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@ARTICLE{Schumann:1030616,
      author       = {Schumann, M. and Wilhelm-Mauch, Frank and Ciani,
                      Alessandro},
      title        = {{E}mergence of noise-induced barren plateaus in arbitrary
                      layered noise models},
      journal      = {Quantum science and technology},
      volume       = {9},
      number       = {4},
      issn         = {2058-9565},
      address      = {Philadelphia, PA},
      publisher    = {IOP Publishing},
      reportid     = {FZJ-2024-05349},
      pages        = {045019 -},
      year         = {2024},
      abstract     = {In variational quantum algorithms the parameters of a
                      parameterized quantum circuit are optimized in order to
                      minimize a cost function that encodes the solution of the
                      problem. The barren plateau phenomenon manifests as an
                      exponentially vanishing dependence of the cost function with
                      respect to the variational parameters, and thus hampers the
                      optimization process. We discuss how, and in which sense,
                      the phenomenon of noise-induced barren plateaus emerges in
                      parameterized quantum circuits with a layered noise model.
                      Previous results have shown the existence of noise-induced
                      barren plateaus in the presence of local Pauli noise (Wang
                      et al 2021 Nat. Commun.12 6961). We extend these results
                      analytically to arbitrary completely-positive trace
                      preserving maps in two cases: (1) when a parameter-shift
                      rule holds, (2) when the parameterized quantum circuit at
                      each layer forms a unitary 2-design. The second example
                      shows how highly expressive unitaries give rise not only to
                      standard barren plateaus (McClean et al 2018 Nat. Commun.9
                      4812), but also to noise-induced ones. In the second part of
                      the paper, we study numerically the emergence of
                      noise-induced barren plateaus in QAOA circuits focusing on
                      the case of MaxCut problems on d-regular graphs and
                      amplitude damping noise.},
      cin          = {PGI-12},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-12-20200716},
      pnm          = {5232 - Computational Principles (POF4-523) / BMBF 13N16149
                      - QSolid (BMBF-13N16149) / DFG project G:(GEPRIS)390534769 -
                      EXC 2004: Materie und Licht für Quanteninformation (ML4Q)
                      (390534769)},
      pid          = {G:(DE-HGF)POF4-5232 / G:(DE-Juel1)BMBF-13N16149 /
                      G:(GEPRIS)390534769},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001282693900001},
      doi          = {10.1088/2058-9565/ad6285},
      url          = {https://juser.fz-juelich.de/record/1030616},
}