On Assessing the Quantum Advantage for MaxCut Provided by Quantum Neural Network Ans\"atze

TL;DR

This paper explores the potential quantum advantage of quantum neural network ans"atze for MaxCut, focusing on the properties of PQCs and their relation to classical neural network features, providing detailed theoretical insights.

Contribution

It offers an in-depth analysis of the oracular formulation of variational quantum algorithms and compares noncommutativity in PQCs to classical nonlinearity, advancing understanding of quantum advantage.

Findings

Noncommutativity in PQCs may be crucial for quantum advantage.

Detailed relationship between ans"atze properties and oracle strength.

Supplementary insights into quantum neural networks for MaxCut.

Abstract

In this thesis we expand upon the results that led to the paper of Lee et al., arXiv:2105.01114 (2021). In particular, we give more details on the oracular formulation of variational quantum algorithms, and the relationship between properties of Ans\"atze and the strength of their corresponding oracles. Furthermore, having identified the importance of noncommutativity in parameterized quantum circuits (PQCs) as likely being crucial to achieving a quantum advantage, we compare this notion to similar properties in classical neural networks such as nonlinearity, based on the perspective of the recent moniker for PQCs as quantum neural networks. While this thesis includes much of the figures and content from the aforementioned paper, it should be considered mainly as a self-contained collection of supplementary materials.