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

TL;DR

This paper explores the relationship between trainability and non-dequantization in variational quantum machine learning models, providing new definitions, theoretical insights, and construction recipes to identify models that are both trainable and non-dequantizable.

Contribution

It introduces operationally motivated definitions and analyzes the interplay between trainability and dequantization, offering methods to construct models with both properties.

Findings

Identifies conditions where trainability and non-dequantization coexist

Provides new definitions for key concepts in variational QML

Offers recipes for building models that are both trainable and non-dequantizable

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.