{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/110429"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/110429","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Disorder-driven phase transitions in weak, boundary-obstructed, and non-Hermitian topological insulators","abstract":"\"This thesis focuses on three main areas in quantum physics. The bulk of this thesis addresses the effects of disorder on novel classes of topological insulators. Topological insulators are states of matter that display properties (most notably, protected anomalous edge states) that are robust to symmetry-preserving disorder. While the properties of \"\"classical\"\" tenfold way topological insulators under disorder are well-understood, there exist other topological phases whose behavior under disorder has yet to be characterized. In this portion of the thesis, we will develop real-space methods to compute weak, boundary-obstructed, and non-Hermitian topological invariants, establish their stability at weak and strong disorder, and connect these disordered topological invariants to physical signatures. The remainder of the thesis contains an eclectic mix of other work that broadly focuses on the intersection of computational complexity and quantum mechanics. The first section addresses the problem of simulating quantum mechanics on a classical computer. While exactly simulating quantum mechanics is NP hard, in this section we develop and approximate variational method to simulate quantum systems at nite temperature. The second section develops a \\randomized benchmarking\"\" method for verifying the gates of a quantum computer, a challenging task as the output of a quantum circuit is generically di cult to simulate. Finally, the third section deals with the ability of a quantum computer to simulate condensed matter systems; we study the ability of a variational quantum circuit to approximate the ground state of the mixed-spin Sherrington-Kirkpatrick spin-glass model.\"","abstract_html":""This thesis focuses on three main areas in quantum physics. The bulk of this thesis addresses the effects of disorder on novel classes of topological insulators. Topological insulators are states of matter that display properties (most notably, protected anomalous edge states) that are robust to symmetry-preserving disorder. While the properties of ""classical"" tenfold way topological insulators under disorder are well-understood, there exist other topological phases whose behavior under disorder has yet to be characterized. In this portion of the thesis, we will develop real-space methods to compute weak, boundary-obstructed, and non-Hermitian topological invariants, establish their stability at weak and strong disorder, and connect these disordered topological invariants to physical signatures. The remainder of the thesis contains an eclectic mix of other work that broadly focuses on the intersection of computational complexity and quantum mechanics. The first section addresses the problem of simulating quantum mechanics on a classical computer. While exactly simulating quantum mechanics is NP hard, in this section we develop and approximate variational method to simulate quantum systems at nite temperature. The second section develops a \\randomized benchmarking"" method for verifying the gates of a quantum computer, a challenging task as the output of a quantum circuit is generically di cult to simulate. Finally, the third section deals with the ability of a quantum computer to simulate condensed matter systems; we study the ability of a variational quantum circuit to approximate the ground state of the mixed-spin Sherrington-Kirkpatrick spin-glass model."","abstract_has_math":false,"creators":["Claes, Jahan"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Hughes, Taylor L","Vishveshwara, Smitha","Clark, Bryan K","Gadway, Bryce"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-09-17T01:10:38Z","date_published":"2021-09-17T01:10:38Z","updated_at":"2026-07-22T22:24:50Z","subjects":["Topological insulators","disorder","non-Hermitian"],"languages":["en"],"rights":["Copyright 2021 Jahan Claes"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/110429","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hughes, Taylor L","Vishveshwara, Smitha","Clark, Bryan K","Gadway, Bryce"]},{"key":"dc:creator","label":"Author","values":["Claes, Jahan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-09-17T01:10:38Z","2021-04-01","2021-05"]},{"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 at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Topological insulators","disorder","non-Hermitian"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2021 Jahan Claes"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/110429"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"This thesis focuses on three main areas in quantum physics. The bulk of this thesis addresses the effects of disorder on novel classes of topological insulators. Topological insulators are states of matter that display properties (most notably, protected anomalous edge states) that are robust to symmetry-preserving disorder. While the properties of \"\"classical\"\" tenfold way topological insulators under disorder are well-understood, there exist other topological phases whose behavior under disorder has yet to be characterized. In this portion of the thesis, we will develop real-space methods to compute weak, boundary-obstructed, and non-Hermitian topological invariants, establish their stability at weak and strong disorder, and connect these disordered topological invariants to physical signatures. The remainder of the thesis contains an eclectic mix of other work that broadly focuses on the intersection of computational complexity and quantum mechanics. The first section addresses the problem of simulating quantum mechanics on a classical computer. While exactly simulating quantum mechanics is NP hard, in this section we develop and approximate variational method to simulate quantum systems at nite temperature. The second section develops a \\randomized benchmarking\"\" method for verifying the gates of a quantum computer, a challenging task as the output of a quantum circuit is generically di cult to simulate. Finally, the third section deals with the ability of a quantum computer to simulate condensed matter systems; we study the ability of a variational quantum circuit to approximate the ground state of the mixed-spin Sherrington-Kirkpatrick spin-glass model.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, Jahan Claes, accepted the attached license on 2021-03-30 at 12:10.","The student, Jahan Claes, submitted this Dissertation for approval on 2021-03-30 at 12:17.","This Dissertation was approved for publication on 2021-04-01 at 09:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16223 on 2021-09-16 at 16:40:22","Made available in DSpace on 2021-09-17T01:10:38Z (GMT). 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Topological insulators are states of matter that display properties (most notably, protected anomalous edge states) that are robust to symmetry-preserving disorder. While the properties of \"\"classical\"\" tenfold way topological insulators under disorder are well-understood, there exist other topological phases whose behavior under disorder has yet to be characterized. In this portion of the thesis, we will develop real-space methods to compute weak, boundary-obstructed, and non-Hermitian topological invariants, establish their stability at weak and strong disorder, and connect these disordered topological invariants to physical signatures. The remainder of the thesis contains an eclectic mix of other work that broadly focuses on the intersection of computational complexity and quantum mechanics. The first section addresses the problem of simulating quantum mechanics on a classical computer. While exactly simulating quantum mechanics is NP hard, in this section we develop and approximate variational method to simulate quantum systems at nite temperature. The second section develops a \\randomized benchmarking\"\" method for verifying the gates of a quantum computer, a challenging task as the output of a quantum circuit is generically di cult to simulate. Finally, the third section deals with the ability of a quantum computer to simulate condensed matter systems; we study the ability of a variational quantum circuit to approximate the ground state of the mixed-spin Sherrington-Kirkpatrick spin-glass model.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms","The student, Jahan Claes, accepted the attached license on 2021-03-30 at 12:10.","The student, Jahan Claes, submitted this Dissertation for approval on 2021-03-30 at 12:17.","This Dissertation was approved for publication on 2021-04-01 at 09:17.","DSpace SAF Submission Ingestion Package generated from Vireo submission #16223 on 2021-09-16 at 16:40:22","Made available in DSpace on 2021-09-17T01:10:38Z (GMT). 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