Learning from imperfect quantum data via unsupervised domain adaptation with classical shadows

TL;DR

This paper introduces an unsupervised domain adaptation method using classical shadows to improve learning from imperfect quantum data, addressing real-world data mismatch issues.

Contribution

It develops a classical pipeline for domain adaptation on quantum data, enabling better performance under realistic conditions without requiring fully labeled data.

Findings

Outperforms baseline methods in quantum phase classification.

Effective in entanglement classification under domain shifts.

Demonstrates practical applicability for real-world quantum data learning.

Abstract

Learning from quantum data using classical machine learning models has emerged as a promising paradigm toward realizing quantum advantages. Despite extensive analyses on their performance, clean and fully labeled quantum data from the target domain are often unavailable in practical scenarios, forcing models to be trained on data collected under conditions that differ from those encountered at deployment. This mismatch highlights the need for new approaches beyond the common assumptions of prior work. In this work, we address this issue by employing an unsupervised domain adaptation framework for learning from imperfect quantum data. Specifically, by leveraging classical representations of quantum states obtained via classical shadows, we perform unsupervised domain adaptation entirely within a classical computational pipeline once measurements on the quantum states are executed. We numerically evaluate the framework on quantum phases of matter and entanglement classification tasks under realistic domain shifts. Across both tasks, our method outperforms source-only non-adaptive baselines and target-only unsupervised learning approaches, demonstrating the practical applicability of domain adaptation to realistic quantum data learning.