On the relation between trainability and dequantization of variational quantum learning models

arXiv (Cornell University)

Abstract

The quest for successful variational quantum machine learning (QML) relies on the design of suitable parametrized quantum circuits (PQCs), as analogues to neural networks in classical machine learning. Successful QML models must fulfill the properties of trainability and non-dequantization, among others. Recent works have highlighted an intricate interplay between trainability and dequantization of such models, which is still unresolved. In this work we contribute to this debate from the perspective of machine learning, proving a number of results identifying, among others when trainability and non-dequantization are not mutually exclusive. We begin by providing a number of new somewhat broader definitions of the relevant concepts, compared to what is found in other literature, which are operationally motivated, and consistent with prior art. With these precise definitions given and motivated, we then study the relation between trainability and dequantization of variational QML. Next, we also discuss the degrees of "variationalness" of QML models, where we distinguish between models like the hardware efficient ansatz and quantum kernel methods. Finally, we introduce recipes for building PQC-based QML models which are both trainable and nondequantizable, and corresponding to different degrees of variationalness. We do not address the practical utility for such models. Our work however does point toward a way forward for finding more general constructions, for which finding applications may become feasible.

Authors 4

1. Elies Gil-Fuster

   Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute · Freie Universität Berlin

   Affiliation as printed

   Dahlem Center for Complex Quantum Systems , Freie Universität Berlin , 14195 Berlin , Germany

   Fraunhofer Heinrich Hertz Institute , 10587 Berlin , Germany

2. Casper Gyurik Aachen $⟨aQa^L⟩$ Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   ⟨aQa L ⟩ Applied Quantum Algorithms , Universiteit Leiden

3. Adrián Pérez-Salinas Aachen Lorentz Instituut $⟨aQa^L⟩$ Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   Lorentz Instituut , Universiteit Leiden , Niels Bohrweg 2 , 2333 CA Leiden , Netherlands

   ⟨aQa L ⟩ Applied Quantum Algorithms , Universiteit Leiden

4. Vedran Dunjko Aachen $⟨aQa^L⟩$ Applied Quantum Algorithms

   Leiden University

   Affiliation as printed

   LIACS , Universiteit Leiden , Niels Bohrweg 1 , 2333 CA Leiden , Netherlands

   ⟨aQa L ⟩ Applied Quantum Algorithms , Universiteit Leiden