Integrating classical and quantum algorithms with machine learning and tensor networks

This dissertation explores innovative intersections of machine learning (ML) and quantum computing with electron microscopy and quantum simulations, aiming to address and overcome significant challenges in physics and chemistry. First, we introduce a cycle generative adversarial network (CycleGAN) equipped with a reciprocal space discriminator for electron microscopy, which enables the autonomous identification of single atom defects in massive datasets. This method underscores a pivotal advancement towards the automation of materials research by allowing the generation of images that are indistinguishable from real data, thereby facilitating rapid and accurate ML applications in electron microscopy. Furthermore, we delve into the realm of quantum computing to enhance molecular dynamics simulations. By leveraging transfer learning, we train models to predict molecular potential energy surfaces with unprecedented accuracy, utilizing data from Density Functional Theory (DFT) and refining it with output from Variational Quantum Eigensolvers (VQE). This dual-step training significantly economizes on quantum resources while maintaining the precision needed for complex quantum chemistry simulations, marking a significant leap toward the practical application of quantum-classical hybrid computational models. Additionally, we present a novel approach to optimizing VQE algorithms by simulating parameterized quantum circuits as matrix product states (MPS) with limited bond dimensions. This strategy, dubbed the Variational Tensor Network Eigensolver (VTNE), demonstrates the potential to alleviate common optimization challenges faced by VQE, such as barren plateaus and slow convergence, by providing a method for pre-optimizing circuit parameters classically. This breakthrough significantly reduces the quantum computational effort required for optimizing quantum simulations of complex systems. Lastly, we introduce a methodology for constructing symmetric MPS with constant-depth circuits, offering a scalable and efficient pathway for state preparation and quantum simulation. This approach is particularly relevant for distributed quantum computing hardware, promising a new direction for efficient quantum simulations. Collectively, these contributions embody a significant stride toward automating material research, enhancing molecular dynamics simulations on quantum hardware, and streamlining quantum computing algorithms, setting the stage for future advancements in physics and chemistry.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Khan, Abid

Contributors dc:contributor

• Clark, Bryan K
• Leigh, Robert G
• Huang, Pinshane
• Stone, Michael

• Tensor Networks
• Quantum Computing
• Machine Learning,

Statement dc:rights

• Copyright 2024 by Abid Khan. All rights reserved.

Language dc:language

eng, en

Handle dc:identifier

https://hdl.handle.net/2142/125504

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F125504