Potential and limitations of random Fourier features for dequantizing quantum machine learning

TL;DR

This paper investigates the potential of random Fourier features to dequantize variational quantum machine learning models, identifying conditions for efficiency and implications for quantum advantage in regression tasks.

Contribution

It establishes necessary and sufficient conditions for RFF-based dequantization of quantum models and guides PQC architecture design for potential quantum advantage.

Findings

RFF can efficiently dequantize certain quantum models under specific conditions

Guidelines for designing PQC architectures for regression tasks

Identification of structures necessary for quantum advantage

Abstract

Quantum machine learning is arguably one of the most explored applications of near-term quantum devices. Much focus has been put on notions of variational quantum machine learning where parameterized quantum circuits (PQCs) are used as learning models. These PQC models have a rich structure which suggests that they might be amenable to efficient dequantization via random Fourier features (RFF). In this work, we establish necessary and sufficient conditions under which RFF does indeed provide an efficient dequantization of variational quantum machine learning for regression. We build on these insights to make concrete suggestions for PQC architecture design, and to identify structures which are necessary for a regression problem to admit a potential quantum advantage via PQC based optimization.