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The research addresses the critical challenge of computational efficiency and resource constraints in analyzing data from the upcoming High Luminosity Large Hadron Collider, presenting the architecture as a potential solution. In particular, we evaluate our method by applying the model to multi-detector jet images from CMS Open Data. The goal is to distinguish quark-initiated from gluon-initiated jets. We successfully train the quantum model and evaluate it via numerical simulations. Using this approach, we achieve classification performance almost on par with the one obtained with the completely classical architecture, considering a similar number of parameters.<\/jats:p>","DOI":"10.3390\/axioms13050323","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T15:18:17Z","timestamp":1715613497000},"page":"323","source":"Crossref","is-referenced-by-count":0,"title":["Quantum Vision Transformers for Quark\u2013Gluon Classification"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"http:\/\/orcid.org\/0009-0001-2626-3752","authenticated-orcid":false,"given":"Mar\u00e7al","family":"Comajoan Cara","sequence":"first","affiliation":[{"name":"Department of Signal Theory and Communications, Polytechnic University of Catalonia, 08034 Barcelona, Spain"}]},{"ORCID":"http:\/\/orcid.org\/0009-0005-8116-1950","authenticated-orcid":false,"given":"Gopal Ramesh","family":"Dahale","sequence":"additional","affiliation":[{"name":"Indian Institute of Technology Bhilai, Bhilai 491001, Chhattisgarh, India"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-1000-3454","authenticated-orcid":false,"given":"Zhongtian","family":"Dong","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0355-2076","authenticated-orcid":false,"given":"Roy T.","family":"Forestano","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-6222-8102","authenticated-orcid":false,"given":"Sergei","family":"Gleyzer","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35401, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5450-2207","authenticated-orcid":false,"given":"Daniel","family":"Justice","sequence":"additional","affiliation":[{"name":"Software Engineering Institute, Carnegie Mellon University, Pittsburgh, PA 15213, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-4515-7303","authenticated-orcid":false,"given":"Kyoungchul","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-3890-0066","authenticated-orcid":false,"given":"Tom","family":"Magorsch","sequence":"additional","affiliation":[{"name":"Physik-Department, Technische Universit\u00e4t M\u00fcnchen, 85748 Garching, Germany"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-4182-9096","authenticated-orcid":false,"given":"Konstantin T.","family":"Matchev","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-3074-998X","authenticated-orcid":false,"given":"Katia","family":"Matcheva","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-6683-6463","authenticated-orcid":false,"given":"Eyup B.","family":"Unlu","sequence":"additional","affiliation":[{"name":"Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,13]]},"reference":[{"key":"ref_1","unstructured":"CERN (2023, September 24). The HL-LHC Project. Available online: https:\/\/hilumilhc.web.cern.ch\/content\/hl-lhc-project."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"HSF Physics Event Generator WG, Valassi, A., Yazgan, E., McFayden, J., Amoroso, S., Bendavid, J., Buckley, A., Cacciari, M., Childers, T., and Ciulli, V. (2021). Challenges in Monte Carlo Event Generator Software for High-Luminosity LHC. Comput. Softw. Big Sci., 5, 12.","DOI":"10.1007\/s41781-021-00055-1"},{"key":"ref_3","unstructured":"Arunachalam, S., and de Wolf, R. (2017). A Survey of Quantum Learning Theory. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/nature23474","article-title":"Quantum machine learning","volume":"549","author":"Biamonte","year":"2017","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"040504","DOI":"10.1103\/PhysRevLett.122.040504","article-title":"Quantum Machine Learning in Feature Hilbert Spaces","volume":"122","author":"Schuld","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10002","DOI":"10.1209\/0295-5075\/134\/10002","article-title":"Quantum computing models for artificial neural networks","volume":"134","author":"Mangini","year":"2021","journal-title":"Europhys. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1038\/s41567-021-01287-z","article-title":"A rigorous and robust quantum speed-up in supervised machine learning","volume":"17","author":"Liu","year":"2021","journal-title":"Nat. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1126\/science.abn7293","article-title":"Quantum advantage in learning from experiments","volume":"376","author":"Huang","year":"2022","journal-title":"Science"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4919","DOI":"10.1038\/s41467-022-32550-3","article-title":"Generalization in quantum machine learning from few training data","volume":"13","author":"Caro","year":"2022","journal-title":"Nat. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Dong, Z., Comajoan Cara, M., Dahale, G.R., Forestano, R.T., Gleyzer, S., Justice, D., Kong, K., Magorsch, T., Matchev, K.T., and Matcheva, K. (2024). Z2 \u00d7 Z2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks. Axioms, 13.","DOI":"10.3390\/axioms13030188"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Forestano, R.T., Comajoan Cara, M., Dahale, G.R., Dong, Z., Gleyzer, S., Justice, D., Kong, K., Magorsch, T., Matchev, K.T., and Matcheva, K. (2024). A Comparison between Invariant and Equivariant Classical and Quantum Graph Neural Networks. Axioms, 13.","DOI":"10.3390\/axioms13030160"},{"key":"ref_12","unstructured":"Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., and Gelly, S. (2021, January 3\u20137). An Image is Worth 16 \u00d7 16 Words: Transformers for Image Recognition at Scale. Proceedings of the International Conference on Learning Representations, Online."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Di Sipio, R., Huang, J.H., Chen, S.Y.C., Mangini, S., and Worring, M. (2022, January 23\u201327). The Dawn of Quantum Natural Language Processing. Proceedings of the ICASSP 2022\u20142022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Singapore.","DOI":"10.1109\/ICASSP43922.2022.9747675"},{"key":"ref_14","unstructured":"Guyon, I., Luxburg, U.V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., and Garnett, R. (2017, January 4\u20139). Attention is All you Need. Proceedings of the Advances in Neural Information Processing Systems, Long Beach, CA, USA."},{"key":"ref_15","unstructured":"Li, G., Zhao, X., and Wang, X. (2022). Quantum Self-Attention Neural Networks for Text Classification. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.22331\/q-2024-02-22-1265","article-title":"Quantum Vision Transformers","volume":"8","author":"Cherrat","year":"2024","journal-title":"Quantum"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Unlu, E.B., Comajoan Cara, M., Dahale, G.R., Dong, Z., Forestano, R.T., Gleyzer, S., Justice, D., Kong, K., Magorsch, T., and Matchev, K.T. (2024). Hybrid Quantum Vision Transformers for Event Classification in High Energy Physics. Axioms, 13.","DOI":"10.3390\/axioms13030187"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kollias, G., Kalantzis, V., Salonidis, T., and Ubaru, S. (2023, January 4\u201310). Quantum Graph Transformers. Proceedings of the ICASSP 2023\u20142023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Rhodes Island, Greece.","DOI":"10.1109\/ICASSP49357.2023.10096345"},{"key":"ref_19","unstructured":"CERN (2023, September 24). CMS Open Data. Available online: http:\/\/opendata.cern.ch\/docs\/about-cms."},{"key":"ref_20","unstructured":"The ATLAS Collaboration (2017). Quark versus Gluon Jet Tagging Using Jet Images with the ATLAS Detector, CERN. Available online: https:\/\/cds.cern.ch\/record\/2275641."},{"key":"ref_21","unstructured":"The CMS Collaboration (2024, May 08). New Developments for Jet Substructure Reconstruction in CMS. Available online: https:\/\/cds.cern.ch\/record\/2275226."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s41781-018-0007-y","article-title":"Recursive Neural Networks in Quark\/Gluon Tagging","volume":"2","author":"Cheng","year":"2018","journal-title":"Comput. Softw. Big Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/JHEP01(2019)057","article-title":"QCD-aware recursive neural networks for jet physics","volume":"2019","author":"Louppe","year":"2019","journal-title":"J. High Energy Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"164304","DOI":"10.1016\/j.nima.2020.164304","article-title":"End-to-end jet classification of quarks and gluons with the CMS Open Data","volume":"977","author":"Andrews","year":"2020","journal-title":"Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_26","unstructured":"Bishop, C.M., and Bishop, H. (2023). Deep Learning, Springer. [1st ed.]."},{"key":"ref_27","unstructured":"Schmidhuber, J. (2022). Annotated History of Modern AI and Deep Learning. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1109\/TSSC.1969.300225","article-title":"Visual Feature Extraction by a Multilayered Network of Analog Threshold Elements","volume":"5","author":"Fukushima","year":"1969","journal-title":"IEEE Trans. Syst. Sci. Cybern."},{"key":"ref_29","unstructured":"Glorot, X., Bordes, A., and Bengio, Y. (2011, January 11\u201313). Deep sparse rectifier neural networks. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics. JMLR Workshop and Conference Proceedings, Fort Lauderdale, FL, USA."},{"key":"ref_30","unstructured":"Hendrycks, D., and Gimpel, K. (2016). Gaussian Error Linear Units (GELUs). arXiv."},{"key":"ref_31","unstructured":"Ba, J.L., Kiros, J.R., and Hinton, G.E. (2016). Layer normalization. arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2015). Deep Residual Learning for Image Recognition. arXiv.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_33","unstructured":"Beyer, L., Zhai, X., and Kolesnikov, A. (2022). Better plain ViT baselines for ImageNet-1k. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"130503","DOI":"10.1103\/PhysRevLett.113.130503","article-title":"Quantum Support Vector Machine for Big Data Classification","volume":"113","author":"Rebentrost","year":"2014","journal-title":"Phys. Rev. Lett."},{"key":"ref_35","first-page":"316","article-title":"Quantum Algorithms for Nearest-Neighbor Methods for Supervised and Unsupervised Learning","volume":"15","author":"Wiebe","year":"2015","journal-title":"Quantum Inf. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1038\/s41534-021-00456-5","article-title":"Nearest centroid classification on a trapped ion quantum computer","volume":"7","author":"Johri","year":"2021","journal-title":"npj Quantum Inf."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"045004","DOI":"10.1103\/RevModPhys.95.045004","article-title":"Kinematic variables and feature engineering for particle phenomenology","volume":"95","author":"Franceschini","year":"2023","journal-title":"Rev. Mod. Phys."},{"key":"ref_38","unstructured":"Ellis, R.K., Stirling, W.J., and Webber, B.R. (2011). QCD and Collider Physics, Cambridge University Press."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1140\/epjc\/s10052-010-1314-6","article-title":"Towards Jetography","volume":"67","author":"Salam","year":"2010","journal-title":"Eur. Phys. J. C"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2019.11.001","article-title":"Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning","volume":"841","author":"Larkoski","year":"2020","journal-title":"Phys. Rept."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"045003","DOI":"10.1103\/RevModPhys.91.045003","article-title":"Jet Substructure at the Large Hadron Collider: Experimental Review","volume":"91","author":"Kogler","year":"2019","journal-title":"Rev. Mod. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Marzani, S., Soyez, G., and Spannowsky, M. (2019). Looking Inside Jets: An Introduction to Jet Substructure and Boosted-Object Phenomenology, Springer.","DOI":"10.1007\/978-3-030-15709-8"},{"key":"ref_43","unstructured":"Feickert, M., and Nachman, B. (2021). A Living Review of Machine Learning for Particle Physics. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1146\/annurev-nucl-101917-021019","article-title":"Deep Learning and its Application to LHC Physics","volume":"68","author":"Guest","year":"2018","journal-title":"Ann. Rev. Nucl. Part. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"022008","DOI":"10.1088\/1742-6596\/1085\/2\/022008","article-title":"Machine Learning in High Energy Physics Community White Paper","volume":"1085","author":"Albertsson","year":"2018","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1038\/s41586-018-0361-2","article-title":"Machine learning at the energy and intensity frontiers of particle physics","volume":"560","author":"Radovic","year":"2018","journal-title":"Nature"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"045002","DOI":"10.1103\/RevModPhys.91.045002","article-title":"Machine learning and the physical sciences","volume":"91","author":"Carleo","year":"2019","journal-title":"Rev. Mod. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1930019","DOI":"10.1142\/S0217751X19300199","article-title":"Machine and Deep Learning Applications in Particle Physics","volume":"34","author":"Bourilkov","year":"2020","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Schwartz, M.D. (2021). Modern Machine Learning and Particle Physics. arXiv.","DOI":"10.1162\/99608f92.beeb1183"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Karagiorgi, G., Kasieczka, G., Kravitz, S., Nachman, B., and Shih, D. (2021). Machine Learning in the Search for New Fundamental Physics. arXiv.","DOI":"10.1038\/s42254-022-00455-1"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"031003","DOI":"10.1103\/RevModPhys.94.031003","article-title":"Colloquium: Machine learning in nuclear physics","volume":"94","author":"Boehnlein","year":"2022","journal-title":"Rev. Mod. Phys."},{"key":"ref_52","unstructured":"Shanahan, P., Terao, K., and Whiteson, D. (2022). Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning. arXiv."},{"key":"ref_53","first-page":"S08004","article-title":"The CMS Experiment at the CERN LHC","volume":"3","author":"Collaboration","year":"2008","journal-title":"JINST"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"CMS Collaboration (2014). Description and performance of track and primary-vertex reconstruction with the CMS tracker. JINST, 9, P10009.","DOI":"10.1088\/1748-0221\/9\/10\/P10009"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"CMS Collaboration (2013). Energy Calibration and Resolution of the CMS Electromagnetic Calorimeter in pp Collisions at \t\t\t\n\t\t s = 7 TeV. JINST, 8, P09009.","DOI":"10.1088\/1748-0221\/8\/09\/P09009"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1140\/epjc\/s10052-008-0573-y","article-title":"Design, performance, and calibration of CMS hadron-barrel calorimeter wedges","volume":"55","author":"Abdullin","year":"2008","journal-title":"Eur. Phys. J. C"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1140\/epjc\/s10052-008-0756-6","article-title":"Design, performance, and calibration of the CMS Hadron-outer calorimeter","volume":"57","author":"Abdullin","year":"2008","journal-title":"Eur. Phys. J. C"},{"key":"ref_58","unstructured":"(2024, March 06). CMS Coordinate System. Available online: https:\/\/tikz.net\/axis3d_cms\/."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Herrmann, N., Arya, D., Doherty, M.W., Mingare, A., Pillay, J.C., Preis, F., and Prestel, S. (2023, January 2\u20138). Quantum utility\u2014Definition and assessment of a practical quantum advantage. Proceedings of the 2023 IEEE International Conference on Quantum Software, Chicago, IL, USA.","DOI":"10.1109\/QSW59989.2023.00028"},{"key":"ref_60","unstructured":"Loshchilov, I., and Hutter, F. (2019). Decoupled Weight Decay Regularization. arXiv."},{"key":"ref_61","unstructured":"Loshchilov, I., and Hutter, F. (2017). SGDR: Stochastic Gradient Descent with Warm Restarts. arXiv."},{"key":"ref_62","unstructured":"Bradbury, J., Frostig, R., Hawkins, P., Johnson, M.J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., and Wanderman-Milne, S. (2023, September 24). JAX: Composable Transformations of Python+NumPy Programs. Available online: http:\/\/github.com\/google\/jax."},{"key":"ref_63","unstructured":"Heek, J., Levskaya, A., Oliver, A., Ritter, M., Rondepierre, B., Steiner, A., and van Zee, M. (2023, September 24). Flax: A Neural Network Library and Ecosystem for JAX. Available online: http:\/\/github.com\/google\/flax."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"912","DOI":"10.22331\/q-2023-02-02-912","article-title":"TensorCircuit: A Quantum Software Framework for the NISQ Era","volume":"7","author":"Zhang","year":"2023","journal-title":"Quantum"},{"key":"ref_65","unstructured":"Steiner, A., Kolesnikov, A., Zhai, X., Wightman, R., Uszkoreit, J., and Beyer, L. (2022). How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers. arXiv."},{"key":"ref_66","first-page":"18613","article-title":"RandAugment: Practical Automated Data Augmentation with a Reduced Search Space","volume":"Volume 33","author":"Larochelle","year":"2020","journal-title":"Proceedings of the Advances in Neural Information Processing Systems"},{"key":"ref_67","unstructured":"Zhang, H., Cisse, M., Dauphin, Y.N., and Lopez-Paz, D. (May, January 30). mixup: Beyond Empirical Risk Minimization. Proceedings of the International Conference on Learning Representations, Vancouver, BC, Canada."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"226","DOI":"10.22331\/q-2020-02-06-226","article-title":"Data re-uploading for a universal quantum classifier","volume":"4","author":"Latorre","year":"2020","journal-title":"Quantum"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"055018","DOI":"10.1103\/PhysRevD.107.055018","article-title":"Is the machine smarter than the theorist: Deriving formulas for particle kinematics with symbolic regression","volume":"107","author":"Dong","year":"2023","journal-title":"Phys. Rev. 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