Classical surrogates for quantum learning models

TL;DR

This paper introduces classical surrogates for quantum machine learning models, showing that many quantum models can be efficiently mimicked classically, which challenges their quantum advantage and highlights the need to understand their generalization capabilities.

Contribution

The paper defines classical surrogates for quantum models, demonstrating their existence for many re-uploading quantum models and providing a benchmark to evaluate quantum advantage.

Findings

Classical surrogates can replicate many quantum models' input-output relations.

Quantum models studied show no advantage in performance or trainability.

Classical surrogates serve as a benchmark, emphasizing the importance of generalization in quantum learning.

Abstract

The advent of noisy intermediate-scale quantum computers has put the search for possible applications to the forefront of quantum information science. One area where hopes for an advantage through near-term quantum computers are high is quantum machine learning, where variational quantum learning models based on parametrized quantum circuits are discussed. In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations. As inference can be performed classically, the existence of a classical surrogate greatly enhances the applicability of a quantum learning strategy. However, the classical surrogate also challenges possible advantages of quantum schemes. As it is possible to directly optimize the ansatz of the classical surrogate, they create a natural benchmark the quantum model has to outperform. We show that large classes of well-analyzed re-uploading models have a classical surrogate. We conducted numerical experiments and found that these quantum models show no advantage in performance or trainability in the problems we analyze. This leaves only generalization capability as possible point of quantum advantage and emphasizes the dire need for a better understanding of inductive biases of quantum learning models.