Few measurement shots challenge generalization in learning to classify entanglement

TL;DR

This paper investigates the challenges of quantum classification with limited measurement data, highlighting the impact of measurement shot noise and proposing a classical shadow-based estimator to improve performance.

Contribution

It identifies measurement shot noise as a key obstacle in quantum learning and introduces a shadow-based estimator to enhance classification with few quantum samples.

Findings

Measurement shot noise significantly affects quantum learning accuracy.

Classical shadows improve classification performance in low-data quantum regimes.

Naive classical ML methods are insufficient for quantum data without proper theoretical grounding.

Abstract

The ability to extract general laws from a few known examples depends on the complexity of the problem and on the amount of training data. In the quantum setting, the learner's generalization performance is further challenged by the destructive nature of quantum measurements that, together with the no-cloning theorem, limits the amount of information that can be extracted from each training sample. In this paper we focus on hybrid quantum learning techniques where classical machine-learning methods are paired with quantum algorithms and show that, in some settings, the uncertainty coming from a few measurement shots can be the dominant source of errors. We identify an instance of this possibly general issue by focusing on the classification of maximally entangled vs. separable states, showing that this toy problem becomes challenging for learners unaware of entanglement theory. Finally, we introduce an estimator based on classical shadows that performs better in the big data, few copy regime. Our results show that the naive application of classical machine-learning methods to the quantum setting is problematic, and that a better theoretical foundation of quantum learning is required.