Quantum Algorithms for Optimization ongoing

💬 Talks and posters

Conference and workshop talks

Research seminar talks

📝 Publications and preprints

1. Gelß, P., Issagali, A., and Kornhuber, R. (2024). Fredholm Integral Equations for Function Approximation and the Training of Neural Networks. SIAM Journal on Mathematics of Data Science. DOI: 10.1137/23M156642X [URL] [arXiv]
   [BibTeX]

   @article{2023_GelssIssagaliKornhuber_Fredholmneuralnetworks,
     year = {2024},
     journal = {SIAM Journal on Mathematics of Data Science},
     doi = {10.1137/23M156642X},
     url = {https://epubs.siam.org/doi/abs/10.1137/23M156642X},
     archiveprefix = {arXiv},
     eprint = {2303.05262},
     primaryclass = {math.NA},
     author = {Gelß, Patrick and Issagali, Aizhan and Kornhuber, Ralf},
     title = {Fredholm Integral Equations for Function Approximation and the Training of Neural Networks}
   }

2. Stengl, S.-M., Gelß, P., Klus, S., and Pokutta, S. (2024). Existence and Uniqueness of Solutions of the Koopman–von Neumann Equation on Bounded Domains. Journal of Physics A: Mathematical and Theoretical. DOI: 10.1088/1751-8121/ad6f7d [URL] [arXiv]
   [BibTeX]

   @article{2023_StenglGelssKlusPokutta_Koopmanvonneumann,
     year = {2024},
     journal = {Journal of Physics A: Mathematical and Theoretical},
     doi = {10.1088/1751-8121/ad6f7d},
     url = {https://iopscience.iop.org/article/10.1088/1751-8121/ad6f7d},
     archiveprefix = {arXiv},
     eprint = {2306.13504},
     primaryclass = {math.AP},
     author = {Stengl, Steven-Marian and Gelß, Patrick and Klus, Stefan and Pokutta, Sebastian},
     title = {Existence and Uniqueness of Solutions of the Koopman--von Neumann Equation on Bounded Domains}
   }

3. Stengl, S.-M. (2024). An Alternative Formulation of the Quantum Phase Estimation Using Projection-based Tensor Decompositions. Quantum Information Processing, 23. DOI: 10.1007/s11128-024-04347-4 [URL] [arXiv]
   [BibTeX]

   @article{2023_Stengl_Quantumphaseestimation,
     year = {2024},
     journal = {Quantum Information Processing},
     volume = {23},
     doi = {10.1007/s11128-024-04347-4},
     url = {https://link.springer.com/article/10.1007/s11128-024-04347-4},
     archiveprefix = {arXiv},
     eprint = {2303.05894},
     primaryclass = {quant-ph},
     author = {Stengl, Steven-Marian},
     title = {An Alternative Formulation of the Quantum Phase Estimation Using Projection-based Tensor Decompositions}
   }

4. Designolle, S., Iommazzo, G., Besançon, M., Knebel, S., Gelß, P., and Pokutta, S. (2023). Improved Local Models and New Bell Inequalities Via Frank-Wolfe Algorithms. Physical Review Research, 5(4). DOI: 10.1103/PhysRevResearch.5.043059 [arXiv] [slides] [code]
   [BibTeX]

   @article{2023_DesignolleEtAl_LocalmodelsBellinequalities,
     year = {2023},
     journal = {Physical Review Research},
     month = oct,
     volume = {5},
     number = {4},
     doi = {10.1103/PhysRevResearch.5.043059},
     archiveprefix = {arXiv},
     eprint = {2302.04721},
     primaryclass = {quant-ph},
     author = {Designolle, Sébastien and Iommazzo, Gabriele and Besançon, Mathieu and Knebel, Sebastian and Gelß, Patrick and Pokutta, Sebastian},
     title = {Improved Local Models and New Bell Inequalities Via Frank-Wolfe Algorithms},
     code = {https://github.com/ZIB-IOL/BellPolytopes.jl},
     slides = {https://www.pokutta.com/slides/20230808-tokyo-bell.pdf}
   }

5. Gelß, P., Klein, R., Matera, S., and Schmidt, B. (2023). Quantum Dynamics of Coupled Excitons and Phonons in Chain-like Systems: Tensor Train Approaches and Higher-order Propagators. [arXiv]
   [BibTeX]

   @misc{2023_GelssKleinMateraSchmidt_QuantumdynamicsTensortrain,
     archiveprefix = {arXiv},
     eprint = {2302.03568},
     primaryclass = {quant-ph},
     year = {2023},
     author = {Gelß, Patrick and Klein, Rupert and Matera, Sebastian and Schmidt, Burkhard},
     title = {Quantum Dynamics of Coupled Excitons and Phonons in Chain-like Systems: Tensor Train Approaches and Higher-order Propagators}
   }

6. Klus, S., and Gelß, P. (2023). Continuous Optimization Methods for the Graph Isomorphism Problem. [arXiv]
   [BibTeX]

   @misc{2023_KlusGelss_Continuousgraphisomorphism,
     archiveprefix = {arXiv},
     eprint = {2311.16912},
     primaryclass = {cs.DM},
     year = {2023},
     author = {Klus, Stefan and Gelß, Patrick},
     title = {Continuous Optimization Methods for the Graph Isomorphism Problem}
   }

7. Riedel, J., Gelß, P., Klein, R., and Schmidt, B. (2023). WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-like Systems Based on Tensor Trains. The Journal of Chemical Physics, 158(16), 164801. DOI: 10.1063/5.0147314 [URL] [arXiv]
   [BibTeX]

   @article{2023_RiedelGelssKleinSchmidt_Wavetrain,
     year = {2023},
     journal = {The Journal of Chemical Physics},
     volume = {158},
     number = {16},
     pages = {164801},
     doi = {10.1063/5.0147314},
     url = {https://pubs.aip.org/aip/jcp/article/158/16/164801/2887212/WaveTrain-A-Python-package-for-numerical-quantum},
     archiveprefix = {arXiv},
     eprint = {2302.03725},
     primaryclass = {quant-ph},
     author = {Riedel, Jerome and Gelß, Patrick and Klein, Rupert and Schmidt, Burkhard},
     title = {WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-like Systems Based on Tensor Trains}
   }

8. Gelß, P., Klein, R., Matera, S., and Schmidt, B. (2022). Solving the Time-independent Schrödinger Equation for Chains of Coupled Excitons and Phonons Using Tensor Trains. The Journal of Chemical Physics, 156, 024109. DOI: 10.1063/5.0074948 [URL] [arXiv]
   [BibTeX]

   @article{2021_GelssKleinMateraSchmidt_Tensortrainschrdinger,
     year = {2022},
     journal = {The Journal of Chemical Physics},
     volume = {156},
     pages = {024109},
     doi = {10.1063/5.0074948},
     url = {https://pubs.aip.org/aip/jcp/article/156/2/024109/2839835/Solving-the-time-independent-Schrodinger-equation},
     archiveprefix = {arXiv},
     eprint = {2109.15104},
     primaryclass = {physics.comp-ph},
     author = {Gelß, Patrick and Klein, Rupert and Matera, Sebastian and Schmidt, Burkhard},
     title = {Solving the Time-independent Schrödinger Equation for Chains of Coupled Excitons and Phonons Using Tensor Trains}
   }

9. Gelß, P., Klus, S., Knebel, S., Shakibaei, Z., and Pokutta, S. (2022). Low-rank Tensor Decompositions of Quantum Circuits. [arXiv]
   [BibTeX]

   @misc{2022_GelssKlusShakibaeiPokutta_Lowranktensordecompositions,
     archiveprefix = {arXiv},
     eprint = {2205.09882},
     primaryclass = {quant-ph},
     year = {2022},
     author = {Gelß, Patrick and Klus, Stefan and Knebel, Sebastian and Shakibaei, Zarin and Pokutta, Sebastian},
     title = {Low-rank Tensor Decompositions of Quantum Circuits}
   }