# Hardware-efficient learning of quantum many-body states

arXiv: https://arxiv.org/abs/2212.06084 · HTML: https://mlsanity.com/paper/2212.06084/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 61 references that are in the map.
- First posted on arXiv 12 Dec 2022.

## Builds on (most cited first, 6 of 6)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [Classical Shadows With Noise](https://mlsanity.com/paper/2011.11580/) (2020)
- [Hamiltonian-Driven Shadow Tomography of Quantum States](https://mlsanity.com/paper/2102.10132/) (2021)

## Built on by (most cited first, 5 of 5)

- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows](https://mlsanity.com/paper/2402.17911/) (2024)
- [Learning topological states from randomized measurements using variational tensor network tomography](https://mlsanity.com/paper/2406.00193/) (2024)
- [Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits](https://mlsanity.com/paper/2412.18973/) (2024)

## Abstract (arXiv)

Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a quantum many-body system. However, implementing such measurements requires complete control over individual particles, which is unavailable in many experimental platforms. In this work, we present rigorous and efficient algorithms for learning quantum many-body states in systems with any degree of control over individual particles, including when every particle is subject to the same global field and no additional ancilla particles are available. We numerically demonstrate the effectiveness of our algorithms for estimating energy densities in a U(1) lattice gauge theory and classifying topological order using very limited measurement capabilities.