# Learning Topological Quantum Phases from Limited Subsystems

arXiv: https://arxiv.org/abs/2607.10656 · HTML: https://mlsanity.com/paper/2607.10656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 58 references that are in the map.
- First posted on arXiv 12 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Statistical Complexity of Quantum Learning](https://mlsanity.com/paper/2309.11617/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Learning quantum properties from short-range correlations using multi-task networks](https://mlsanity.com/paper/2310.11807/) (2023)
- [Analysis of Quantum Image Representations for Supervised Classification](https://mlsanity.com/paper/2507.22039/) (2025)
- [Quantum Inception Score](https://mlsanity.com/paper/2311.12163/) (2023)
- [Learning to Classify Quantum Phases of Matter with a Few Measurements](https://mlsanity.com/paper/2409.05188/) (2024)

## Abstract (arXiv)

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.