Please use this identifier to cite or link to this item:
http://arks.princeton.edu/ark:/88435/dsp01hm50tv83v
Title: | On Assessing the Quantum Advantage for MaxCut Provided by Quantum Neural Network Ansätze |
Authors: | Lee, Juneseo |
Advisors: | Zhandry, Mark McConnell, Mark Rabitz, Herschel |
Department: | Mathematics |
Certificate Program: | Center for Statistics and Machine Learning |
Class Year: | 2021 |
Abstract: | In this work we design a class of Ansätze to solve MaxCut on a parameterized quantum circuit (PQC). Gaining inspiration from properties of quantum optimal control landscapes, we consider the presence of optimization traps as a measure of complexity for hybrid variational quantum algorithms. In particular, we analytically show that no simple Ansatz, satisfying certain criteria, can provide a superpolynomial quantum advantage in solving MaxCut while nevertheless creating entanglement. Furthermore, in order to characterize properties of Ansätze that could provide a quantum advantage, we study the role of noncommutativity in PQCs through a series of numerical experiments. Finally, 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. |
URI: | http://arks.princeton.edu/ark:/88435/dsp01hm50tv83v |
Type of Material: | Princeton University Senior Theses |
Language: | en |
Appears in Collections: | Mathematics, 1934-2023 |
Files in This Item:
File | Description | Size | Format | |
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LEE-JUNESEO-THESIS.pdf | 1.24 MB | Adobe PDF | Request a copy |
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