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Learning symmetry-protected topological order from trapped-ion experiments

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Learning symmetry-protected topological order from trapped-ion experiments

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AbstractClassical machine learning has proven remarkably useful in post-processing quantum data, yet typical learning algorithms often require prior training to be effective. In this work, we employ a tensorial kernel support vector machine (TK-SVM) to analyze experimental data produced by trapped-ion quantum computers. This unsupervised method benefits from directly interpretable training parameters, allowing it to identify the non-trivial string-order characterizing symmetry-protected topological (SPT) phases. We apply our technique to two examples: a spin-1/2 model and a spin-1 model, featuring the cluster state and the AKLT state as paradigmatic instances of SPT order, respectively. Using matrix product states, we generate a family of quantum circuits that host a trivial phase and an SPT phase, with a sharp phase transition between them. For the spin-1 case, we implement these circuits on two distinct trapped-ion machines based on qubits and qutrits. Our results demonstrate that the TK-SVM method successfully distinguishes the two phases across all noisy experimental datasets, highlighting its robustness and effectiveness in quantum data interpretation.► BibTeX data@article{Sadoune2026learningsymmetry, doi = {10.22331/q-2026-05-12-2100}, url = {https://doi.org/10.22331/q-2026-05-12-2100}, title = {Learning symmetry-protected topological order from trapped-ion experiments}, author = {Sadoune, Nicolas and Pogorelov, Ivan and Edmunds, Claire L. and Giudici, Giuliano and Giudice, Giacomo and Marciniak, Christian D. and Ringbauer, Martin and Monz, Thomas and Pollet, Lode}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2100}, month = may, year = {2026} }► References [1] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2: 79, August 2018. ISSN 2521-327X. 10.22331/q-2018-08-06-79. 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[4] Jiaxin Huang, Yan Zhu, Giulio Chiribella, and Ya-Dong Wu, "Sequence-Model-Guided Measurement Selection for Quantum State Learning", arXiv:2507.09891, (2025). [5] C. L. Edmunds, E. Rico, I. Arrazola, G. K. Brennen, M. Meth, R. Blatt, and M. Ringbauer, "Symmetry-Protected Topological Haldane Phase on a Qudit Quantum Processor", PRX Quantum 6 2, 020349 (2025). The above citations are from SAO/NASA ADS (last updated successfully 2026-05-12 12:35:15). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-05-12 12:35:14: Could not fetch cited-by data for 10.22331/q-2026-05-12-2100 from Crossref. This is normal if the DOI was registered recently.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractClassical machine learning has proven remarkably useful in post-processing quantum data, yet typical learning algorithms often require prior training to be effective. In this work, we employ a tensorial kernel support vector machine (TK-SVM) to analyze experimental data produced by trapped-ion quantum computers. This unsupervised method benefits from directly interpretable training parameters, allowing it to identify the non-trivial string-order characterizing symmetry-protected topological (SPT) phases. We apply our technique to two examples: a spin-1/2 model and a spin-1 model, featuring the cluster state and the AKLT state as paradigmatic instances of SPT order, respectively. Using matrix product states, we generate a family of quantum circuits that host a trivial phase and an SPT phase, with a sharp phase transition between them. For the spin-1 case, we implement these circuits on two distinct trapped-ion machines based on qubits and qutrits. 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Learning symmetry-protected topological order from trapped-ion experiments

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