Style-based quantum generative adversarial networks for Monte Carlo events

Carlos Bravo-Prieto1,2, Julien Baglio3, Marco Cè3, Anthony Francis3,4, Dorota M. Grabowska3, and Stefano Carrazza1,3,5

1Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE
2Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Barcelona, Spain.
3Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland.
4Institute of Physics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan.
5TIF Lab, Dipartimento di Fisica, Università degli Studi di Milano and INFN Sezione di Milano, Milan, Italy.

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We propose and assess an alternative quantum generator architecture in the context of generative adversarial learning for Monte Carlo event generation, used to simulate particle physics processes at the Large Hadron Collider (LHC). We validate this methodology by implementing the quantum network on artificial data generated from known underlying distributions. The network is then applied to Monte Carlo-generated datasets of specific LHC scattering processes. The new quantum generator architecture leads to a generalization of the state-of-the-art implementations, achieving smaller Kullback-Leibler divergences even with shallow-depth networks. Moreover, the quantum generator successfully learns the underlying distribution functions even if trained with small training sample sets; this is particularly interesting for data augmentation applications. We deploy this novel methodology on two different quantum hardware architectures, trapped-ion and superconducting technologies, to test its hardware-independent viability.

► BibTeX data

► References

[1] J. Preskill, Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[2] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, et al., Nature 574, 505 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[3] H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, et al., Science 370, 1460 (2020).
https:/​/​doi.org/​10.1126/​science.abe8770

[4] M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al., Nature Reviews Physics 3, 625–644 (2021).
https:/​/​doi.org/​10.1038/​s42254-021-00348-9

[5] K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru-Guzik, Reviews of Modern Physics 94, 015004 (2022).
https:/​/​doi.org/​10.1103/​RevModPhys.94.015004

[6] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Nature 549, 195 (2017).
https:/​/​doi.org/​10.1038/​nature23474

[7] M. Schuld and F. Petruccione, Supervised learning with quantum computers, Vol. 17 (Springer, 2018).
https:/​/​doi.org/​10.1007/​978-3-319-96424-9

[8] N. Wiebe, D. Braun, and S. Lloyd, Physical Review Letters 109, 050505 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.050505

[9] S. Lloyd, M. Mohseni, and P. Rebentrost, arXiv preprint arXiv:1307.0411 (2013).
https:/​/​doi.org/​10.48550/​arXiv.1307.0411
arXiv:1307.0411

[10] P. Rebentrost, M. Mohseni, and S. Lloyd, Physical Review Letters 113, 130503 (2014).
https:/​/​doi.org/​10.1103/​physrevlett.113.130503

[11] I. Kerenidis and A. Prakash, Physical Review A 101, 022316 (2020).
https:/​/​doi.org/​10.1103/​PhysRevA.101.022316

[12] A. W. Harrow, A. Hassidim, and S. Lloyd, Physical Review Letters 103, 150502 (2009).
https:/​/​doi.org/​10.1103/​PhysRevLett.103.150502

[13] M. Benedetti, E. Lloyd, S. Sack, and M. Fiorentini, Quantum Science and Technology 4, 043001 (2019a).
https:/​/​doi.org/​10.1088/​2058-9565/​ab4eb5

[14] S. Sim, P. D. Johnson, and A. Aspuru-Guzik, Advanced Quantum Technologies 2, 1900070 (2019).
https:/​/​doi.org/​10.1002/​qute.201900070

[15] C. Bravo-Prieto, J. Lumbreras-Zarapico, L. Tagliacozzo, and J. I. Latorre, Quantum 4, 272 (2020).
https:/​/​doi.org/​10.22331/​q-2020-05-28-272

[16] M. Larocca, N. Ju, D. García-Martín, P. J. Coles, and M. Cerezo, arXiv preprint arXiv:2109.11676 (2021).
https:/​/​doi.org/​10.48550/​arXiv.2109.11676
arXiv:2109.11676

[17] M. Schuld, R. Sweke, and J. J. Meyer, Physical Review A 103, 032430 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.103.032430

[18] T. Goto, Q. H. Tran, and K. Nakajima, Physical Review Letters 127, 090506 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.127.090506

[19] A. Pérez-Salinas, D. López-Núñez, A. García-Sáez, P. Forn-Díaz, and J. I. Latorre, Physical Review A 104, 012405 (2021).
https:/​/​doi.org/​10.1103/​PhysRevA.104.012405

[20] V. Havlíček, A. D. Córcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Nature 567, 209 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-0980-2

[21] M. Schuld, A. Bocharov, K. M. Svore, and N. Wiebe, Physical Review A 101, 032308 (2020).
https:/​/​doi.org/​10.1103/​physreva.101.032308

[22] A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, Quantum 4, 226 (2020).
https:/​/​doi.org/​10.22331/​q-2020-02-06-226

[23] T. Dutta, A. Pérez-Salinas, J. P. S. Cheng, J. I. Latorre, and M. Mukherjee, Physical Review A 106, 012411 (2022).
https:/​/​doi.org/​10.1103/​PhysRevA.106.012411

[24] J. Romero, J. P. Olson, and A. Aspuru-Guzik, Quantum Science and Technology 2, 045001 (2017).
https:/​/​doi.org/​10.1088/​2058-9565/​aa8072

[25] A. Pepper, N. Tischler, and G. J. Pryde, Physical Review Letters 122, 060501 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.122.060501

[26] C. Bravo-Prieto, Machine Learning: Science and Technology 2, 035028 (2021).
https:/​/​doi.org/​10.1088/​2632-2153/​ac0616

[27] C. Cao and X. Wang, Physical Review Applied 15, 054012 (2021).
https:/​/​doi.org/​10.1103/​PhysRevApplied.15.054012

[28] M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, npj Quantum Information 5, 1 (2019b).
https:/​/​doi.org/​10.1038/​s41534-019-0157-8

[29] K. E. Hamilton, E. F. Dumitrescu, and R. C. Pooser, Physical Review A 99, 062323 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.99.062323

[30] B. Coyle, D. Mills, V. Danos, and E. Kashefi, npj Quantum Information 6, 1 (2020).
https:/​/​doi.org/​10.1038/​s41534-020-00288-9

[31] P.-L. Dallaire-Demers and N. Killoran, Physical Review A 98, 012324 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.012324

[32] S. Lloyd and C. Weedbrook, Physical Review Letters 121, 040502 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.040502

[33] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, Communications of the ACM 63, 139–144 (2020).
https:/​/​doi.org/​10.1145/​3422622

[34] C. Zoufal, A. Lucchi, and S. Woerner, npj Quantum Information 5, 1 (2019).
https:/​/​doi.org/​10.1038/​s41534-019-0223-2

[35] J. Zeng, Y. Wu, J.-G. Liu, L. Wang, and J. Hu, Physical Review A 99, 052306 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.99.052306

[36] H. Situ, Z. He, Y. Wang, L. Li, and S. Zheng, Information Sciences 538, 193 (2020).
https:/​/​doi.org/​10.1016/​j.ins.2020.05.127

[37] L. Hu, S.-H. Wu, W. Cai, Y. Ma, X. Mu, Y. Xu, H. Wang, Y. Song, D.-L. Deng, C.-L. Zou, et al., Science advances 5, eaav2761 (2019).
https:/​/​doi.org/​10.1126/​sciadv.aav2761

[38] M. Benedetti, E. Grant, L. Wossnig, and S. Severini, New Journal of Physics 21, 043023 (2019c).
https:/​/​doi.org/​10.1088/​1367-2630/​ab14b5

[39] J. Romero and A. Aspuru-Guzik, Advanced Quantum Technologies 4, 2000003 (2021).
https:/​/​doi.org/​10.1002/​qute.202000003

[40] M. Y. Niu, A. Zlokapa, M. Broughton, S. Boixo, M. Mohseni, V. Smelyanskyi, and H. Neven, Physical Review Letters 128, 220505 (2022).
https:/​/​doi.org/​10.1103/​PhysRevLett.128.220505

[41] T. Karras, S. Laine, and T. Aila, IEEE Transactions on Pattern Analysis and Machine Intelligence 43, 4217 (2021).
https:/​/​doi.org/​10.1109/​TPAMI.2020.2970919

[42] A. Pérez-Salinas, J. Cruz-Martinez, A. A. Alhajri, and S. Carrazza, Physical Review D 103, 034027 (2021).
https:/​/​doi.org/​10.1103/​PhysRevD.103.034027

[43] W. Guan, G. Perdue, A. Pesah, M. Schuld, K. Terashi, S. Vallecorsa, and J.-R. Vlimant, Machine Learning: Science and Technology 2, 011003 (2021).
https:/​/​doi.org/​10.1088/​2632-2153/​abc17d

[44] S. Y. Chang, S. Vallecorsa, E. F. Combarro, and F. Carminati, arXiv preprint arXiv:2101.11132 (2021a).
https:/​/​doi.org/​10.48550/​arXiv.2101.11132
arXiv:2101.11132

[45] S. Y. Chang, S. Herbert, S. Vallecorsa, E. F. Combarro, and R. Duncan, EPJ Web of Conferences 251, 03050 (2021b).
https:/​/​doi.org/​10.1051/​epjconf/​202125103050

[46] V. Belis, S. González-Castillo, C. Reissel, S. Vallecorsa, E. F. Combarro, G. Dissertori, and F. Reiter, EPJ Web of Conferences 251, 03070 (2021).
https:/​/​doi.org/​10.1051/​epjconf/​202125103070

[47] G. R. Khattak, S. Vallecorsa, F. Carminati, and G. M. Khan, The European Physical Journal C 82, 1 (2022).
https:/​/​doi.org/​10.1140/​epjc/​s10052-022-10258-4

[48] P. Baldi, L. Blecher, A. Butter, J. Collado, J. N. Howard, F. Keilbach, T. Plehn, G. Kasieczka, and D. Whiteson, arXiv preprint arXiv:2012.11944 (2021).
https:/​/​doi.org/​10.48550/​arXiv.2012.11944
arXiv:2012.11944

[49] M. Backes, A. Butter, T. Plehn, and R. Winterhalder, SciPost Physics 10, 89 (2021).
https:/​/​doi.org/​10.21468/​SciPostPhys.10.4.089

[50] A. Butter and T. Plehn, in Artificial Intelligence For High Energy Physics (World Scientific, 2022) pp. 191–240.
https:/​/​doi.org/​10.1142/​9789811234033_0007

[51] A. Butter, S. Diefenbacher, G. Kasieczka, B. Nachman, and T. Plehn, SciPost Physics 10, 139 (2021).
https:/​/​doi.org/​10.21468/​SciPostPhys.10.6.139

[52] A. Butter, T. Plehn, and R. Winterhalder, SciPost Physics Core 3, 9 (2020).
https:/​/​doi.org/​10.21468/​SciPostPhysCore.3.2.009

[53] M. Bellagente, A. Butter, G. Kasieczka, T. Plehn, and R. Winterhalder, SciPost Physics 8, 70 (2020).
https:/​/​doi.org/​10.21468/​SciPostPhys.8.4.070

[54] A. Butter, T. Plehn, and R. Winterhalder, SciPost Physics 7, 75 (2019).
https:/​/​doi.org/​10.21468/​SciPostPhys.7.6.075

[55] S. Efthymiou, S. Ramos-Calderer, C. Bravo-Prieto, A. Pérez-Salinas, D. García-Martín, A. Garcia-Saez, J. I. Latorre, and S. Carrazza, Quantum Science and Technology 7, 015018 (2021a).
https:/​/​doi.org/​10.1088/​2058-9565/​ac39f5

[56] S. Efthymiou, S. Carrazza, S. Ramos, bpcarlos, AdrianPerezSalinas, D. García-Martín, Paul, J. Serrano, and atomicprinter, qiboteam/​qibo: Qibo 0.1.6-rc1 (2021b).
https:/​/​doi.org/​10.5281/​zenodo.5088103

[57] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, et al., TensorFlow: Large-scale machine learning on heterogeneous systems (2015), software available from tensorflow.org.
https:/​/​www.tensorflow.org/​

[58] afrancis heplat, C. Bravo-Prieto, S. Carrazza, M. Cè, J. Baglio, and d-m grabowska, Qti-th/​style-qgan: v1.0.0 (2021).
https:/​/​doi.org/​10.5281/​zenodo.5567077

[59] M. D. Zeiler, arXiv preprint arXiv:1212.5701 (2012).
https:/​/​doi.org/​10.48550/​arXiv.1212.5701
arXiv:1212.5701

[60] M. Ostaszewski, E. Grant, and M. Benedetti, Quantum 5, 391 (2021).
https:/​/​doi.org/​10.22331/​q-2021-01-28-391

[61] S. Kullback and R. A. Leibler, The Annals of Mathematical Statistics 22, 79 (1951).
https:/​/​doi.org/​10.1214/​aoms/​1177729694

[62] M. Frid-Adar, E. Klang, M. Amitai, J. Goldberger, and H. Greenspan, in 2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018) (2018) pp. 289–293.
https:/​/​doi.org/​10.1109/​ISBI.2018.8363576

[63] F. H. K. dos Santos Tanaka and C. Aranha, arXiv preprint arXiv:1904.09135 (2019).
https:/​/​doi.org/​10.48550/​arXiv.1904.09135
arXiv:1904.09135

[64] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, Journal of High Energy Physics 07, 079 (2014).
https:/​/​doi.org/​10.1007/​JHEP07(2014)079

[65] R. Frederix, S. Frixione, V. Hirschi, D. Pagani, H. S. Shao, and M. Zaro, Journal of High Energy Physics 07, 185 (2018).
https:/​/​doi.org/​10.1007/​JHEP07(2018)185

[66] I.-K. Yeo and R. A. Johnson, Biometrika 87, 954 (2000).
https:/​/​doi.org/​10.1093/​biomet/​87.4.954

[67] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Journal of Machine Learning Research 12, 2825–2830 (2011).
https:/​/​dl.acm.org/​doi/​10.5555/​1953048.2078195

[68] G. Aleksandrowicz, T. Alexander, P. Barkoutsos, L. Bello, Y. Ben-Haim, D. Bucher, F. J. Cabrera-Hernández, J. Carballo-Franquis, A. Chen, C.-F. Chen, et al., Qiskit: An Open-source Framework for Quantum Computing (2019).
https:/​/​doi.org/​10.5281/​zenodo.2562111

Cited by

[1] Mujahidul Islam, Serkan Turkeli, and Fatih Ozaydin, "Quantum generative adversarial networks: architectures, use cases, and real-world implementations", Quantum Information Processing 25 1, 11 (2026).

[2] Jack Y. Araz and Michael Spannowsky, "Quantum-probabilistic Hamiltonian learning for generative modeling and anomaly detection", Physical Review A 108 6, 062422 (2023).

[3] Giuliana Siddi Moreau, Lorenzo Pisani, Manuela Profir, Carlo Podda, Lidia Leoni, and Giacomo Cao, "Quantum Artificial Intelligence Scalability in the NISQ Era: Pathways to Quantum Utility", Advanced Quantum Technologies 8 10, 2400716 (2025).

[4] Stavros Efthymiou, Alvaro Orgaz-Fuertes, Rodolfo Carobene, Juan Cereijo, Andrea Pasquale, Sergi Ramos-Calderer, Simone Bordoni, David Fuentes-Ruiz, Alessandro Candido, Edoardo Pedicillo, Matteo Robbiati, Yuanzheng Paul Tan, Jadwiga Wilkens, Ingo Roth, José Ignacio Latorre, and Stefano Carrazza, "Qibolab: an open-source hybrid quantum operating system", Quantum 8, 1247 (2024).

[5] Andrea Delgado and Kathleen E. Hamilton, "Unsupervised quantum circuit learning in high energy physics", Physical Review D 106 9, 096006 (2022).

[6] Sulaiman Alvi, Christian W. Bauer, and Benjamin Nachman, "Quantum anomaly detection for collider physics", Journal of High Energy Physics 2023 2, 220 (2023).

[7] Benjamin Nachman and Ramon Winterhalder, "Elsa: enhanced latent spaces for improved collider simulations", The European Physical Journal C 83 9, 843 (2023).

[8] Ifan Williams and Mathieu Pellen, "A general approach to quantum integration of cross sections in high-energy physics", Quantum Science and Technology 10 4, 045017 (2025).

[9] Yaswitha Gujju, Atsushi Matsuo, and Rudy Raymond, "Quantum machine learning on near-term quantum devices: Current state of supervised and unsupervised techniques for real-world applications", Physical Review Applied 21 6, 067001 (2024).

[10] Manuel S. Rudolph, Sacha Lerch, Supanut Thanasilp, Oriel Kiss, Oxana Shaya, Sofia Vallecorsa, Michele Grossi, and Zoë Holmes, "Trainability barriers and opportunities in quantum generative modeling", npj Quantum Information 10 1, 116 (2024).

[11] Jack Y. Araz and Michael Spannowsky, "Classical versus quantum: Comparing tensor-network-based quantum circuits on Large Hadron Collider data", Physical Review A 106 6, 062423 (2022).

[12] Francesca De Falco, Andrea Ceschini, Alessandro Sebastianelli, Bertrand Le Saux, and Massimo Panella, "Quantum Hybrid Diffusion Models for Image Synthesis", KI - Künstliche Intelligenz 38 4, 311 (2024).

[13] Carlos A. Riofrio, Oliver Mitevski, Caitlin Jones, Florian Krellner, Aleksandar Vuckovic, Joseph Doetsch, Johannes Klepsch, Thomas Ehmer, and Andre Luckow, "A Characterization of Quantum Generative Models", ACM Transactions on Quantum Computing 5 2, 1 (2024).

[14] Vasilis Belis, Patrick Odagiu, and Thea Klaeboe Aarrestad, "Machine learning for anomaly detection in particle physics", Reviews in Physics 12, 100091 (2024).

[15] Yaquan Fang, Christina Gao, Ying-Ying Li, Jing Shu, Yusheng Wu, Hongxi Xing, Bin Xu, Lailin Xu, and Chen Zhou, "Quantum frontiers in high energy physics", Science China Physics, Mechanics & Astronomy 68 6, 260301 (2025).

[16] Aaron Mark Thomas, Harry Youel, and Sharu Theresa Jose, "VAE-QWGAN: addressing mode collapse in quantum GANs via autoencoding priors", Quantum Machine Intelligence 7 2, 91 (2025).

[17] Baran Hashemi and Claudius Krause, "Deep generative models for detector signature simulation: A taxonomic review", Reviews in Physics 12, 100092 (2024).

[18] Vasilis Belis, Patrick Odagiu, Michele Grossi, Florentin Reiter, Günther Dissertori, and Sofia Vallecorsa, "Guided quantum compression for high dimensional data classification", Machine Learning: Science and Technology 5 3, 035010 (2024).

[19] Nishant Saurabh, Shantenu Jha, and Andre Luckow, 2023 IEEE International Conference on Quantum Software (QSW) 116 (2023) ISBN:979-8-3503-0479-4.

[20] Yi-An Chen and Kai-Feng Chen, "Jet discrimination with a quantum complete graph neural network", Physical Review D 111 1, 016020 (2025).

[21] Armand Rousselot and Michael Spannowsky, "Generative invertible quantum neural networks", SciPost Physics 16 6, 146 (2024).

[22] Smit Chaudhary, Patrick Huembeli, Ian MacCormack, Taylor L Patti, Jean Kossaifi, and Alexey Galda, "Towards a scalable discrete quantum generative adversarial neural network", Quantum Science and Technology 8 3, 035002 (2023).

[23] Elies Gil-Fuster, Jens Eisert, and Carlos Bravo-Prieto, "Understanding quantum machine learning also requires rethinking generalization", Nature Communications 15 1, 2277 (2024).

[24] Herschel Chawdhry and Mathieu Pellen, "Quantum simulation of colour in perturbative quantum chromodynamics", SciPost Physics 15 5, 205 (2023).

[25] Alice Barthe, Michele Grossi, Sofia Vallecorsa, Jordi Tura, and Vedran Dunjko, "Parameterized quantum circuits as universal generative models for continuous multivariate distributions", npj Quantum Information 11 1, 121 (2025).

[26] Matteo Robbiati, Juan M. Cruz-Martinez, and Stefano Carrazza, "Determining probability density functions with adiabatic quantum computing", Quantum Machine Intelligence 7 1, 5 (2025).

[27] Erik Bashore, Stefano Moretti, and Timea Vitos, "A quantum algorithm for the n-gluon MHV scattering amplitude", SciPost Physics 20 4, 114 (2026).

[28] Simone Bordoni, Denis Stanev, Tommaso Santantonio, and Stefano Giagu, "Long-Lived Particles Anomaly Detection with Parametrized Quantum Circuits", Particles 6 1, 297 (2023).

[29] Oriel Kiss, Michele Grossi, Enrique Kajomovitz, and Sofia Vallecorsa, "Conditional Born machine for Monte Carlo event generation", Physical Review A 106 2, 022612 (2022).

[30] Julien Baglio, "Cross-platform hardware benchmark of style-based quantum GANs for data augmentation on superconducting and trapped-ion processors", AIP Advances 16 6, 065008 (2026).

[31] LI JiaChong, DING GeYi, YUAN Quan, YUAN MingZhe, and FENG Mang, "Machine learning for quantum control and information processing in trapped-ion systems", SCIENTIA SINICA Physica, Mechanica & Astronomica 56 2, 223001 (2026).

[32] Abdul Qadir, Rabbia Mahum, Mohammed A. El-Meligy, Adham E. Ragab, Abdulmalik AlSalman, and Muhammad Awais, "An efficient deepfake video detection using robust deep learning", Heliyon 10 5, e25757 (2024).

[33] Andreas Adelmann, Walter Hopkins, Evangelos Kourlitis, Michael Kagan, Gregor Kasieczka, Claudius Krause, David Shih, Vinicius Mikuni, Benjamin Nachman, Kevin Pedro, and Daniel Winklehner, "New directions for surrogate models and differentiable programming for High Energy Physics detector simulation", arXiv:2203.08806, (2022).

[34] Andrea Delgado, Kathleen E. Hamilton, Prasanna Date, Jean-Roch Vlimant, Duarte Magano, Yasser Omar, Pedrame Bargassa, Anthony Francis, Alessio Gianelle, Lorenzo Sestini, Donatella Lucchesi, Davide Zuliani, Davide Nicotra, Jacco de Vries, Dominica Dibenedetto, Miriam Lucio Martinez, Eduardo Rodrigues, Carlos Vazquez Sierra, Sofia Vallecorsa, Jesse Thaler, Carlos Bravo-Prieto, su Yeon Chang, Jeffrey Lazar, Carlos A. Argüelles, and Jorge J. Martinez de Lejarza, "Quantum computing for data analysis in high energy physics", arXiv:2203.08805, (2022).

[35] Herschel A. Chawdhry, Mathieu Pellen, and Simon Williams, "Quantum simulation of scattering amplitudes and interferences in perturbative QCD", arXiv:2507.07194, (2025).

[36] Gabriele Agliardi, Michele Grossi, Mathieu Pellen, and Enrico Prati, "Quantum integration of elementary particle processes", Physics Letters B 832, 137228 (2022).

[37] Travis S. Humble, Andrea Delgado, Raphael Pooser, Christopher Seck, Ryan Bennink, Vicente Leyton-Ortega, C.-C. Joseph Wang, Eugene Dumitrescu, Titus Morris, Kathleen Hamilton, Dmitry Lyakh, Prasanna Date, Yan Wang, Nicholas A. Peters, Katherine J. Evans, Marcel Demarteau, Alex McCaskey, Thien Nguyen, Susan Clark, Melissa Reville, Alberto Di Meglio, Michele Grossi, Sofia Vallecorsa, Kerstin Borras, Karl Jansen, and Dirk Krücker, "Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research", arXiv:2203.07091, (2022).

[38] Yuxuan Du, Zhuozhuo Tu, Bujiao Wu, Xiao Yuan, and Dacheng Tao, "Power of Quantum Generative Learning", arXiv:2205.04730, (2022).

[39] Baran Hashemi, "Deep Generative Models for Ultra-High Granularity Particle Physics Detector Simulation: A Voyage From Emulation to Extrapolation", arXiv:2403.13825, (2024).

[40] Andrea Pasquale, Andrea Papaluca, Renato M. S. Farias, Matteo Robbiati, Edoardo Pedicillo, and Stefano Carrazza, "Beyond full statevector simulation with Qibo", arXiv:2408.00384, (2024).

[41] S. Carrazza, S. Efthymiou, M. Lazzarin, and A. Pasquale, "An open-source modular framework for quantum computing", Journal of Physics Conference Series 2438 1, 012148 (2023).

[42] Carlos A. Riofrío, Oliver Mitevski, Caitlin Jones, Florian Krellner, Aleksandar Vučković, Joseph Doetsch, Johannes Klepsch, Thomas Ehmer, and Andre Luckow, "A performance characterization of quantum generative models", arXiv:2301.09363, (2023).

[43] Aaron Mark Thomas, Harry Youel, and Sharu Theresa Jose, "VAE-QWGAN: Addressing Mode Collapse in Quantum GANs via Autoencoding Priors", arXiv:2409.10339, (2024).

[44] Herschel A. Chawdhry and Mathieu Pellen, "Quantum algorithms for the simulation of QCD processes in the perturbative regime", arXiv:2412.21177, (2024).

[45] Sandra Nguemto and Vicente Leyton-Ortega, "Re-QGAN: an optimized adversarial quantum circuit learning framework", arXiv:2208.02165, (2022).

[46] Abdullah Ash Saki, Rasit Onur Topaloglu, and Swaroop Ghosh, "Shuttle-Exploiting Attacks and Their Defenses in Trapped-Ion Quantum Computers", IEEE Access 10, 2686 (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2026-07-17 06:39:15) and SAO/NASA ADS (last updated successfully 2026-07-16 16:46:07). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch ADS cited-by data during last attempt 2026-07-17 06:39:15: Cannot retrieve data from ADS due to rate limitations.