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001019430 0247_ $$2doi$$a10.1103/PRXQuantum.4.030335
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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$$c2023
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001019430 520__ $$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$$x2
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001019430 7001_ $$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
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