Transforming graph states via Bell state measurements

Matthias C. Löbl; Love A. Pettersson; Stefano Paesani; Anders S. Sørensen

doi:10.22331/q-2025-07-14-1795

Transforming graph states via Bell state measurements

Matthias C. Löbl¹, Love A. Pettersson¹, Stefano Paesani^1,2, and Anders S. Sørensen¹

¹Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
²NNF Quantum Computing Programme, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark.

Published:	2025-07-14, volume 9, page 1795
Editor:	Anna Pappa
Eprint:	arXiv:2405.02414v2
Doi:	https://doi.org/10.22331/q-2025-07-14-1795
Citation:	Quantum 9, 1795 (2025).

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Abstract

Graph states are key resources for measurement-based quantum computing, which is particularly promising for photonic systems. Fusions are probabilistic Bell state measurements, measuring pairs of parity operators of two qubits. Fusions can be used to connect/entangle different graph states, making them a powerful resource for measurement-based and related fusion-based quantum computing. There are several different graph structures and types of Bell state measurements, yet the associated graph transformations have only been analyzed for specific cases. Here, we provide a full set of graph transformation rules and give an intuitive visualization based on Venn diagrams of local neighborhoods of graph nodes. We derive these graph transformations for all types of rotated type-II fusion, showing that there are five different fusion success cases. Finally, we give application examples of the derived graph transformation rules and show that they can be used to construct graph codes or simulate fusion networks.

► BibTeX data

@article{Lobl2025transforminggraph,
  doi = {10.22331/q-2025-07-14-1795},
  url = {https://doi.org/10.22331/q-2025-07-14-1795},
  title = {Transforming graph states via {B}ell state measurements},
  author = {L{\"{o}}bl, Matthias C. and Pettersson, Love A. and Paesani, Stefano and S{\o{}}rensen, Anders S.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1795},
  month = jul,
  year = {2025}
}

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Cited by

[1] Susan X. Chen, Matthias C. Löbl, Ming Lai Chan, Anders S. Sørensen, and Stefano Paesani, "Fusion-based implementation of qLDPC codes with quantum emitters", npj Quantum Information 12 1, 90 (2026).

[2] Love Pettersson and Anders S. Sørensen, "Long-distance quantum communication using concatenated ring graph codes", Physical Review Applied 24 4, 044090 (2025).

[3] Love A. Pettersson, Anders S. Sørensen, and Stefano Paesani, "Deterministic Generation of Concatenated Graph Codes from Quantum Emitters", PRX Quantum 6 1, 010305 (2025).

[4] Matthias C. Löbl, Love A. Pettersson, Andrew Jena, Luca Dellantonio, Stefano Paesani, and Anders S. Sørensen, "Generating graph states with a single quantum emitter and the minimum number of fusions", Physical Review A 111 5, 052604 (2025).

[5] Giovanni de Felice, Boldizsár Poór, Lia Yeh, and William Cashman, "Fusion and flow: formal protocols to reliably build photonic graph states", arXiv:2409.13541, (2024).

[6] Korbinian Staudacher, Bhilahari Jeevanesan, and Tobias Guggemos, "Adaptive Framework for Failure-Aware Protocols in Fusion-Based Graph-State Generation", arXiv:2601.02087, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-18 01:54:03) and SAO/NASA ADS (last updated successfully 2026-08-18 01:54:09). The list may be incomplete as not all publishers provide suitable and complete citation data.

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