# Learning phases with Quantum Monte Carlo simulation cell

arXiv: https://arxiv.org/abs/2503.23098 · HTML: https://mlsanity.com/paper/2503.23098/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 52 references that are in the map.
- First posted on arXiv 29 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [iNNvestigate neural networks!](https://mlsanity.com/paper/1808.04260/) (2018)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Machine Learning for Condensed Matter Physics](https://mlsanity.com/paper/2005.14228/) (2020)
- [Interpreting the Predictions of Complex ML Models by Layer-wise Relevance Propagation](https://mlsanity.com/paper/1611.08191/) (2016)

## Built on by (most cited first, 1 of 1)

- [Why is topology hard to learn?](https://mlsanity.com/paper/2509.26261/) (2025)

## Abstract (arXiv)

We propose the use of the ``spin-opstring", derived from Stochastic Series Expansion Quantum Monte Carlo (QMC) simulations as machine learning (ML) input data. It offers a compact, memory-efficient representation of QMC simulation cells, combining the initial state with an operator string that encodes the state's evolution through imaginary time. Using supervised ML, we demonstrate the input's effectiveness in capturing both conventional and topological phase transitions, and in a regression task to predict non-local observables. We also demonstrate the capability of spin-opstring data in transfer learning by training models on one quantum system and successfully predicting on another, as well as showing that models trained on smaller system sizes generalize well to larger ones. Importantly, we illustrate a clear advantage of spin-opstring over conventional spin configurations in the accurate prediction of a quantum phase transition. Finally, we show how the inherent structure of spin-opstring provides an elegant framework for the interpretability of ML predictions. Using two state-of-the-art interpretability techniques, Layer-wise Relevance Propagation and SHapley Additive exPlanations, we show that the ML models learn and rely on physically meaningful features from the input data. Together, these findings establish the spin-opstring as a broadly-applicable and interpretable input format for ML in quantum many-body physics.