# Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithms

arXiv: https://arxiv.org/abs/2405.18489 · HTML: https://mlsanity.com/paper/2405.18489/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 97 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [On the Sample Complexity of Quantum Boltzmann Machine Learning](https://mlsanity.com/paper/2306.14969/) (2023)
- [Predicting Properties of Quantum Systems with Conditional Generative Models](https://mlsanity.com/paper/2211.16943/) (2022)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)

## Built on by (most cited first, 7 of 7)

- [Rethink the Role of Deep Learning towards Large-scale Quantum Systems](https://mlsanity.com/paper/2505.13852/) (2025)
- [Quantum circuit complexity and unsupervised machine learning of topological order](https://mlsanity.com/paper/2508.04486/) (2025)
- [Provably scalable learning from quantum many-body data via locality](https://mlsanity.com/paper/2509.13705/) (2025)
- [Parametric Quantum State Tomography with HyperRBMs](https://mlsanity.com/paper/2601.20950/) (2026)
- [Provable learning separation for predicting time-evolution of quantum many-body systems](https://mlsanity.com/paper/2607.06472/) (2026)
- [Differential equation quantum solvers: engineering measurements to reduce cost](https://mlsanity.com/paper/2503.22656/) (2025)
- [Learning ground state observables from quantum computing experiments](https://mlsanity.com/paper/2606.15983/) (2026)

## Abstract (arXiv)

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 nO(1) data points sampled from Hamiltonians in the same phase of matter. This was subsequently improved by [Lewis et al. Nature Communications 2024], to 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.