{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/132466"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/132466","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Simulation algorithms, Floquet phenomena and superconducting qubits","abstract":"This thesis explores topics that span the abstraction stack of quantum computing: from physical properties of superconducting qubits to computational properties of algorithms for quantum simulation. In the introduction, we begin by reviewing the circuit model of quantum computing. We then introduce circuit quantum electrodynamics (QED), the framework by which superconducting electrical circuits are theoretically modeled, as well as Floquet physics. After a primer on numerical analysis of these systems, we conclude with a discussion of logical errors in physical qubits. In Chapter 2 we present the Floquet fluxonium molecule, a new highly coherent superconducting qubit which is stabilized against ambient noise effects with a strong drive. In Chapter 3 we discuss phenomena related to dispersive readout of fluxonium qubits. In that Chapter we present a new classical simulation algorithm for simulating Floquet dynamics of dispersive readout out to large photon populations using asymptotically fewer computational resources than the prior state of the art. In Chapter 4 we investigate the quantum computational complexity of preparing ground states of Hamiltonians, focusing on the role of frustration. We identify a class of Hamiltonians which are close to being frustration free and point out that they have interesting complexity properties. We give a quantum algorithm for preparing ground states of these Hamiltonians and show that the quantum query complexity is asymptotically improved compared to the general case.","abstract_html":"This thesis explores topics that span the abstraction stack of quantum computing: from physical properties of superconducting qubits to computational properties of algorithms for quantum simulation. In the introduction, we begin by reviewing the circuit model of quantum computing. We then introduce circuit quantum electrodynamics (QED), the framework by which superconducting electrical circuits are theoretically modeled, as well as Floquet physics. After a primer on numerical analysis of these systems, we conclude with a discussion of logical errors in physical qubits. In Chapter 2 we present the Floquet fluxonium molecule, a new highly coherent superconducting qubit which is stabilized against ambient noise effects with a strong drive. In Chapter 3 we discuss phenomena related to dispersive readout of fluxonium qubits. In that Chapter we present a new classical simulation algorithm for simulating Floquet dynamics of dispersive readout out to large photon populations using asymptotically fewer computational resources than the prior state of the art. In Chapter 4 we investigate the quantum computational complexity of preparing ground states of Hamiltonians, focusing on the role of frustration. We identify a class of Hamiltonians which are close to being frustration free and point out that they have interesting complexity properties. We give a quantum algorithm for preparing ground states of these Hamiltonians and show that the quantum query complexity is asymptotically improved compared to the general case.","abstract_has_math":false,"creators":["Thibodeau, Matthew G."],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Clark, Bryan K","Stone, Michael","Leditzky, Felix","Kou, Angela"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-12","date_published":"2025-12","updated_at":"2026-07-22T22:25:07Z","subjects":["quantum","qubit","qubits","superconducting","Floquet","simulation"],"languages":["en"],"rights":["Copyright 2025 Matthew Thibodeau"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/132466","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Clark, Bryan K","Stone, Michael","Leditzky, Felix","Kou, Angela"]},{"key":"dc:creator","label":"Author","values":["Thibodeau, Matthew G."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-12","2025-09-29"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"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 Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["quantum","qubit","qubits","superconducting","Floquet","simulation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Matthew Thibodeau"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/132466"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis explores topics that span the abstraction stack of quantum computing: from physical properties of superconducting qubits to computational properties of algorithms for quantum simulation. In the introduction, we begin by reviewing the circuit model of quantum computing. We then introduce circuit quantum electrodynamics (QED), the framework by which superconducting electrical circuits are theoretically modeled, as well as Floquet physics. After a primer on numerical analysis of these systems, we conclude with a discussion of logical errors in physical qubits. In Chapter 2 we present the Floquet fluxonium molecule, a new highly coherent superconducting qubit which is stabilized against ambient noise effects with a strong drive. In Chapter 3 we discuss phenomena related to dispersive readout of fluxonium qubits. In that Chapter we present a new classical simulation algorithm for simulating Floquet dynamics of dispersive readout out to large photon populations using asymptotically fewer computational resources than the prior state of the art. In Chapter 4 we investigate the quantum computational complexity of preparing ground states of Hamiltonians, focusing on the role of frustration. We identify a class of Hamiltonians which are close to being frustration free and point out that they have interesting complexity properties. We give a quantum algorithm for preparing ground states of these Hamiltonians and show that the quantum query complexity is asymptotically improved compared to the general case.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Matthew Thibodeau, accepted the attached license on 2025-09-22 at 19:21.","The student, Matthew Thibodeau, submitted this Dissertation for approval on 2025-09-22 at 19:24.","This Dissertation was approved for publication on 2025-09-29 at 09:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22807 on 2026-02-19 at 18:24:18"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Simulation algorithms, Floquet phenomena and superconducting qubits"]}]}],"canonical_facts":{"dc:contributor":["Clark, Bryan K","Stone, Michael","Leditzky, Felix","Kou, Angela"],"dc:creator":["Thibodeau, Matthew G."],"dc:date":["2025-12","2025-09-29"],"dc:description":["This thesis explores topics that span the abstraction stack of quantum computing: from physical properties of superconducting qubits to computational properties of algorithms for quantum simulation. In the introduction, we begin by reviewing the circuit model of quantum computing. We then introduce circuit quantum electrodynamics (QED), the framework by which superconducting electrical circuits are theoretically modeled, as well as Floquet physics. After a primer on numerical analysis of these systems, we conclude with a discussion of logical errors in physical qubits. In Chapter 2 we present the Floquet fluxonium molecule, a new highly coherent superconducting qubit which is stabilized against ambient noise effects with a strong drive. In Chapter 3 we discuss phenomena related to dispersive readout of fluxonium qubits. In that Chapter we present a new classical simulation algorithm for simulating Floquet dynamics of dispersive readout out to large photon populations using asymptotically fewer computational resources than the prior state of the art. In Chapter 4 we investigate the quantum computational complexity of preparing ground states of Hamiltonians, focusing on the role of frustration. We identify a class of Hamiltonians which are close to being frustration free and point out that they have interesting complexity properties. We give a quantum algorithm for preparing ground states of these Hamiltonians and show that the quantum query complexity is asymptotically improved compared to the general case.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Matthew Thibodeau, accepted the attached license on 2025-09-22 at 19:21.","The student, Matthew Thibodeau, submitted this Dissertation for approval on 2025-09-22 at 19:24.","This Dissertation was approved for publication on 2025-09-29 at 09:32.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22807 on 2026-02-19 at 18:24:18"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/132466"],"dc:language":["en"],"dc:rights":["Copyright 2025 Matthew Thibodeau"],"dc:subject":["quantum","qubit","qubits","superconducting","Floquet","simulation"],"dc:title":["Simulation algorithms, Floquet phenomena and superconducting qubits"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:07Z"}