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@INPROCEEDINGS{Vyas:1033654,
      author       = {Vyas, Kunal and Jin, Fengping and Michielsen, Kristel},
      title        = {{I}nvestigating scaling properties for quantum annealing to
                      solve the {F}ermi-{H}ubbard model using the kinetic energy
                      part as the driving {H}amiltonian},
      school       = {RWTH Aachen},
      reportid     = {FZJ-2024-06526},
      year         = {2024},
      abstract     = {Quantum annealing can help in finding the ground state of
                      Hamiltonians describing many body systems. One such
                      Hamiltonian is the Fermi-Hubbard Hamiltonian. We investigate
                      the scaling complexity for the quantum annealing process
                      carried out using the kinetic energy part of the Hubbard
                      model as driving Hamiltonian for ground state calculations.
                      The way we do this is by studying the gaps between the
                      ground state and the 1st relevant excited state that
                      participates in the diabatic evolution for a 1-dimensional
                      system. The behavior of these gaps with increasing system
                      size could hint at polynomial scaling of required annealing
                      time for finding the ground state of the Hubbard
                      Hamiltonian. We also try to extend this idea to a Hubbard
                      model ladder to learn more about the scaling behavior of
                      gaps relevant to adiabatic evolution. Further, we discuss
                      about initial state preparation for the quantum annealing
                      strategy under study. Information on the complexity coupled
                      with an efficient way of preparing the initial state could
                      bolster our hopes for using adiabatic quantum computation
                      for solving correlated many-body Hamiltonians.},
      month         = {Jun},
      date          = {2024-06-10},
      organization  = {Adiabatic Quantum Computing 2024,
                       Glasgow (UK), 10 Jun 2024 - 14 Jun
                       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) / DFG project
                      G:(GEPRIS)355031190 - FOR 2692: Fundamental Aspects of
                      Statistical Mechanics and the Emergence of Thermodynamics in
                      Non-Equilibrium Systems (355031190)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(GEPRIS)355031190},
      typ          = {PUB:(DE-HGF)6},
      doi          = {10.34734/FZJ-2024-06526},
      url          = {https://juser.fz-juelich.de/record/1033654},
}