% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@INPROCEEDINGS{Schulz:1037282,
      author       = {Schulz, Sebastian and Willsch, Dennis and Michielsen,
                      Kristel},
      title        = {{G}uided {Q}uantum {W}alk},
      reportid     = {FZJ-2025-00610},
      year         = {2024},
      abstract     = {Quantum algorithms, such as quantum walks (QWs) and quantum
                      annealing (QA), have generated significant attention for
                      their potential to solve large-scale combinatorial
                      optimization problems. In this research, we utilize the
                      theory of local amplitude transfer (LAT) to delve into the
                      operational principles of these algorithms beyond the
                      adiabatic theorem, providing insights into the design of
                      optimal quantum evolutions. 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 and garden
                      optimization problems with 12 to 40 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.},
      month         = {May},
      date          = {2024-05-12},
      organization  = {ISC High Performance 2024, Hamburg
                       (Germany), 12 May 2024 - 16 May 2024},
      subtyp        = {After Call},
      cin          = {JSC},
      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)24},
      url          = {https://juser.fz-juelich.de/record/1037282},
}