Organizations: Department of Physics and Astronomy, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy · Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom · INFN Sezione di Firenze, via G. Sansone 1, I-50019, Sesto Fiorentino (FI), Italy · ISC-CNR, UOS Dipartimento di Fisica, Universit`a di Firenze, I-50019, Sesto Fiorentino (FI), Italy · Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
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.