Learning Topological Quantum Phases from Limited Subsystems

2026-07-12

AI Summary

Experimentally accessing the full quantum state to measure nonlocal string order parameters remains challenging, hindering the characterization of topological quantum phases. This work proposes a data-efficient supervised learning framework that demonstrates, for the first time, that local reduced density matrices—constructed from as few as one to four lattice sites—already encode essential information about global topological order. Leveraging this insight, the authors construct a quantum kernel capable of achieving high-accuracy phase classification using only experimentally accessible local observables. The approach exhibits excellent performance in both the generalized cluster-Ising model and the anisotropic Haldane spin chain, and shows strong potential for generalization to larger systems.

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.

Problem

• topological quantum phases
• subsystem characterization
• non-local order
• quantum many-body systems
• phase classification

Innovation

• topological quantum phases
• supervised learning
• quantum kernel
• reduced density matrices
• subsystem-based classification