Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime
Ryu, Christopher Jayun
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https://hdl.handle.net/2142/124300
Description
Title
Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime
Author(s)
Ryu, Christopher Jayun
Issue Date
2024-04-16
Director of Research (if dissertation) or Advisor (if thesis)
Chew, Weng C
Doctoral Committee Chair(s)
Chew, Weng C
Committee Member(s)
Kudeki, Erhan
Peng, Zhen
Bogdanov, Simeon
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Tensor Network Algorithm
Matrix Product State
Computational Electromagnetics
Discrete Exterior Calculus
Language
eng
Abstract
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.
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