@phdthesis{304061a8-ed85-4b51-b56a-c8c35a4eb677,
  abstract     = {{Quantum computing has progressed from a theoretical concept to a practical experimental technology. By processing information according to quantum mechanics rather than classical rules, quantum computers may offer advantages for certain problems. Although a few algorithms have proven speedups, it remains unclear where quantum computers will be practically useful, especially since current devices are noisy, small, and not yet fault tolerant. This thesis explores quantum computing for biophysically motivated combinatorial problems, with a focus on lattice protein models. In these simplified models, a protein is represented as a chain on a discrete lattice. Despite their simplicity, lattice proteins retain important features of real proteins, such as such as the folding of a chain with exponentially many possible shapes to a unique minimum-energy structure and steric constraints.<br/><br/>To run lattice protein problems on quantum hardware, they must first be formulated using binary variables and objective functions. The latter typically contain soft constraints needed to ensure physical solutions. In Papers~\I--\II, we developed and extended a coordinate-based mapping for lattice protein folding, enabling D-Wave's hybrid quantum-classical annealer to fold both $2$D hydrophobic-polar and $3$D Miyazawa-Jernigan lattice proteins. In Paper~\III, we adapted the approach to the gate-based paradigm and showed how quadratic soft constraints could be removed by a mixer developed for the maximum-independent-set problem. Papers~\IV--\V addressed lattice protein design using quantum annealing, quantum approximate optimization algorithm, quantum alternating operator ansatz and hardware-efficient ansatz, while Paper~\VI extended the framework to multi-chain thermodynamics and the reconstruction of densities of states and heat-capacity features.<br/><br/>Together, these papers show how folding, design, and multi-chain thermodynamics can be formulated, implemented, and analyzed using present-day quantum and hybrid hardware. A recurring limitation is the treatment of soft constraints. In quantum annealing, their high connectivity leads to error accumulation. On gate-based hardware, they increase circuit depth and sensitivity to noise. At the same time, temporary constraint violations can provide useful freedom during optimization. Further progress will therefore require improved formulations, algorithms and hardware that reduce the cost of enforcing physical solutions while retaining this flexibility.}},
  author       = {{Knuthson, Lucas}},
  isbn         = {{978-91-90202-76-0}},
  keywords     = {{quantum annealing; quantum computing; statistical physics; optimization; Markoc chains; Monte Carlo; biophysics; lattice proteins}},
  language     = {{eng}},
  publisher    = {{Lund University}},
  school       = {{Lund University}},
  title        = {{Solving lattice protein problems with quantum computing}},
  url          = {{https://lup.lub.lu.se/search/files/258552384/Lucas_Knuthson_-_WEBB.pdf}},
  year         = {{2026}},
}