Quantum machine learning beyond kernel methods

TL;DR

This paper provides a unified framework for understanding quantum machine learning models based on parametrized circuits, compares their resource requirements, and highlights the advantages of data re-uploading models over kernel methods in near-term quantum computing.

Contribution

It introduces a linear quantum model framework that encompasses existing models and analyzes their resource needs, revealing the efficiency of data re-uploading models compared to kernel methods.

Findings

Data re-uploading circuits can be mapped to linear quantum models.

Linear quantum models require exponentially fewer qubits than data re-uploading models for certain tasks.

Kernel methods need exponentially more data points, highlighting resource advantages of certain models.

Abstract

Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and studied extensively. Yet, our understanding of how these models compare, both mutually and to classical models, remains limited. In this work, we identify a constructive framework that captures all standard models based on parametrized quantum circuits: that of linear quantum models. In particular, we show using tools from quantum information theory how data re-uploading circuits, an apparent outlier of this framework, can be efficiently mapped into the simpler picture of linear models in quantum Hilbert spaces. Furthermore, we analyze the experimentally-relevant resource requirements of these models in terms of qubit number and amount of data needed to learn. Based on recent results from classical machine learning, we prove that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points. Our results provide a more comprehensive view of quantum machine learning models as well as insights on the compatibility of different models with NISQ constraints.