{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/39822"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/39822","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"A study on complexity","abstract":"This thesis explores quantum complexity for various quantum systems. Quantum complexity is a well defined quantity in quantum information theory that measures the difficulty of constructing a quantum state from a given reference state and so far, various methods within high energy physics communities have been proposed for computing complexity. In this thesis, we will first review the computations of the different methods used for computing complexity, such as the circuit complexity that uses the wave function, Fubini-Study complexity, and finally the recently proposed Krylov complexity for closed quantum systems. We then extend our investigation and review the complexity for some open quantum systems that have already been explored in literature and finally, we will make some progress by also extending the investigation towards computing the complexity of a new open quantum system, namely the non-gaussian random matrix model.","abstract_html":"This thesis explores quantum complexity for various quantum systems. Quantum complexity is a well defined quantity in quantum information theory that measures the difficulty of constructing a quantum state from a given reference state and so far, various methods within high energy physics communities have been proposed for computing complexity. In this thesis, we will first review the computations of the different methods used for computing complexity, such as the circuit complexity that uses the wave function, Fubini-Study complexity, and finally the recently proposed Krylov complexity for closed quantum systems. We then extend our investigation and review the complexity for some open quantum systems that have already been explored in literature and finally, we will make some progress by also extending the investigation towards computing the complexity of a new open quantum system, namely the non-gaussian random matrix model.","abstract_has_math":false,"creators":["Rapotu, Dimakatso"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Haque, Shajid","Murugan Jeffrey"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023","date_published":"2023","updated_at":"2026-07-22T22:23:24Z","subjects":["Mathematics and Applied Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/39822","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Haque, Shajid","Murugan Jeffrey"]},{"key":"dc:creator","label":"Author","values":["Rapotu, Dimakatso"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-06-03T07:42:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-06-03T07:42:36Z"]},{"key":"dc:date.issued","label":"Date","values":["2023"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:type","label":"Dc Type","values":["Thesis / Dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters","MSc"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics and Applied Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/39822"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis explores quantum complexity for various quantum systems. Quantum complexity is a well defined quantity in quantum information theory that measures the difficulty of constructing a quantum state from a given reference state and so far, various methods within high energy physics communities have been proposed for computing complexity. In this thesis, we will first review the computations of the different methods used for computing complexity, such as the circuit complexity that uses the wave function, Fubini-Study complexity, and finally the recently proposed Krylov complexity for closed quantum systems. We then extend our investigation and review the complexity for some open quantum systems that have already been explored in literature and finally, we will make some progress by also extending the investigation towards computing the complexity of a new open quantum system, namely the non-gaussian random matrix model."]},{"key":"dc:title","label":"Title","values":["A study on complexity"]}]}],"canonical_facts":{"dc:contributor.advisor":["Haque, Shajid","Murugan Jeffrey"],"dc:creator":["Rapotu, Dimakatso"],"dc:date.accessioned":["2024-06-03T07:42:36Z"],"dc:date.available":["2024-06-03T07:42:36Z"],"dc:date.issued":["2023"],"dc:description.abstract":["This thesis explores quantum complexity for various quantum systems. Quantum complexity is a well defined quantity in quantum information theory that measures the difficulty of constructing a quantum state from a given reference state and so far, various methods within high energy physics communities have been proposed for computing complexity. In this thesis, we will first review the computations of the different methods used for computing complexity, such as the circuit complexity that uses the wave function, Fubini-Study complexity, and finally the recently proposed Krylov complexity for closed quantum systems. We then extend our investigation and review the complexity for some open quantum systems that have already been explored in literature and finally, we will make some progress by also extending the investigation towards computing the complexity of a new open quantum system, namely the non-gaussian random matrix model."],"dc:identifier.uri":["http://hdl.handle.net/11427/39822"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:subject":["Mathematics and Applied Mathematics"],"dc:title":["A study on complexity"],"dc:type":["Thesis / Dissertation"],"dc:type.qualificationlevel":["Masters","MSc"]},"updated_at":"2026-07-22T22:23:24Z"}