, for learning ground state properties. Our first algorithm consists of a simple
modification of the ML model used by Lewis et al. and applies to a property of interest known beforehand. Our second algorithm, which applies even if a description of
the property is not known, is a deep neural network model. While empirical results showing the
performance of neural networks have been demonstrated, to our knowledge, this is the first rigorous
sample complexity bound on a neural network model for predicting ground state properties. We also perform numerical experiments that confirm the improved scaling of our approach compared to earlier results.
Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithms
Marc Wanner Laura Lewis Chiranjib Bhattacharyya Devdatt Dubhashi Alexandru Gheorghiu