# Machine learning discovery of new phases in programmable quantum simulator snapshots

arXiv: https://arxiv.org/abs/2112.10789 · HTML: https://mlsanity.com/paper/2112.10789/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 58 references that are in the map.
- First posted on arXiv 20 Dec 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Correlator Convolutional Neural Networks: An Interpretable Architecture for Image-like Quantum Matter Data](https://mlsanity.com/paper/2011.03474/) (2020)

## Built on by (most cited first, 13 of 13)

- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Predicting Properties of Quantum Systems with Conditional Generative Models](https://mlsanity.com/paper/2211.16943/) (2022)
- [Machine learning phase transitions: Connections to the Fisher information](https://mlsanity.com/paper/2311.10710/) (2023)
- [Investigating Topological Order using Recurrent Neural Networks](https://mlsanity.com/paper/2303.11207/) (2023)
- [Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders](https://mlsanity.com/paper/2506.11982/) (2025)
- [Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator](https://mlsanity.com/paper/2509.13821/) (2025)
- [Discovering quantum phenomena with Interpretable Machine Learning](https://mlsanity.com/paper/2604.16015/) (2026)
- [Fluctuation based interpretable analysis scheme for quantum many-body snapshots](https://mlsanity.com/paper/2304.06029/) (2023)
- [Scalable approach to many-body localization via quantum data](https://mlsanity.com/paper/2202.08853/) (2022)
- [Machine learning reveals features of spinon Fermi surface](https://mlsanity.com/paper/2306.03143/) (2023)
- [TetrisCNN for interpretable detection of phases of matter from experimental quantum simulator data](https://mlsanity.com/paper/2609.20693/) (2026)
- [Autonomous phase discovery](https://mlsanity.com/paper/2609.33802/) (2026)

## Abstract (arXiv)

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in experimental datasets that manual inspection may miss. Here, we introduce an interpretable unsupervised-supervised hybrid machine learning approach, the hybrid-correlation convolutional neural network (Hybrid-CCNN), and apply it to experimental data generated using a programmable quantum simulator based on Rydberg atom arrays. Specifically, we apply Hybrid-CCNN to analyze new quantum phases on square lattices with programmable interactions. The initial unsupervised dimensionality reduction and clustering stage first reveals five distinct quantum phase regions. In a second supervised stage, we refine these phase boundaries and characterize each phase by training fully interpretable CCNNs and extracting the relevant correlations for each phase. The characteristic spatial weightings and snippets of correlations specifically recognized in each phase capture quantum fluctuations in the striated phase and identify two previously undetected phases, the rhombic and boundary-ordered phases. These observations demonstrate that a combination of programmable quantum simulators with machine learning can be used as a powerful tool for detailed exploration of correlated quantum states of matter.