{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/124300"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/124300","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Ryu, Christopher Jayun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Chew, Weng C","Kudeki, Erhan","Peng, Zhen","Bogdanov, Simeon"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-04-16","date_published":"2024-04-16","updated_at":"2026-07-22T22:25:00Z","subjects":["Tensor Network Algorithm","Matrix Product State","Computational Electromagnetics","Discrete Exterior Calculus"],"languages":["eng","en"],"rights":["Copyright 2024 Christopher Ryu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/124300","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chew, Weng C","Kudeki, Erhan","Peng, Zhen","Bogdanov, Simeon"]},{"key":"dc:creator","label":"Author","values":["Ryu, Christopher Jayun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-04-16","2024-05"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Tensor Network Algorithm","Matrix Product State","Computational Electromagnetics","Discrete Exterior Calculus"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng","en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Christopher Ryu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/124300"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","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"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime"]}]}],"canonical_facts":{"dc:contributor":["Chew, Weng C","Kudeki, Erhan","Peng, Zhen","Bogdanov, Simeon"],"dc:creator":["Ryu, Christopher Jayun"],"dc:date":["2024-04-16","2024-05"],"dc:description":["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.","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"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/124300"],"dc:language":["eng","en"],"dc:rights":["Copyright 2024 Christopher Ryu"],"dc:subject":["Tensor Network Algorithm","Matrix Product State","Computational Electromagnetics","Discrete Exterior Calculus"],"dc:title":["Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime"],"dc:type":["Text"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:00Z"}