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@ARTICLE{Schulz:1023092,
      author       = {Schulz, Sebastian and Willsch, Dennis and Michielsen,
                      Kristel},
      title        = {{G}uided quantum walk},
      journal      = {Physical review research},
      volume       = {6},
      number       = {1},
      issn         = {2643-1564},
      address      = {College Park, MD},
      publisher    = {APS},
      reportid     = {FZJ-2024-01662},
      pages        = {013312},
      year         = {2024},
      abstract     = {We utilize the theory of local amplitude transfer (LAT) to
                      gain insights into quantum walks (QWs) and quantum annealing
                      (QA) beyond the adiabatic theorem. By representing the
                      eigenspace of the problem Hamiltonian as a hypercube graph,
                      we demonstrate that probability amplitude traverses the
                      search space through a series of local Rabi oscillations. We
                      argue that the amplitude movement can be systematically
                      guided towards the ground state using a time-dependent
                      hopping rate based solely on the problem's energy spectrum.
                      Building upon these insights, we extend the concept of
                      multistage QW by introducing the guided quantum walk (GQW)
                      as a bridge between QW-like and QA-like procedures. We
                      assess the performance of the GQW on exact cover, traveling
                      salesperson, and garden optimization problems with 9 to 30
                      qubits. Our results provide evidence for the existence of
                      optimal annealing schedules, beyond the requirement of
                      adiabatic time evolutions. These schedules might be capable
                      of solving large-scale combinatorial optimization problems
                      within evolution times that scale linearly in the problem
                      size.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5111 - Domain-Specific Simulation $\&$ Data Life Cycle Labs
                      (SDLs) and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5111},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001195754800002},
      doi          = {10.1103/PhysRevResearch.6.013312},
      url          = {https://juser.fz-juelich.de/record/1023092},
}