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@INPROCEEDINGS{vandenHeuvel:1030625,
      author       = {van den Heuvel, Pim and Montanez-Barrera, Jhon Alejandro
                      and Willsch, Dennis and Michielsen, Kristel},
      title        = {{S}olving constrained combinatorial optimization problems
                      on quantum devices with linear penalty terms},
      reportid     = {FZJ-2024-05358},
      year         = {2024},
      abstract     = {Quantum computing approaches to solving constrained
                      combinatorial optimization problems, such as Quantum
                      Annealing (QA) and the Quantum Approximate Optimization
                      Algorithm (QAOA), are often impeded by the fact that
                      constraints are typically implemented as costly quadratic
                      penalty terms in the cost function. It was recently found
                      that linear penalty terms might suffice to solve a specific
                      class of constrained optimizationproblems [1]. Here,
                      conditions are outlined under which linear penalty terms can
                      correctly encode two other constrained optimization
                      problems, namely the Quadratic Knapsack Problem (QKP) and
                      the Portfolio Optimization (PO) problem. For these two
                      problems, our QAOA simulations suggest that problem
                      Hamiltonians with a linear penaltyterm can yield a higher
                      success probability than those with the usual quadratic
                      penaltyterm. However, algorithm performance depends on the
                      precise specification of the problems, e.g., the
                      distribution of the covariances between assets in the PO
                      problem. Additionally, for the fully connected PO problem it
                      seems possible to neglect some of the connections between
                      qubits by setting the corresponding problem coefficients to
                      zero,while maintaining similar performance. Since the linear
                      penalty terms can be implemented as single-qubit gates or
                      biases, such problems require lower connectivity of
                      thequantum hardware or can be run with shallower circuits,
                      which should lead to improvedperformance on today’s noisy
                      quantum processors.[1] Puya Mirkarimi, Ishaan Shukla, David
                      C. Hoyle, Ross Williams, and Nicholas Chancellor. Quantum
                      optimization with linear Ising penalty functions for
                      customer data science. 2024. arXiv: 2404.05467[quant-ph].},
      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) / BMBF 13N16149 -
                      QSolid (BMBF-13N16149)},
      pid          = {G:(DE-HGF)POF4-5111 / G:(DE-Juel1)BMBF-13N16149},
      typ          = {PUB:(DE-HGF)24},
      doi          = {10.34734/FZJ-2024-05358},
      url          = {https://juser.fz-juelich.de/record/1030625},
}