Citation

If you use this software in your research or publications, please cite the following

 @software{monaco_2026_18698922,
   author       = {Monaco, Saverio and
                   Slim, Jamal and
                   Krücker, Dirk and
                   Borras, Kerstin},
   title        = {Pauli-Propagator},
   month        = feb,
   year         = 2026,
   publisher    = {Zenodo},
   version      = {v2.0.0},
   doi          = {10.5281/zenodo.18698922},
   url          = {https://doi.org/10.5281/zenodo.18698922},
   swhid        = {swh:1:dir:026dd224bb89ab9621c3cd71e4b40b35893daec9
                    ;origin=https://doi.org/10.5281/zenodo.16028009;vi
                    sit=swh:1:snp:bd930acf4a272c46ad4c03fe5c2be479bf6f
                    a062;anchor=swh:1:rel:373751cc26e9c1690da10b184a2e
                    cc753ee21f1e;path=desyqml-Pauli-Propagator-a1192ad
                   },
 }

@article{monaco2025symbolicpaulipropagationgradientenabled,
  abstract = {Quantum Machine Learning models typically require expensive on-chip training procedures and often lack efficient gradient estimation methods. By employing Pauli propagation, it is possible to derive a symbolic representation of observables as analytic functions of a circuit's parameters. Although the number of terms in such functional representations grows rapidly with circuit depth, suitable choices of ansatz and controlled truncations on Pauli weights and frequency components yield accurate yet tractable estimators of the target},
  author = {Monaco, Saverio and Slim, Jamal and Rehm, Florian and Kr{\"u}cker, Dirk and Borras, Kerstin},
  journal = {arXiv preprint arXiv:2512.16674},
  pub_year = {2025},
  title = {Symbolic Pauli Propagation for Gradient-Enabled Pre-Training of Quantum Circuits},
  venue = {arXiv preprint arXiv …},
  url = {https://arxiv.org/abs/2512.16674},
}