Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime

Ryu, Christopher Jayun

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

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

Copyright and License Information

Copyright 2024 Christopher Ryu

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