Learning Topological Quantum Phases from Limited Subsystems
2026-07-12 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a way to recognize complex quantum phases by looking at only small parts of a system, instead of the whole thing, which is usually very hard. They use a special method that compares small snapshots of the system's quantum state to identify different phases accurately. They tested this on two different quantum spin chains and found their method works well even with very limited data. This suggests that important information about the overall quantum behavior is visible locally, making it easier to study these systems experimentally.
quantum topological phasesstring order parametersreduced density matrixquantum kernelsupervised learningspin-1/2 chainHaldane chainphase classificationquantum many-body systemslocal vs global properties
Authors
Mehran Khosrojerdi, Sougato Bose, Alessandro Cuccoli, Paola Verrucchi, Abolfazl Bayat, Leonardo Banchi
Abstract
Characterizing quantum topological phases requires measuring non-local string order parameters, demanding access to the full system, which is often experimentally unfeasible. In this work, we introduce a data-efficient supervised learning framework that circumvents this limitation by recognizing quantum phases from small subsystems. Our protocol utilizes a quantum kernel constructed from the reduced density matrices of these subsystems, which can be efficiently estimated experimentally. We benchmark our framework with the classification of the phase diagrams of two spin models on one-dimensional lattices, namely the generalized cluster-Ising spin-1/2 chain and the anisotropic Haldane spin-1 chain. Remarkably, our approach achieves high accuracy in phase classification when operations are limited to as few as one to four sites, and it also generalizes to longer chains even when trained on moderate system sizes. These findings demonstrate that local reduced density matrices preserve vital signatures of global topological phases, offering a practical route to characterize rich phase diagrams of quantum many-body systems.