2026-09-18T18:53:23Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/124300 2024-09-16 col_2142_5131 col_2142_8888 com_2142_5130 com_2142_8887 com_2142_234

Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime Ryu, Christopher Jayun 2024-04-16 Tensor Network Algorithm Matrix Product State Computational Electromagnetics Discrete Exterior Calculus 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. Text eng https://hdl.handle.net/2142/124300 Copyright 2024 Christopher Ryu Chew, Weng C Chew, Weng C Kudeki, Erhan Peng, Zhen Bogdanov, Simeon 2024-05 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms The student, Christopher Ryu, accepted the attached license on 2024-04-16 at 12:32. The student, Christopher Ryu, submitted this Dissertation for approval on 2024-04-16 at 12:46. This Dissertation was approved for publication on 2024-04-16 at 16:49. DSpace SAF Submission Ingestion Package generated from Vireo submission #20438 on 2024-09-16 at 00:34:39 Ph.D. Dissertation Electrical & Computer Engr University of Illinois at Urbana-Champaign Electrical & Computer Eng