2024/08/06 by Victor Kasatkin, Evgeny Mozgunov, Kasatkin, Victor +5 · 1 citation
Computer Science · Decision Sciences · Physics and Astronomy · #FOS: Physical sciences #Forecasting Techniques and Applications #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2408.03418
openalex publication_date 2024/08/06 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28
The detection of quantum and classical phase transitions in the absence of an order parameter is possible using the Fisher information metric (FIM), also known as fidelity susceptibility. Here, we propose and investigate an unsupervised machine learning (ML) task: estimating the FIM given limited samples from a multivariate probability distribution of measurements made throughout the phase diagram. We utilize an unsupervised ML method called ClassiFIM (developed in a companion paper) to solve this task and demonstrate its empirical effectiveness in detecting both quantum and classical phase transitions using a variety of spin and fermionic models, for which we generate several publicly available datasets with accompanying ground-truth FIM. We find that ClassiFIM reliably detects both topological (e.g., XXZ chain) and dynamical (e.g., metal-insulator transition in Hubbard model) quantum phase transitions. We perform a detailed quantitative comparison with prior unsupervised ML methods for detecting quantum phase transitions. We demonstrate that ClassiFIM is competitive with these prior methods in terms of appropriate accuracy metrics while requiring significantly less resource-intensive training data compared to the original formulation of the prior methods. In particular, ClassiFIM only requires classical (single-basis) measurements. As part of our methodology development, we prove several theorems connecting the classical and quantum fidelity susceptibilities through equalities or bounds. We also significantly expand the existence conditions of the fidelity susceptibility, e.g., by relaxing standard differentiability conditions. These results may be of independent interest to the mathematical physics community.