Distinguishing Ordered Phases using Machine Learning and Classical Shadows

TL;DR

This paper introduces a scalable machine learning framework using classical shadows to identify quantum phase transitions in many-body systems efficiently, even with limited qubits.

Contribution

It combines classical shadows with unsupervised learning to distinguish phases using few qubits and local observables, improving scalability.

Findings

Effective phase distinction with few qubits.

Sample complexity scales logarithmically with features.

Applicable to complex models like Kitaev-Heisenberg.

Abstract

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. {Furthermore, by relying on a restricted set of local observables, such as pairwise correlations and plaquette operators, the sample complexity of the classical shadows protocol scales logarithmically with the number of measured features. This makes our approach a scalable and efficient tool for studying phase transitions in larger many-body systems where classical verification becomes intractable.