# Improved machine learning algorithm for predicting ground state properties

arXiv: https://arxiv.org/abs/2301.13169 · HTML: https://mlsanity.com/paper/2301.13169/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 104 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 22 of 22)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [Learning Thermodynamics with Boltzmann Machines](https://mlsanity.com/paper/1606.02718/) (2016)
- [Foundations for learning from noisy quantum experiments](https://mlsanity.com/paper/2204.13691/) (2022)
- [Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints](https://mlsanity.com/paper/2110.13086/) (2021)
- [Predicting Properties of Quantum Systems with Conditional Generative Models](https://mlsanity.com/paper/2211.16943/) (2022)
- [Hardware-efficient learning of quantum many-body states](https://mlsanity.com/paper/2212.06084/) (2022)

## Built on by (most cited first, 22 of 22)

- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Multimodal deep representation learning for quantum cross-platform verification](https://mlsanity.com/paper/2311.03713/) (2023)
- [Equivariant Symmetry Breaking Sets](https://mlsanity.com/paper/2402.02681/) (2024)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [Rethink the Role of Deep Learning towards Large-scale Quantum Systems](https://mlsanity.com/paper/2505.13852/) (2025)
- [Efficient Learning of Long-Range and Equivariant Quantum Systems](https://mlsanity.com/paper/2312.17019/) (2023)
- [Concept learning of parameterized quantum models from limited measurements](https://mlsanity.com/paper/2408.05116/) (2024)
- [Efficient Hamiltonian, structure and trace distance learning of Gaussian states](https://mlsanity.com/paper/2411.03163/) (2024)
- [Accurate Learning of Equivariant Quantum Systems from a Single Ground State](https://mlsanity.com/paper/2405.12309/) (2024)
- [Sequence-Model-Guided Measurement Selection for Quantum State Learning](https://mlsanity.com/paper/2507.09891/) (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)
- [Nonstabilizerness Estimation using Graph Neural Networks](https://mlsanity.com/paper/2511.23224/) (2025)
- [Parametric Quantum State Tomography with HyperRBMs](https://mlsanity.com/paper/2601.20950/) (2026)
- [Classical Shadows with Improved Median-of-Means Estimation](https://mlsanity.com/paper/2412.03381/) (2024)
- [Learning thermodynamic master equations for open quantum systems](https://mlsanity.com/paper/2506.01882/) (2025)
- [Physical probes expose and alleviate chemical-environment collapse in molecular representations](https://mlsanity.com/paper/2605.10429/) (2026)
- [Learning ground state observables from quantum computing experiments](https://mlsanity.com/paper/2606.15983/) (2026)
- [A Quantum/Classical Example Oracle Separation for Making Things Up](https://mlsanity.com/paper/2608.11648/) (2026)

## Abstract (arXiv)

Finding the ground state of a quantum many-body system is a fundamental problem in quantum physics. In this work, we give a classical machine learning (ML) algorithm for predicting ground state properties with an inductive bias encoding geometric locality. The proposed ML model can efficiently predict ground state properties of an n-qubit gapped local Hamiltonian after learning from only O(log(n)) data about other Hamiltonians in the same quantum phase of matter. This improves substantially upon previous results that require O(nc) data for a large constant c. Furthermore, the training and prediction time of the proposed ML model scale as O(n log n) in the number of qubits n. Numerical experiments on physical systems with up to 45 qubits confirm the favorable scaling in predicting ground state properties using a small training dataset.