Graphical Framework for Non-Gaussian Quantum States

Lina Vandré; Boxuan Jing; Yu Xiang; Otfried Gühne; Qiongyi He

doi:10.22331/q-2025-07-23-1809

Graphical Framework for Non-Gaussian Quantum States

Lina Vandré^1,2,3, Boxuan Jing¹, Yu Xiang^1,4, Otfried Gühne², and Qiongyi He^1,5,6

¹State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics, Peking University, Beijing 100871, China
²Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
³Technische Universität Wien, Atominstitut, Vienna Center for Quantum Science and Technology, Stadionallee 2, 1020 Vienna, Austria
⁴Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
⁵Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
⁶Hefei National Laboratory, Hefei 230088, China

Published:	2025-07-23, volume 9, page 1809
Editor:	Christos Gagatsos
Eprint:	arXiv:2409.07300v3
Doi:	https://doi.org/10.22331/q-2025-07-23-1809
Citation:	Quantum 9, 1809 (2025).

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Abstract

We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered by their complex high-order correlations. The framework encapsulates transformation rules for a series of typical Gaussian unitary operation and local quadrature measurement, offering a visually intuitive tool for manipulating such states through experimentally feasible pathways. Notably, we develop methods for the generation of complex hypergraph states with more or higher-order hyperedges from simple structures through Gaussian operations only, facilitated by our graphical rules. We present illustrative examples on the preparation of non-Gaussian states rooted in these graph-based formalisms, revealing their potential to advance continuous-variable general quantum computing capabilities.

Popular summary

In this article, we introduce a graphical framework for analysing and manipulating non-Gaussian quantum states using hypergraphs. Non-Gaussian states are crucial for advancements in quantum computing, communication and metrology, yet their complex higher-order correlations pose significant challenges for characterisation and experimental implementation. Our proposed framework provides graphical transformation rules for typical Gaussian unitary operations and local quadrature measurements, making it easier to visualise and implement operations on these states.

► BibTeX data

@article{Vandre2025graphicalframework,
  doi = {10.22331/q-2025-07-23-1809},
  url = {https://doi.org/10.22331/q-2025-07-23-1809},
  title = {Graphical {F}ramework for {N}on-{G}aussian {Q}uantum {S}tates},
  author = {Vandr{\'{e}}, Lina and Jing, Boxuan and Xiang, Yu and G{\"{u}}hne, Otfried and He, Qiongyi},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1809},
  month = jul,
  year = {2025}
}

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[2] Davide Poderini, Dagmar Bruß, and Chiara Macchiavello, "Quantum hypergraph states: a review", Reports on Progress in Physics 89 6, 066001 (2026).

[3] Abhijith Ravikumar, Darren W. Moore, and Radim Filip, "Nonclassical nullifiers for quantum hypergraph states", Quantum 10, 2091 (2026).

[4] Huan Zhang, Ying Xia, Xiuxing Zhang, and Zeyang Liao, "Quantum Precision Measurement Based On Non-Gaussian Quantum States: An Introductory Review", Fluctuation and Noise Letters 25 02, 2540035 (2026).

[5] Eric Chitambar, Kenneth Goodenough, Otfried Gühne, Rose McCarty, Simon Perdrix, Vito Scarola, Shuo Sun, and Quntao Zhang, "Quantum Graph States: Bridging Classical Theory and Quantum Innovation, Workshop Summary", arXiv:2508.04823, (2025).

[6] Luca Ornigotti, Darren W. Moore, and Radim Filip, "Nonlinear stochastic and quantum motion from Coulomb forces", Communications Physics 8 1, 195 (2025).

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