Research Interests

Quantum-accelerated Scientific Computing

Since a few years, I am interested in practical quantum computing with special focus on realizing quantum algorithms for solving problems arising in linear algebra and scientific computing. This often involved the solution of linear and nonlinear systems of equations, which arise from the discretization of partial differential equations by numerical methods such the as Finite Element Method and Isogeometric Analysis. I am convinced that in a few years from now we will be using quantum computers as special-purpose accelerators as part of heterogeneous HPC clusters like we are using GPUs today. Similarly to the early years of GPU-computing, real quantum computers are scarcely available and their capabilities are very limited.

Our group is developing the open-source software LibKet, which is a cross-platform expression template library for developing quantum algorithms for todays and near-future quantum computers and simulators. In contrast to other quantum computing SDKs our focus is on making quantum computers usable as accelerators for computational science and engineering application.

Selected contributions

  • Zeynab Kaseb, Matthias Möller, Pedro P. Vergara, and Peter Palensky. Adiabatic quantum power flow. May 2024. [ DOI | http ]
  • Wolfgang Nowak, Tim Bruennette, Merel Annelise Schalkers, and Matthias Möller. Overdispersion in gate tomography: Experiments and continuous, two-scale random walk model on the bloch sphere. ACM Transactions on Quantum Computing, August 2024. [ DOI | http ]
  • Merel A. Schalkers and Matthias Möller. Efficient and fail-safe quantum algorithm for the transport equation. Journal of Computational Physics, 502:112816, April 2024. [ DOI | http ]
  • Merel A. Schalkers and Matthias Möller. On the importance of data encoding in quantum Boltzmann methods. Quantum Information Processing, 23(1), January 2024. [ DOI | http ]
  • Merel A. Schalkers and Matthias Möller. Momentum exchange method for quantum Boltzmann methods, 2024. [ arXiv ]
  • Arne Wulff, Boyang Chen, Matthew Steinberg, Yinglu Tang, Matthias Möller, and Sebastian Feld. Quantum computing and tensor networks for laminate design: A novel approach to stacking sequence retrieval. Computer Methods in Applied Mechanics and Engineering, 432:117380, December 2024. [ DOI | http ]
  • Tim Driebergen. QAOA mixing Hamiltonians for MinVertexCover, 2023. [ http ]
  • Giorgio Tosti Balducci, Boyang Chen, Matthias Möller, Marc Gerritsma, and Roeland De Breuker. Review and perspectives in quantum computing for partial differential equations in structural mechanics. Frontiers in Mechanical Engineering, 8, September 2022. [ DOI | http ]
  • Huub Donkers. QPack: A cross-platform quantum benchmark-suite, 2022. [ http ]
  • Huub Donkers, Koen Mesman, Zaid Al-Ars, and Matthias Möller. QPack scores: Quantitative performance metrics for application-oriented quantum computer benchmark, 2022. [ arXiv | http ]
  • Marcin Dukalski, Diego Rovetta, Stan van der Linde, Matthias Möller, Niels Neumann, and Frank Phillipson. Quantum computer-assisted global optimization in geophysics illustrated with stack power maximization for refraction residual statics estimation. GEOPHYSICS, pages 1--74, November 2022. [ DOI | http ]
  • Stan van der Linde, Marcin Dukalski, Matthias Möller, Niels Neumann, Frank Phillipson, and Diego Rovetta. Residual statics estimation with quantum annealing. In 83rd EAGE Annual Conference & Exhibition. European Association of Geoscientists & Engineers, 2022.
  • Merel Schalkers and Matthias Möller. Learning based hardware-centric quantum circuit generation. In Proceedings of the 22nd International Conference on Innovations for Community Services (I4CS 2022). Springer, Cham, 2022. [ DOI | http ]
  • Smaran Adarsh. Resource optimal executable quantum circuit generation using approximate computing, 2021. [ http ]
  • Smaran Adarsh and Matthias Möller. Resource optimal executable quantum circuit generation using approximate computing. In Proceedings of the IEEE International Conference on Quantum Computing and Engineering (QCE21). IEEE, 2021. [ DOI ]
  • Koen Mesman, Zaid Al-Ars, and Matthias Möller. QPack: Quantum approximate optimization algorithms as universal benchmark for quantum computers, 2021. [ arXiv | http ]
  • Merel Schalkers. Learning based hardware-centric quantum circuit generation, 2021. [ http ]
  • Sigurdur Ag. Sigurdsson. Implementations of quantum algorithms for solving linear systems, 2021. [ http ]
  • Giorgio Tosti Balducci, Boyang Chen, Matthias Möller, and Roeland De Breuker. Solving tridiagonal linear systems with a variational quantum algorithm, 2021.
  • Stan van der Linde. Quantum annealing for seismic imaging, 2021. [ http ]
  • Joost C.P. Bus. The quantum approximate optimization algorithm: Performance on max-cut using heuristic parameter determination, 2020. [ http ]
  • Matthias Möller and Merel Schalkers. LibKet: A cross-platform programming framework for quantum-accelerated scientific computing. In Valeria V. Krzhizhanovskaya, Gábor Závodszky, Michael H. Lees, Jack J. Dongarra, Peter M. A. Sloot, Sérgio Brissos, and João Teixeira, editors, Computational Science - ICCS 2020, pages 451--464, Cham, 2020. Springer International Publishing. [ DOI | http ]
  • Matthias Möller and Cornelis Vuik. A conceptual framework for quantum accelerated automated design optimization. Microprocessors and Microsystems, 66:67--71, apr 2019. [ DOI | http ]
  • Tim Driebergen. Designing a quantum algorithm for real-valued addition using posit arithmetic, 2019. [ http ]
  • Menno Looman. Implementation and analysis of an algorithm on positive integer addition for quantum computing, 2018. [ http ]
  • Mike van der Lans. Quantum algorithms and their implementation on quantum computer simulators, 2018. [ http ]
  • Matthias Möller and Cornelis Vuik. On the impact of quantum computing technology on future developments in high-performance scientific computing. Ethics and Information Technology, 19(4):253--269, aug 2017. [ DOI | arXiv | http ]