Classical simulation and quantum resource theory of non-Gaussian optics

Oliver Hahn; Ryuji Takagi; Giulia Ferrini; Hayata Yamasaki

doi:10.22331/q-2025-10-13-1881

Classical simulation and quantum resource theory of non-Gaussian optics

Oliver Hahn^1,2, Ryuji Takagi², Giulia Ferrini¹, and Hayata Yamasaki^3,4

¹Wallenberg Centre for Quantum Technology, Department of Microtechnology and Nanoscience, Chalmers University of Technology, Sweden , SE-412 96 Göteborg, Sweden
²Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902, Japan
³Department of Physics, Graduate School of Science, The University of Tokyo, 7–3–1 Hongo, Bunkyo-ku, Tokyo, 113–0033, Japan
⁴Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan

Published:	2025-10-13, volume 9, page 1881
Editor:	Christos Gagatsos
Eprint:	arXiv:2404.07115v5
Doi:	https://doi.org/10.22331/q-2025-10-13-1881
Citation:	Quantum 9, 1881 (2025).

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Updated after initial publication: This publication was updated to version v5 after the initial publication. The authors left the following comment on the arXiv:

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Abstract

We propose efficient algorithms for classically simulating Gaussian unitaries and measurements applied to non-Gaussian initial states. The constructions are based on decomposing the non-Gaussian states into linear combinations of Gaussian states. We use an extension of the covariance matrix formalism to efficiently track relative phases in the superpositions of Gaussian states. We get an exact simulation algorithm, which costs quadratically with the number of Gaussian states required to represent the initial state, and an approximate simulation algorithm, which costs linearly with the $l_1$ norm of the coefficients associated with the superposition. We define measures of non-Gaussianity quantifying this simulation cost, which we call the Gaussian rank and the Gaussian extent. From the perspective of quantum resource theories, we investigate the properties of this type of non-Gaussianity measure and compute optimal decompositions for states relevant to continuous-variable quantum computing.

► BibTeX data

@article{Hahn2025classicalsimulation,
  doi = {10.22331/q-2025-10-13-1881},
  url = {https://doi.org/10.22331/q-2025-10-13-1881},
  title = {Classical simulation and quantum resource theory of non-{G}aussian optics},
  author = {Hahn, Oliver and Takagi, Ryuji and Ferrini, Giulia and Yamasaki, Hayata},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1881},
  month = oct,
  year = {2025}
}

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