001019430 001__ 1019430 001019430 005__ 20250206215501.0 001019430 0247_ $$2doi$$a10.1103/PRXQuantum.4.030335 001019430 0247_ $$2datacite_doi$$a10.34734/FZJ-2023-05387 001019430 0247_ $$2WOS$$aWOS:001123002800001 001019430 037__ $$aFZJ-2023-05387 001019430 041__ $$aEnglish 001019430 082__ $$a530 001019430 1001_ $$0P:(DE-Juel1)187545$$aMisra-Spieldenner, Aditi$$b0 001019430 245__ $$aMean-Field Approximate Optimization Algorithm 001019430 260__ $$aCollege Park, MD$$bAmerican Physical Society$$c2023 001019430 3367_ $$2DRIVER$$aarticle 001019430 3367_ $$2DataCite$$aOutput Types/Journal article 001019430 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1738825092_24858 001019430 3367_ $$2BibTeX$$aARTICLE 001019430 3367_ $$2ORCID$$aJOURNAL_ARTICLE 001019430 3367_ $$00$$2EndNote$$aJournal Article 001019430 520__ $$aThe quantum approximate optimization algorithm (QAOA) is suggested as a promising application on early quantum computers. Here a quantum-inspired classical algorithm, the mean-field approximate optimization algorithm (mean-field AOA), is developed by replacement of the quantum evolution of the QAOA with classical spin dynamics through the mean-field approximation. Because of the alternating structure of the QAOA, this classical dynamics can be found exactly for any number of QAOA layers. We benchmark its performance against the QAOA on the Sherrington-Kirkpatrick model and the partition problem, and find that the mean-field AOA outperforms the QAOA in both cases for most instances. Our algorithm can thus serve as a tool to delineate optimization problems that can be solved classically from those that cannot, i.e., we believe that it will help to identify instances where a true quantum advantage can be expected from the QAOA. To quantify quantum fluctuations around the mean-field trajectories, we solve an effective scattering problem in time, which is characterized by a spectrum of time-dependent Lyapunov exponents. These provide an indicator for the hardness of a given optimization problem relative to the mean-field AOA. 001019430 536__ $$0G:(DE-HGF)POF4-5223$$a5223 - Quantum-Computer Control Systems and Cryoelectronics (POF4-522)$$cPOF4-522$$fPOF IV$$x0 001019430 536__ $$0G:(BMBF)13N15688$$aVerbundprojekt: Digital-Analoge Quantencomputer (DAQC) - Teilvorhaben: DAQC Kontrolle, Kalibrierung und Charakterisierung (13N15688)$$c13N15688$$x1 001019430 536__ $$0G:(BMBF)13N15584$$aVerbundprojekt, Quantum Artificial Intelligence for the Automotive Industry (Q(AI)2) - Teilvorhaben: Implementierung, Benchmarking, und Management (13N15584)$$c13N15584$$x2 001019430 588__ $$aDataset connected to CrossRef, Journals: juser.fz-juelich.de 001019430 7001_ $$0P:(DE-Juel1)195623$$aBode, Tim$$b1$$eCorresponding author 001019430 7001_ $$0P:(DE-HGF)0$$aSchuhmacher, Peter K.$$b2 001019430 7001_ $$0P:(DE-Juel1)194697$$aStollenwerk, Tobias$$b3 001019430 7001_ $$0P:(DE-Juel1)194613$$aBagrets, Dmitry$$b4 001019430 7001_ $$0P:(DE-Juel1)184630$$aWilhelm-Mauch, Frank$$b5 001019430 773__ $$0PERI:(DE-600)3063626-7$$a10.1103/PRXQuantum.4.030335$$gVol. 4, no. 3, p. 030335$$n3$$p030335$$tPRX quantum$$v4$$x2691-3399$$y2023 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/INV_23_AUG_011649.pdf 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/INV_23_AUG_011649.gif?subformat=icon$$xicon 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/INV_23_AUG_011649.jpg?subformat=icon-1440$$xicon-1440 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/INV_23_AUG_011649.jpg?subformat=icon-180$$xicon-180 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/INV_23_AUG_011649.jpg?subformat=icon-640$$xicon-640 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/PRXQuantum.4.030335.pdf$$yOpenAccess 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/PRXQuantum.4.030335.gif?subformat=icon$$xicon$$yOpenAccess 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/PRXQuantum.4.030335.jpg?subformat=icon-1440$$xicon-1440$$yOpenAccess 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/PRXQuantum.4.030335.jpg?subformat=icon-180$$xicon-180$$yOpenAccess 001019430 8564_ $$uhttps://juser.fz-juelich.de/record/1019430/files/PRXQuantum.4.030335.jpg?subformat=icon-640$$xicon-640$$yOpenAccess 001019430 8767_ $$8INV/23/AUG/011649$$92023-08-18$$a1200195833$$d2023-08-24$$eAPC$$jZahlung erfolgt 001019430 8767_ $$8INV/23/AUG/011649$$92023-08-18$$a1200195833$$d2023-08-24$$eAPC$$jZahlung erfolgt 001019430 909CO $$ooai:juser.fz-juelich.de:1019430$$pdnbdelivery$$popenCost$$pVDB$$pdriver$$pOpenAPC$$popen_access$$popenaire 001019430 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)187545$$aForschungszentrum Jülich$$b0$$kFZJ 001019430 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)195623$$aForschungszentrum Jülich$$b1$$kFZJ 001019430 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)194697$$aForschungszentrum Jülich$$b3$$kFZJ 001019430 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)194613$$aForschungszentrum Jülich$$b4$$kFZJ 001019430 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)184630$$aForschungszentrum Jülich$$b5$$kFZJ 001019430 9131_ $$0G:(DE-HGF)POF4-522$$1G:(DE-HGF)POF4-520$$2G:(DE-HGF)POF4-500$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$9G:(DE-HGF)POF4-5223$$aDE-HGF$$bKey Technologies$$lNatural, Artificial and Cognitive Information Processing$$vQuantum Computing$$x0 001019430 9141_ $$y2023 001019430 915pc $$0PC:(DE-HGF)0000$$2APC$$aAPC keys set 001019430 915pc $$0PC:(DE-HGF)0001$$2APC$$aLocal Funding 001019430 915pc $$0PC:(DE-HGF)0002$$2APC$$aDFG OA Publikationskosten 001019430 915pc $$0PC:(DE-HGF)0003$$2APC$$aDOAJ Journal 001019430 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)0160$$2StatID$$aDBCoverage$$bEssential Science Indicators$$d2023-10-27 001019430 915__ $$0LIC:(DE-HGF)CCBY4$$2HGFVOC$$aCreative Commons Attribution CC BY 4.0 001019430 915__ $$0StatID:(DE-HGF)0100$$2StatID$$aJCR$$bPRX QUANTUM : 2022$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)9905$$2StatID$$aIF >= 5$$bPRX QUANTUM : 2022$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)0501$$2StatID$$aDBCoverage$$bDOAJ Seal$$d2021-12-20T16:22:33Z 001019430 915__ $$0StatID:(DE-HGF)0500$$2StatID$$aDBCoverage$$bDOAJ$$d2021-12-20T16:22:33Z 001019430 915__ $$0StatID:(DE-HGF)0113$$2StatID$$aWoS$$bScience Citation Index Expanded$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)0700$$2StatID$$aFees$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)0150$$2StatID$$aDBCoverage$$bWeb of Science Core Collection$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 001019430 915__ $$0StatID:(DE-HGF)0030$$2StatID$$aPeer Review$$bDOAJ : Anonymous peer review$$d2021-12-20T16:22:33Z 001019430 915__ $$0StatID:(DE-HGF)0561$$2StatID$$aArticle Processing Charges$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)1150$$2StatID$$aDBCoverage$$bCurrent Contents - Physical, Chemical and Earth Sciences$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)0300$$2StatID$$aDBCoverage$$bMedline$$d2023-10-27 001019430 915__ $$0StatID:(DE-HGF)0199$$2StatID$$aDBCoverage$$bClarivate Analytics Master Journal List$$d2023-10-27 001019430 920__ $$lyes 001019430 9201_ $$0I:(DE-Juel1)PGI-12-20200716$$kPGI-12$$lQuantum Computing Analytics$$x0 001019430 980__ $$ajournal 001019430 980__ $$aVDB 001019430 980__ $$aI:(DE-Juel1)PGI-12-20200716 001019430 980__ $$aAPC 001019430 980__ $$aUNRESTRICTED 001019430 9801_ $$aAPC 001019430 9801_ $$aFullTexts