# Learning to Classify Quantum Phases of Matter with a Few Measurements

arXiv: https://arxiv.org/abs/2409.05188 · HTML: https://mlsanity.com/paper/2409.05188/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 8 Sep 2024.

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

- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Quantum Kernel Alignment with Stochastic Gradient Descent](https://mlsanity.com/paper/2304.09899/) (2023)
- [Machine Learning Phase Transitions with a Quantum Processor](https://mlsanity.com/paper/1906.10155/) (2019)
- [Statistical Complexity of Quantum Learning](https://mlsanity.com/paper/2309.11617/) (2023)
- [Certifying almost all quantum states with few single-qubit measurements](https://mlsanity.com/paper/2404.07281/) (2024)
- [Quantum Adversarial Learning for Kernel Methods](https://mlsanity.com/paper/2404.05824/) (2024)
- [Quantum Inception Score](https://mlsanity.com/paper/2311.12163/) (2023)

## Built on by (most cited first, 2 of 2)

- [Analysis of Quantum Image Representations for Supervised Classification](https://mlsanity.com/paper/2507.22039/) (2025)
- [Learning Topological Quantum Phases from Limited Subsystems](https://mlsanity.com/paper/2607.10656/) (2026)

## Abstract (arXiv)

We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance. Following a supervised learning approach, we show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region. By using a combination of classical and quantum techniques, such as tensor networks, kernel methods, generalization bounds, quantum algorithms, and shadow estimators, we show that, in some cases, the certification of new ground states can be obtained with a polynomial number of measurements. An important application of our findings is the classification of the phases of matter obtained in quantum simulators, e.g., cold atom experiments, capable of efficiently preparing ground states of complex many-particle systems and applying simple measurements, e.g., single qubit measurements, but unable to perform a universal set of gates.