001010673 001__ 1010673 001010673 005__ 20231004201829.0 001010673 0247_ $$2datacite_doi$$a10.34734/FZJ-2023-03182 001010673 0247_ $$2URN$$aurn:nbn:de:0001-20231004085351526-3932686-7 001010673 020__ $$a978-3-95806-700-4 001010673 037__ $$aFZJ-2023-03182 001010673 1001_ $$0P:(DE-Juel1)174485$$aJattana, Manpreet Singh$$b0$$eCorresponding author$$ufzj 001010673 245__ $$aApplications of variational methods for quantum computers$$f- 2022-11-30 001010673 260__ $$aJülich$$bForschungszentrum Jülich GmbH Zentralbibliothek, Verlag$$c2023 001010673 300__ $$avii, 160 001010673 3367_ $$2DataCite$$aOutput Types/Dissertation 001010673 3367_ $$0PUB:(DE-HGF)3$$2PUB:(DE-HGF)$$aBook$$mbook 001010673 3367_ $$2ORCID$$aDISSERTATION 001010673 3367_ $$2BibTeX$$aPHDTHESIS 001010673 3367_ $$02$$2EndNote$$aThesis 001010673 3367_ $$0PUB:(DE-HGF)11$$2PUB:(DE-HGF)$$aDissertation / PhD Thesis$$bphd$$mphd$$s1695296365_9510 001010673 3367_ $$2DRIVER$$adoctoralThesis 001010673 4900_ $$aSchriften des Forschungszentrums Jülich IAS Series$$v53 001010673 502__ $$aDissertation, RWTH Aachen, 2022$$bDissertation$$cRWTH Aachen$$d2022 001010673 520__ $$aThe primary subject of this dissertation is the analysis and improvement of variational methods that combine the use of classical and gate based quantum computers. The secondary subject is the development of matrix based error mitigation and benchmarking protocols fornoisy quantum computers. Variational methods run on quantum computer emulators are used to find the ground state energies of the Heisenberg and Hubbard models and selected molecules in chemistry. An algorithm is developed and deployed to automate the creation of variational circuits. The theory and overview of variational methods and gradient based optimisation algorithms are presented. We learn that while variational methods make it possible to use current generation quantum computers, guarantees of always finding the ground state energy are elusive.We introduce noise in our emulations and adapt the optimisation algorithms to withstand it. We observe the emergence of local minima and barren plateaus which hinder variational methods from finding the ground state energies. It is discerned that clever choices of initial states and parameters are necessary ingredients for success. We develop the technique of quasi-dynamical evolution inspired by quantum annealing. It overcomes the limitations of standard variational algorithms by systematically improving the ground state energy estimate. Our tests show that the heuristic improves the energy estimate even in facile settings. We introduce seven criteria for ideal error mitigation protocols. A new protocol is developedon its basis. Our tests on IBM Q quantum computers show noticeable error mitigation.The matrix generated during the execution of the protocol helps detect and visualise errorsand biases. We invent and use small depth quantum circuits for benchmarking quantumcomputers. 001010673 536__ $$0G:(DE-HGF)POF4-5111$$a5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511)$$cPOF4-511$$fPOF IV$$x0 001010673 588__ $$aDataset connected to DataCite 001010673 8564_ $$uhttps://juser.fz-juelich.de/record/1010673/files/IAS_Series_53.pdf$$yOpenAccess 001010673 909CO $$ooai:juser.fz-juelich.de:1010673$$pVDB$$pdriver$$purn$$popen_access$$popenaire$$pdnbdelivery 001010673 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 001010673 915__ $$0LIC:(DE-HGF)CCBY4$$2HGFVOC$$aCreative Commons Attribution CC BY 4.0 001010673 9141_ $$y2023 001010673 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)174485$$aForschungszentrum Jülich$$b0$$kFZJ 001010673 9131_ $$0G:(DE-HGF)POF4-511$$1G:(DE-HGF)POF4-510$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5111$$aDE-HGF$$bKey Technologies$$lEngineering Digital Futures – Supercomputing, Data Management and Information Security for Knowledge and Action$$vEnabling Computational- & Data-Intensive Science and Engineering$$x0 001010673 920__ $$lyes 001010673 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0 001010673 980__ $$aphd 001010673 980__ $$aVDB 001010673 980__ $$aUNRESTRICTED 001010673 980__ $$abook 001010673 980__ $$aI:(DE-Juel1)JSC-20090406 001010673 9801_ $$aFullTexts