Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime

In the race towards achieving true quantum advantage, the development of a scalable and reliable quantum computer demands lower gate error rates, longer qubit coherence times, increased qubit connectivity, and enhanced controllability of qubit couplings. Addressing these challenges necessitates accurate simulations of quantum devices, beginning with the foundational task of properly selecting or deriving the Hamiltonian that faithfully represents the underlying physical system. This thesis explores the gauge-invariance issues of various Hamiltonians that are utilized in quantum electrodynamics. With the validated Hamiltonians, numerical transformations aimed at producing Hamiltonians that are more amenable to tensor network algorithms are developed. Furthermore, discrete exterior calculus (DEC) is considered for electromagnetic analysis of quantum devices. The study investigates the satisfaction of the generalized Helmholtz decomposition in DEC simulations in the presence of multiple types of boundary conditions, paving the way for its application in analyzing a superconducting qubit-resonator system.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Ryu, Christopher Jayun

Contributors dc:contributor

• Chew, Weng C
• Kudeki, Erhan
• Peng, Zhen
• Bogdanov, Simeon

• Tensor Network Algorithm
• Matrix Product State
• Computational Electromagnetics
• Discrete Exterior Calculus

Statement dc:rights

• Copyright 2024 Christopher Ryu

Language dc:language

eng, en

Handle dc:identifier

https://hdl.handle.net/2142/124300

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/124300