Quantum algorithmic improvements for noisy intermediate scale quantum computers

The future of quantum computing promises a potential paradigm shift in computer science. In quantum computing hardware research, much effort and progress have been made in realizing quantum computers using silicon defects, ion traps, photonic chips, superconducting devices, and neutral atom traps. In quantum computing theory, there have been advances in device characterization, quantum complexity theory, and in novel algorithms for quantum computers. Quantum algorithms on quantum computers could help resolve previously intractable problems in disciplines ranging from finance to biology. However, when designing and applying quantum algorithms to solve any problem careful analysis is required in order to achieve an advantage over known classical algorithms. The work presented in this thesis represents several contributions to the careful design and analysis of quantum algorithms. In Chapter 2, I introduce a novel method for optimizing variational quantum circuits that mitigates many of the issues with training variational quantum circuits. In Chapter 3, I introduce a variational quantum circuit ansatz version of a two-dimensional tensor network and demonstrated its improved performance for two-dimensional physics problems. In Chapter 4, I perform a numerical study on the potential quantum advantage for a popular quantum machine learning model in the literature. Using analytical bounds, I demonstrate that for this particular model a quantum advantage is unlikely.

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

2023

Author dc:creator

• Slattery, Lucas

Contributors dc:contributor

• Clark, Bryan
• DeMarco, Brian
• Kou, Angela
• Pfaff, Wolfgang

• Quantum Computing

Statement dc:rights

• Copyright 2023 Lucas Slattery

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120332

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120332