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@ARTICLE{MisraSpieldenner:1019430,
      author       = {Misra-Spieldenner, Aditi and Bode, Tim and Schuhmacher,
                      Peter K. and Stollenwerk, Tobias and Bagrets, Dmitry and
                      Wilhelm-Mauch, Frank},
      title        = {{M}ean-{F}ield {A}pproximate {O}ptimization {A}lgorithm},
      journal      = {PRX quantum},
      volume       = {4},
      number       = {3},
      issn         = {2691-3399},
      address      = {College Park, MD},
      publisher    = {American Physical Society},
      reportid     = {FZJ-2023-05387},
      pages        = {030335},
      year         = {2023},
      abstract     = {The 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.},
      cin          = {PGI-12},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-12-20200716},
      pnm          = {5223 - Quantum-Computer Control Systems and Cryoelectronics
                      (POF4-522) / Verbundprojekt: Digital-Analoge Quantencomputer
                      (DAQC) - Teilvorhaben: DAQC Kontrolle, Kalibrierung und
                      Charakterisierung (13N15688) / Verbundprojekt, Quantum
                      Artificial Intelligence for the Automotive Industry (Q(AI)2)
                      - Teilvorhaben: Implementierung, Benchmarking, und
                      Management (13N15584)},
      pid          = {G:(DE-HGF)POF4-5223 / G:(BMBF)13N15688 / G:(BMBF)13N15584},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001123002800001},
      doi          = {10.1103/PRXQuantum.4.030335},
      url          = {https://juser.fz-juelich.de/record/1019430},
}