University of Illinois Urbana-Champaign

Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime

Ryu, Christopher Jayun

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RYU-DISSERTATION-2024.pdf

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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
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.
Graduation Semester
2024-05
Type of Resource
Thesis
Handle URL
https://hdl.handle.net/2142/124300
Copyright and License Information
Copyright 2024 Christopher Ryu

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