Problem-Specific Quantum Machine Learning and Quantum Algorithms: Data Embeddings, Symmetries and Structure

Developments in physics, mathematics, computer science and engineering have contributed to the rise of the field of quantum computing over the last few decades. Quantum devices are becoming more powerful and more reliable than ever, poised to disrupt a variety of areas within both research and industry. Despite this promise, there are many challenges that need to be overcome before quantum computers become a widespread practical tool. One of the keys to unlocking the potential of quantum computing is the development of quantum algorithms which boast an advantage over classical protocols for solving problems. This thesis presents some original approaches to tackling this task. Specifically, I present several quantum machine learning and algorithmic procedures, some adapted from established protocols, others novel. Throughout the thesis, I introduce and make use of several state-of-the-art quantum subroutines, including linear combinations of unitaries, quantum singular value transformation, and several techniques for ground state preparation. Our algorithms are all motivated by specific problems, interesting from a theoretical and practical point of view, including tasks from quantum chemistry, function and image classification, and graph analysis. Our general algorithm design process is based upon three foundation stones: data embeddings, symmetries and structure. Through theoretical investigations, simulations and scaling analysis, we demonstrate the utility of our protocols, paving incremental yet meaningful steps toward the realisation of practical quantum advantage.<p></p>

Author dc:creator

• Chukwudubem Umeano (21052130)

• Quantum Machine Learning
• Quantum Algorithms
• Quantum Simulation
• Quantum Computing

Statement dc:rights

• All rights reserved

Identifier

10779/exe.31169083.v1

OAI identifier oai:identifier

oai:figshare.com:article/31169083