Learning Topological Quantum Phases from Limited Subsystems

Characterizing topological quantum phases typically requires measuring non-local string order parameters, which necessitates access to the entire quantum system. This is often experimentally impossible in large many-body systems. The authors investigate whether it is possible to identify these global topological phases by observing only small, local subsystems, thereby reducing the experimental burden.

The researchers developed a supervised learning framework using Support Vector Machines (SVMs) with a quantum kernel. Instead of using global observables, the kernel is constructed from the reduced density matrices of small subsystems (1 to 4 sites). These matrices represent the local state information. The framework was benchmarked against two 1D spin models: the generalized cluster-Ising spin-1/2 chain and the anisotropic Haldane spin-1 chain. The ground states were simulated using Matrix Product States (MPS) to represent large systems, and the model was trained on these local density matrices to classify different phases of matter.

The study demonstrates that local reduced density matrices contain sufficient information to identify global topological phases. For both the cluster-Ising and Haldane models, the SVM classifier achieved high accuracy in phase identification using only a few sites. Furthermore, the researchers found that the model could be trained on smaller chains (e.g., 31 sites) and successfully generalize to larger chains (e.g., 51 sites), suggesting that the local signatures of these phases converge rapidly with system size. Central subsystems generally provided more robust classification than edge subsystems.

This work provides a practical, data-efficient pathway for experimentalists to map out complex quantum phase diagrams without requiring full-system tomography or non-local measurements. By proving that local information is sufficient for topological phase classification, this approach lowers the barrier for studying quantum many-body systems on current and near-term quantum hardware.