Quantum Mathematics

📝 Publications and preprints

1. Designolle, S., Vértesi, T., and Pokutta, S. (2024). Symmetric Multipartite Bell Inequalities Via Frank-Wolfe Algorithms. Physics Review A. [arXiv]
   [BibTeX]

   @article{symmetricBell2023,
     year = {2024},
     journal = {Physics Review A},
     archiveprefix = {arXiv},
     eprint = {2310.20677},
     primaryclass = {quant-ph},
     author = {Designolle, Sébastien and Vértesi, Tamás and Pokutta, Sebastian},
     title = {Symmetric Multipartite Bell Inequalities Via Frank-Wolfe Algorithms}
   }

2. 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{dibkgp_bell_23,
     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}
   }

3. Gelß, P., Issagali, A., and Kornhuber, R. (2023). Fredholm Integral Equations for Function Approximation and the Training of Neural Networks. [arXiv]
   [BibTeX]

   @misc{gik_fredholm_23,
     archiveprefix = {arXiv},
     eprint = {2303.05262},
     primaryclass = {math.NA},
     year = {2023},
     author = {Gelß, Patrick and Issagali, Aizhan and Kornhuber, Ralf},
     title = {Fredholm Integral Equations for Function Approximation and the Training of Neural Networks}
   }

4. 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{gkms_tdse_23,
     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}
   }

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

   @misc{kg_graph_isomorphism,
     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}
   }

6. 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{rgks_wavetrain_23,
     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}
   }

7. Stengl, S.-M. (2023). An Alternative Formulation of the Quantum Phase Estimation Using Projection-based Tensor Decompositions. [arXiv]
   [BibTeX]

   @misc{stengl_qpe_23,
     archiveprefix = {arXiv},
     eprint = {2303.05894},
     primaryclass = {quant-ph},
     year = {2023},
     author = {Stengl, Steven-Marian},
     title = {An Alternative Formulation of the Quantum Phase Estimation Using Projection-based Tensor Decompositions}
   }

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{gkms_tise_22,
     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., Shakibaei, Z., and Pokutta, S. (2022). Low-rank Tensor Decompositions of Quantum Circuits. [arXiv]
   [BibTeX]

   @misc{gksp_lowrankqc_22,
     archiveprefix = {arXiv},
     eprint = {2205.09882},
     primaryclass = {quant-ph},
     year = {2022},
     author = {Gelß, Patrick and Klus, Stefan and Shakibaei, Zarin and Pokutta, Sebastian},
     title = {Low-rank Tensor Decompositions of Quantum Circuits}
   }

10. Gelß, P., Klus, S., Schuster, I., and Schütte, C. (2021). Feature Space Approximation for Kernel-based Supervised Learning. Knowledge-Based Systems, 221, 106935. DOI: 10.1016/j.knosys.2021.106935 [URL] [arXiv]
    [BibTeX]

    @article{gkss_fsa_21,
      year = {2021},
      journal = {Knowledge-Based Systems},
      volume = {221},
      pages = {106935},
      doi = {10.1016/j.knosys.2021.106935},
      url = {https://sciencedirect.com/science/article/abs/pii/S0950705121001982},
      archiveprefix = {arXiv},
      eprint = {2011.12651},
      primaryclass = {stat.ML},
      author = {Gelß, Patrick and Klus, Stefan and Schuster, Ingmar and Schütte, Christof},
      title = {Feature Space Approximation for Kernel-based Supervised Learning}
    }

11. Klus, S., Gelß, P., Nüske, F., and Noé, F. (2021). Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry. Machine Learning: Science and Technology, 2(4), 18958. DOI: 10.1088/2632-2153/ac14ad [URL] [arXiv]
    [BibTeX]

    @article{kgnn_antisymmetric_21,
      year = {2021},
      journal = {Machine Learning: Science and Technology},
      volume = {2},
      number = {4},
      pages = {18958},
      doi = {10.1088/2632-2153/ac14ad},
      url = {https://iopscience.iop.org/article/10.1088/2632-2153/ac14ad},
      archiveprefix = {arXiv},
      eprint = {2103.17233},
      primaryclass = {quant-ph},
      author = {Klus, Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank},
      title = {Symmetric and Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry}
    }

12. Nüske, F., Gelß, P., Klus, S., and Clementi, C. (2021). Tensor-based Computation of Metastable and Coherent Sets. Physica D: Nonlinear Phenomena, 427, 133018. DOI: 10.1016/j.physd.2021.133018 [URL] [arXiv]
    [BibTeX]

    @article{ngkc_metastable_2021,
      year = {2021},
      journal = {Physica D: Nonlinear Phenomena},
      volume = {427},
      pages = {133018},
      doi = {10.1016/j.physd.2021.133018},
      url = {https://sciencedirect.com/science/article/abs/pii/S0167278921001755},
      archiveprefix = {arXiv},
      eprint = {1908.04741},
      primaryclass = {math.NA},
      author = {Nüske, Feliks and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia},
      title = {Tensor-based Computation of Metastable and Coherent Sets}
    }