Universal quantum phase classification on quantum computers from machine learning

The classification of quantum phases of matter remains a fundamental challenge in condensed matter physics. We present a novel framework that combines shadow tomography with modern time-series machine learning models to enable efficient and practical quantum phase classification. Our approach leverages the definition of quantum phases based on connectivity through finite-depth local unitary circuits, generating abundant training data by applying Haar random evolution to representative quantum states for a given phase. In this way, the training data can be efficiently obtained from a quantum simulator. Additionally, we demonstrate that advanced time-series models can be used to process the training data and achieve universal quantum phase classification that does not rely on local order parameters. To validate the universality and versatility of our method, we test the model against one-dimensional quantum spin chains such as the Ising model and the axial next-nearest-neighbor Ising (ANNNI) model, showing excellent agreement with known phase boundaries.