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Nonclassical nullifiers for quantum hypergraph states

Quantum Science and Technology (arXiv overlay)

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Researchers Abhijith Ravikumar, Darren W. Moore, and Radim Filip introduced criteria for verifying quantum hypergraph states—generalized graph states enabling universal continuous-variable quantum computation with Gaussian measurements alone. The team established nonclassicality benchmarks using simultaneous nonlinear squeezing in hypergraph nullifiers, addressing a gap in experimental validation for these theoretically powerful but unobserved states. Their analysis evaluates robustness against thermal noise and photon loss, providing critical insights into scalability challenges for real-world quantum systems. Proposed proof-of-principle experiments offer practical pathways to observe hypergraph nonclassicality, leveraging existing continuous-variable platforms like optical frequency combs or trapped ions. This work bridges theory and experiment, advancing measurement-based quantum computation beyond pairwise interactions toward fault-tolerant, scalable architectures.

Nonclassical nullifiers for quantum hypergraph states

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AbstractQuantum hypergraph states form a generalisation of the graph state formalism that goes beyond the pairwise (dyadic) interactions imposed by remaining inside the Gaussian approximation. Networks of such states are able to achieve universality for continuous variable measurement based quantum computation with only Gaussian measurements. For normalised states, the simplest hypergraph states are formed from $k$-adic interactions among a collection of $k$ harmonic oscillator ground states. However such powerful resources have not yet been observed in experiments and their robustness and scalability have not been tested. Here we develop and analyse necessary criteria for hypergraph nonclassicality based on simultaneous nonlinear squeezing in the nullifiers of hypergraph states. We put forward an essential analysis of their robustness to realistic scenarios involving thermalisation or loss and suggest several basic proof-of-principle options for experiments to observe nonclassicality in hypergraph states.► BibTeX data@article{Ravikumar2026nonclassical, doi = {10.22331/q-2026-05-05-2091}, url = {https://doi.org/10.22331/q-2026-05-05-2091}, title = {Nonclassical nullifiers for quantum hypergraph states}, author = {Ravikumar, Abhijith and Moore, Darren W. and Filip, Radim}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2091}, month = may, year = {2026} }► References [1] Ri Qu, Juan Wang, Zong-shang Li, and Yan-ru Bao. ``Encoding hypergraphs into quantum states''. Physical Review A 87, 022311 (2013). https://doi.org/10.1103/PhysRevA.87.022311 [2] M. Rossi, M. Huber, D. Bruß, and C. Macchiavello. ``Quantum hypergraph states''. New Journal of Physics 15, 113022 (2013). https://doi.org/10.1088/1367-2630/15/11/113022 [3] Robert Raussendorf and Hans J. Briegel. ``A One-Way Quantum Computer''.

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Nonclassical nullifiers for quantum hypergraph states

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