{"ddc":["530"],"date_created":"2023-11-28T10:58:13Z","related_material":{"record":[{"id":"13125","status":"public","relation":"part_of_dissertation"},{"id":"11471","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"9760"}]},"abstract":[{"lang":"eng","text":"This Ph.D. thesis presents a detailed investigation into Variational Quantum Algorithms\r\n(VQAs), a promising class of quantum algorithms that are well suited for near-term quantum\r\ncomputation due to their moderate hardware requirements and resilience to noise. Our\r\nprimary focus lies on two particular types of VQAs: the Quantum Approximate Optimization\r\nAlgorithm (QAOA), used for solving binary optimization problems, and the Variational Quantum\r\nEigensolver (VQE), utilized for finding ground states of quantum many-body systems.\r\nIn the first part of the thesis, we examine the issue of effective parameter initialization for\r\nthe QAOA. The work demonstrates that random initialization of the QAOA often leads to\r\nconvergence in local minima with sub-optimal performance. To mitigate this issue, we propose\r\nan initialization of QAOA parameters based on the Trotterized Quantum Annealing (TQA).\r\nWe show that TQA initialization leads to the same performance as the best of an exponentially\r\nscaling number of random initializations.\r\nThe second study introduces Transition States (TS), stationary points with a single direction\r\nof descent, as a tool for systematically exploring the QAOA optimization landscape. This\r\nleads us to propose a novel greedy parameter initialization strategy that guarantees for the\r\nenergy to decrease with increasing number of circuit layers.\r\nIn the third section, we extend the QAOA to qudit systems, which are higher-dimensional\r\ngeneralizations of qubits. This chapter provides theoretical insights and practical strategies for\r\nleveraging the increased computational power of qudits in the context of quantum optimization\r\nalgorithms and suggests a quantum circuit for implementing the algorithm on an ion trap\r\nquantum computer.\r\nFinally, we propose an algorithm to avoid “barren plateaus”, regions in parameter space with\r\nvanishing gradients that obstruct efficient parameter optimization. This novel approach relies\r\non defining a notion of weak barren plateaus based on the entropies of local reduced density\r\nmatrices and showcases how these can be efficiently quantified using shadow tomography.\r\nTo illustrate the approach we employ the strategy in the VQE and show that it allows to\r\nsuccessfully avoid barren plateaus in the initialization and throughout the optimization.\r\nTaken together, this thesis greatly enhances our understanding of parameter initialization and\r\noptimization in VQAs, expands the scope of QAOA to higher-dimensional quantum systems,\r\nand presents a method to address the challenge of barren plateaus using the VQE. These\r\ninsights are instrumental in advancing the field of near-term quantum computation."}],"tmp":{"short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","project":[{"_id":"bd660c93-d553-11ed-ba76-fb0fb6f49c0d","name":"IMB PhD Nomination Fellowship - Stefan Sack"},{"call_identifier":"H2020","grant_number":"850899","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control"}],"author":[{"id":"dd622248-f6e0-11ea-865d-ce382a1c81a5","last_name":"Sack","first_name":"Stefan","full_name":"Sack, Stefan","orcid":"0000-0001-5400-8508"}],"oa":1,"publication_identifier":{"issn":["2663-337X"]},"has_accepted_license":"1","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","language":[{"iso":"eng"}],"page":"142","article_processing_charge":"No","ec_funded":1,"_id":"14622","OA_place":"repository","status":"public","department":[{"_id":"GradSch"},{"_id":"MaSe"}],"year":"2023","doi":"10.15479/at:ista:14622","publication_status":"published","date_updated":"2025-04-22T22:30:31Z","alternative_title":["ISTA Thesis"],"day":"30","oa_version":"Published Version","date_published":"2023-11-30T00:00:00Z","file":[{"embargo":"2024-11-30","date_updated":"2024-11-30T23:30:03Z","file_size":11947523,"file_id":"14635","creator":"ssack","checksum":"068fd3570506ec42b2faa390de784bc4","file_name":"PhD_Thesis.pdf","relation":"main_file","access_level":"open_access","date_created":"2023-11-30T15:53:10Z","content_type":"application/pdf"},{"relation":"source_file","file_name":"PhD Thesis (1).zip","date_created":"2023-11-30T15:54:11Z","access_level":"closed","content_type":"application/zip","embargo_to":"open_access","file_size":18422964,"date_updated":"2024-11-30T23:30:03Z","file_id":"14636","checksum":"0fa3bc0d108aed0ac59d2c6beef2220a","creator":"ssack"}],"degree_awarded":"PhD","publisher":"Institute of Science and Technology Austria","month":"11","file_date_updated":"2024-11-30T23:30:03Z","title":"Improving variational quantum algorithms : Innovative initialization techniques and extensions to qudit systems","citation":{"ama":"Sack S. Improving variational quantum algorithms : Innovative initialization techniques and extensions to qudit systems. 2023. doi:<a href=\"https://doi.org/10.15479/at:ista:14622\">10.15479/at:ista:14622</a>","apa":"Sack, S. (2023). <i>Improving variational quantum algorithms : Innovative initialization techniques and extensions to qudit systems</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:14622\">https://doi.org/10.15479/at:ista:14622</a>","ista":"Sack S. 2023. Improving variational quantum algorithms : Innovative initialization techniques and extensions to qudit systems. Institute of Science and Technology Austria.","mla":"Sack, Stefan. <i>Improving Variational Quantum Algorithms : Innovative Initialization Techniques and Extensions to Qudit Systems</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/at:ista:14622\">10.15479/at:ista:14622</a>.","ieee":"S. Sack, “Improving variational quantum algorithms : Innovative initialization techniques and extensions to qudit systems,” Institute of Science and Technology Austria, 2023.","short":"S. Sack, Improving Variational Quantum Algorithms : Innovative Initialization Techniques and Extensions to Qudit Systems, Institute of Science and Technology Austria, 2023.","chicago":"Sack, Stefan. “Improving Variational Quantum Algorithms : Innovative Initialization Techniques and Extensions to Qudit Systems.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/at:ista:14622\">https://doi.org/10.15479/at:ista:14622</a>."},"supervisor":[{"orcid":"0000-0002-2399-5827","full_name":"Serbyn, Maksym","first_name":"Maksym","last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"}],"type":"dissertation"}