Distinguishing Ordered Phases using Machine Learning and Classical Shadows

Leandro Morais, Tiago Pernambuco, Rodrigo G. Pereira, Askery Canabarro, Diogo O. Soares-Pinto, Rafael Chaves

Published 2025-01-29Version 1

Classifying phase transitions is a fundamental and complex challenge in condensed matter physics. This work proposes a framework for identifying quantum phase transitions by combining classical shadows with unsupervised machine learning. We use the axial next-nearest neighbor Ising model as our benchmark and extend the analysis to the Kitaev-Heisenberg model on a two-leg ladder. Even with few qubits, we can effectively distinguish between the different phases of the Hamiltonian models. Moreover, given that we only rely on two-point correlator functions, the classical shadows protocol enables the cost of the analysis to scale logarithmically with the number of qubits, making our approach a scalable and efficient way to study phase transitions in many-body systems.