Research Interests

Quantum-accelerated Scientific Computing

For several 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 involves the solution of linear and nonlinear systems of equations, which arise from the discretization of partial differential equations by numerical methods such 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 today's 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 applications.

Selected contributions

  1. Luca Hofstadler, Catalin Gavriluta, Jochen Stiasny, Matthias Möller, Carsten Hartmann, Andrea Benigni, and Jochen Lorenz Cremer. A compact QUBO formulation for solving transmission expansion planning. Electric Power Systems Research, 262:113655, January 2027. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scopus 0 | Scholar 0 )
  2. Giorgio Tosti Balducci, Boyang Chen, Matthias Möller, Marc Gerritsma, and Roeland De Breuker. Predicting open-hole laminates failure using support vector machines with classical and quantum kernels. Acta Mechanica Sinica, 42(6), March 2026. [ DOI | http | bib ] ( citation counts in OpenAlex 2 | Scopus 1 | Scholar 5 )
  3. Trong Duong, Matthias Möller, and Norbert Hosters. Quantum lattice Boltzmann with denoising collision operators, 2026. [ DOI | http | bib ] ( citation counts in OpenAlex 0 )
  4. Călin A. Georgescu and Matthias Möller. Efficient and expressive boundary conditions in quantum lattice Boltzmann methods, 2026. [ arXiv | http | bib ] 
  5. Zeynab Kaseb, Rahul Rane, Aleksandra Lekić, Matthias Möller, Amin Khodaei, Peter Palensky, and Pedro P. Vergara. Quantum hardware-in-the-loop for optimal power flow in renewable-integrated power systems. IEEE Transactions on Power Systems, page 1–11, 2026. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scopus 0 | Scholar 3 )
  6. Monica Lăcătuş, Matthias Möller, and Sauro Succi. Reduced basis algorithm for solving nonlinear differential equations on quantum computers, 2026. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scholar 0 )
  7. Swapan Madabhushi Venkata, Arne Wulff, Boyang Chen, Roeland De Breuker, Sebastian Feld, Matthias Möller, and Yinglu Tang. Determining feasibility bounds of lamination parameters using neural networks. In Heinz E. Pettermann, Clara Schuecker, and Martin Fagerström, editors, Composites 2025: Book of Abstracts: 10th ECCOMAS Thematic Conference on the Mechanical Response of Composites, page 95, 2026. One-page conference abstract. Conference held 9--11 September 2025 in Vienna; the TU Wien repository dates publication of the abstract book to 2026. Book DOI: 10.34726/11919. [ http | bib ] 
  8. Koen Mesman, Yinglu Tang, Matthias Moller, Boyang Chen, and Sebastian Feld. MOSAIQC: Mixed-topology-aware optimization for scalable approximate noise-informed quantum circuit cutting, 2026. [ DOI | http | bib ] ( citation counts in OpenAlex 0 )
  9. Arne Wulff, Swapan Madabhushi Venkata, Boyang Chen, Yinglu Tang, Matthias Möller, and Sebastian Feld. Quantum-assisted stacking sequence retrieval and laminated composite design. In Heinz E. Pettermann, Clara Schuecker, and Martin Fagerström, editors, Composites 2025: Book of Abstracts: 10th ECCOMAS Thematic Conference on the Mechanical Response of Composites, page 20, 2026. One-page conference abstract. Conference held 9--11 September 2025 in Vienna; the TU Wien repository dates publication of the abstract book to 2026. Book DOI: 10.34726/11919. [ http | bib ] 
  10. Stefan Berger, Norbert Hosters, and Matthias Möller. Trainable embedding quantum physics informed neural networks for solving nonlinear PDEs. Scientific Reports, 15(1), May 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 13 | Scopus 11 | Scholar 20 )
  11. Călin A. Georgescu and Matthias Möller. Quantum search in superposed quantum lattice gas automata and lattice Boltzmann systems, 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 0 )
  12. Călin A. Georgescu and Matthias Möller. A practical implementation of quantum lattice Boltzmann algorithms. Proceedings of the 35th Parallel CFD International Conference 2024 35th Parallel CFD International Conference 2024, ParCFD 2024:23--26 (2025). doi:10.34734/FZJ, 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 0 )
  13. Călin A. Georgescu, Merel A. Schalkers, and Matthias Möller. Fully quantum lattice gas automata building blocks for computational basis state encodings. Journal of Computational Physics, 549:114595, March 2026. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scopus 0 | Scholar 5 )
  14. Zeynab Kaseb, Matthias Möller, Markus Kirsch, Peter Palensky, and Pedro P. Vergara. Combinatorial power flow analysis using adiabatic quantum algorithms. In 2025 IEEE Kiel PowerTech, page 1–6. IEEE, 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scopus 0 | Scholar 2 )
  15. Zeynab Kaseb, Matthias Möller, Peter Palensky, and Pedro P. Vergara. Performance comparison of gate-based and adiabatic quantum computing for ac power flow problem, 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scholar 0 )
  16. Zeynab Kaseb, Matthias Möller, Pedro P. Vergara, and Peter Palensky. Quantum-enhanced power flow and optimal power flow based on combinatorial reformulation, 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 1 )
  17. Zeynab Kaseb, Matthias Moller, Lindsay Spoor, Jerry J. Guo, Yu Xiang, Peter Palensky, and Pedro P. Vergara. Quantum-enhanced reinforcement learning for accelerating Newton-Raphson convergence with Ising machines: A case study for power flow analysis, 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scholar 2 )
  18. Monica Lăcătuş and Matthias Möller. Surrogate quantum circuit design for the lattice Boltzmann collision operator. International Journal for Numerical Methods in Engineering, 127(4):e70286, 2026. [ DOI | arXiv | http | bib ] 
  19. Giorgio Tosti Balducci, Boyang Chen, Matthias Möller, and Roeland De Breuker. Solving 1d Poisson problem with a variational quantum linear solver, 2024. [ DOI | http | bib ] ( citation counts in OpenAlex 0 | Scholar 2 )
  20. Călin A. Georgescu, Merel A. Schalkers, and Matthias Möller. qlbm - a quantum lattice Boltzmann software framework. Computer Physics Communications, 315:109699, October 2025. [ DOI | http | bib ] ( citation counts in OpenAlex 3 | Scopus 5 | Scholar 10 )
  21. Zeynab Kaseb, Matthias Möller, Markus Kirsch, Peter Palensky, and Pedro P. Vergara. Adiabatic computing for power flow analysis. In 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), page 543–544. IEEE, 2024. [ DOI | http | bib ] ( citation counts in OpenAlex 1 | Scopus 1 | Scholar 1 )
  22. Zeynab Kaseb, Matthias Möller, Peter Palensky, and Pedro P. Vergara. A framework for solving continuous energy and power system problems using adiabatic quantum computing, 2025. [ DOI | arXiv | http | bib ] ( citation counts in OpenAlex 0 )
  23. Zeynab Kaseb, Matthias Möller, Pedro P. Vergara, and Peter Palensky. Adiabatic quantum power flow. May 2024. [ DOI | http | bib ] ( citation counts in OpenAlex 0 )
  24. Koen J. Mesman, Ward van der Schoot, Matthias Möller, and Niels M. P. Neumann. QuAS: Quantum application score for benchmarking the utility of quantum computers. In 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), page 921–929. IEEE, 2024. [ DOI | http | bib ] ( citation counts in OpenAlex 4 | Scopus 3 | Scholar 5 )
  25. 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 | bib ] ( citation counts in OpenAlex 2 | Scopus 1 | Scholar 2 )
  26. 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 | bib ] ( citation counts in OpenAlex 17 | Scopus 18 | Scholar 35 )
  27. 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 | bib ] ( citation counts in OpenAlex 20 | Scholar 31 )
  28. Merel A. Schalkers and Matthias Möller. Momentum exchange method for quantum Boltzmann methods. Computers and Fluids, 285:106453, December 2024. [ DOI | http | bib ] ( citation counts in OpenAlex 4 | Scopus 5 | Scholar 14 )
  29. 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 | bib ] ( citation counts in OpenAlex 14 | Scopus 12 | Scholar 18 )
  30. Arne Wulff, Swapan Madabhushi Venkata, Boyang Chen, Sebastian Feld, Matthias Möller, and Yinglu Tang. Quantum-assisted stacking sequence retrieval and laminated composite design, 2024. [ DOI | arXiv | http | bib ] ( citation counts in OpenAlex 0 | Scholar 0 )
  31. Tim Driebergen. QAOA mixing Hamiltonians for MinVertexCover, 2023. [ http | bib ] 
  32. 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 | bib ] ( citation counts in OpenAlex 42 | Scopus 36 | Scholar 45 )
  33. Huub Donkers. QPack: A cross-platform quantum benchmark-suite, 2022. [ http | bib ] 
  34. Huub Donkers, Koen Mesman, Zaid Al-Ars, and Matthias Möller. QPack scores: Quantitative performance metrics for application-oriented quantum computer benchmarking, 2022. [ DOI | arXiv | http | bib ] ( citation counts in OpenAlex 6 | Scholar 22 )
  35. 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 | bib ] ( citation counts in OpenAlex 16 | Scopus 20 | Scholar 14 )
  36. 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| bib ] 
  37. 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 | bib ] ( citation counts in OpenAlex 1 | Scopus 1 | Scholar 1 )
  38. Smaran Adarsh. Resource optimal executable quantum circuit generation using approximate computing, 2021. [ http | bib ] 
  39. 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 | http | bib ] ( citation counts in OpenAlex 4 | Scopus 4 | Scholar 2 )
  40. Giorgio Tosti Balducci, Boyang Chen, Matthias Möller, and Roeland De Breuker. Solving tridiagonal linear systems with a variational quantum algorithm, 2021| bib ] 
  41. Koen Mesman, Zaid Al-Ars, and Matthias Möller. QPack: Quantum approximate optimization algorithms as universal benchmark for quantum computers, 2021. [ DOI | arXiv | http | bib ] ( citation counts in OpenAlex 1 )
  42. Merel Schalkers. Learning based hardware-centric quantum circuit generation, 2021. [ http | bib ] 
  43. Sigurdur Ag. Sigurdsson. Implementations of quantum algorithms for solving linear systems, 2021. [ http | bib ] 
  44. Stan van der Linde. Quantum annealing for seismic imaging, 2021. [ http | bib ] 
  45. Joost C.P. Bus. The quantum approximate optimization algorithm: Performance on max-cut using heuristic parameter determination, 2020. [ http | bib ] 
  46. 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 | bib ] ( citation counts in OpenAlex 7 | Scopus 4 | Scholar 7 )
  47. Matthias Möller and Cornelis Vuik. A conceptual framework for quantum accelerated automated design optimization. Microprocessors and Microsystems, 66:67--71, apr 2019. [ DOI | http | bib ] ( citation counts in OpenAlex 8 | Scopus 9 | Scholar 9 )
  48. Tim Driebergen. Designing a quantum algorithm for real-valued addition using posit arithmetic, 2019. [ http | bib ] 
  49. Menno Looman. Implementation and analysis of an algorithm on positive integer addition for quantum computing, 2018. [ http | bib ] 
  50. Mike van der Lans. Quantum algorithms and their implementation on quantum computer simulators, 2018. [ http | bib ] 
  51. 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 | bib ] ( citation counts in OpenAlex 137 | Scopus 121 | Scholar 120 )