# Explainable Representation Learning of Small Quantum States

arXiv: https://arxiv.org/abs/2306.05694 · HTML: https://mlsanity.com/paper/2306.05694/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Variational Autoencoders for New Physics Mining at the Large Hadron Collider](https://mlsanity.com/paper/1811.10276/) (2018)
- [Extracting Interpretable Physical Parameters from Spatiotemporal Systems using Unsupervised Learning](https://mlsanity.com/paper/1907.06011/) (2019)
- [Learning hard quantum distributions with variational autoencoders](https://mlsanity.com/paper/1710.00725/) (2017)
- [Operationally meaningful representations of physical systems in neural networks](https://mlsanity.com/paper/2001.00593/) (2020)
- [Flexible learning of quantum states with generative query neural networks](https://mlsanity.com/paper/2202.06804/) (2022)
- [Learning Interpretable Representations of Entanglement in Quantum Optics Experiments using Deep Generative Models](https://mlsanity.com/paper/2109.02490/) (2021)
- [Machine learning of Kondo physics using variational autoencoders and symbolic regression](https://mlsanity.com/paper/2107.08013/) (2021)
- [Learning entanglement breakdown as a phase transition by confusion](https://mlsanity.com/paper/2202.00348/) (2022)

## Built on by (most cited first, 10 of 10)

- [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)
- [Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders](https://mlsanity.com/paper/2506.11982/) (2025)
- [Deep Quantum Graph Dreaming: Deciphering Neural Network Insights into Quantum Experiments](https://mlsanity.com/paper/2309.07056/) (2023)
- [Adiabatic Fine-Tuning of Neural Quantum States Enables Detection of Phase Transitions in Weight Space](https://mlsanity.com/paper/2503.17140/) (2025)
- [Discovering quantum phenomena with Interpretable Machine Learning](https://mlsanity.com/paper/2604.16015/) (2026)
- [Closed-Form Interpretation of Neural Network Latent Spaces with Symbolic Gradients](https://mlsanity.com/paper/2409.05305/) (2024)
- [Discover physical concepts and equations with machine learning](https://mlsanity.com/paper/2412.12161/) (2024)
- [Interpretable Feature Interaction via Statistical Self-supervised Learning on Tabular Data](https://mlsanity.com/paper/2503.18048/) (2025)
- [Learning Minimal Representations of Fermionic Ground States](https://mlsanity.com/paper/2512.11767/) (2025)

## Abstract (arXiv)

Unsupervised machine learning models build an internal representation of their training data without the need for explicit human guidance or feature engineering. This learned representation provides insights into which features of the data are relevant for the task at hand. In the context of quantum physics, training models to describe quantum states without human intervention offers a promising approach to gaining insight into how machines represent complex quantum states. The ability to interpret the learned representation may offer a new perspective on non-trivial features of quantum systems and their efficient representation. We train a generative model on two-qubit density matrices generated by a parameterized quantum circuit. In a series of computational experiments, we investigate the learned representation of the model and its internal understanding of the data. We observe that the model learns an interpretable representation which relates the quantum states to their underlying entanglement characteristics. In particular, our results demonstrate that the latent representation of the model is directly correlated with the entanglement measure concurrence. The insights from this study represent proof of concept towards interpretable machine learning of quantum states. Our approach offers insight into how machines learn to represent small-scale quantum systems autonomously.