{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T05:35:34Z","timestamp":1780551334500,"version":"3.54.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T00:00:00Z","timestamp":1766620800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T00:00:00Z","timestamp":1766620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Liaoning Provincial Department of Education Research","award":["20240248"],"award-info":[{"award-number":["20240248"]}]},{"name":"Liaoning Provincial Department of Education Research","award":["20240248"],"award-info":[{"award-number":["20240248"]}]},{"name":"Scientific Research Foundation for Advanced Talents from Shenyang Aerospace University","award":["18YB06"],"award-info":[{"award-number":["18YB06"]}]},{"name":"Scientific Research Foundation for Advanced Talents from Shenyang Aerospace University","award":["18YB06"],"award-info":[{"award-number":["18YB06"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-025-08172-z","type":"journal-article","created":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T09:42:09Z","timestamp":1766655729000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["HQWGAN: a hybrid quantum\u2013classical Wasserstein generative adversarial network for image generation"],"prefix":"10.1007","volume":"82","author":[{"given":"Han","family":"Qi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yihan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdullah","family":"Gani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lip Yee","family":"Por","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,12,25]]},"reference":[{"issue":"5","key":"8172_CR1","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1007\/s11227-025-07047-7","volume":"81","author":"M AbuGhanem","year":"2025","unstructured":"AbuGhanem M (2025) IBM quantum computers: evolution, performance, and future directions. J Supercomput 81(5):687. https:\/\/doi.org\/10.1007\/s11227-025-07047-7","journal-title":"J Supercomput"},{"issue":"1","key":"8172_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42484-025-00266-4","volume":"7","author":"B Majid","year":"2025","unstructured":"Majid B, Sofi SA, Jabeen Z (2025) Quantum machine learning: a systematic categorization based on learning paradigms, NISQ suitability, and fault tolerance. Quant Mach Intell 7(1):1\u201355. https:\/\/doi.org\/10.1007\/s42484-025-00266-4","journal-title":"Quant Mach Intell"},{"key":"8172_CR3","doi-asserted-by":"publisher","unstructured":"Khanal B, Rivas P, Sanjel A, Sooksatra K, Quevedo E, Rodriguez A (2024) Generalization error bound for quantum machine learning in nisq era\u00e2\u20ac\u201da survey. Quant Mach Intell 6(2):90. https:\/\/doi.org\/10.1007\/s42484-024-00204-w","DOI":"10.1007\/s42484-024-00204-w"},{"issue":"4","key":"8172_CR4","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1007\/s11227-025-07083-3","volume":"81","author":"H Wu","year":"2025","unstructured":"Wu H, Zhang J, Wang L, Li D, Kong D, Han Y (2025) A survey on quantum deep learning. J Supercomput 81(4):564. https:\/\/doi.org\/10.1007\/s11227-025-07083-3","journal-title":"J Supercomput"},{"issue":"1","key":"8172_CR5","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s11227-024-06636-2","volume":"81","author":"H Qi","year":"2025","unstructured":"Qi H, Lv X, Gong C, Gani A (2025) Enhanced quantum long short-term memory by using bidirectional ring variational quantum circuit. J Supercomput 81(1):117. https:\/\/doi.org\/10.1007\/s11227-024-06636-2","journal-title":"J Supercomput"},{"issue":"1","key":"8172_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.012324","volume":"98","author":"P-L Dallaire-Demers","year":"2018","unstructured":"Dallaire-Demers P-L, Killoran N (2018) Quantum generative adversarial networks. Phys Rev A 98(1):012324. https:\/\/doi.org\/10.1103\/PhysRevA.98.012324","journal-title":"Phys Rev A"},{"key":"8172_CR7","unstructured":"Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2014) Generative adversarial nets. Adv Neural Inf Process Syst 27"},{"issue":"2","key":"8172_CR8","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.1007\/s11831-024-10174-8","volume":"32","author":"M Ali","year":"2025","unstructured":"Ali M, Ali M, Hussain M, Koundal D (2025) Generative adversarial networks (GANs) for medical image processing: recent advancements. Arch Comput Methods Eng 32(2):1185\u20131198. https:\/\/doi.org\/10.1007\/s11831-024-10174-8","journal-title":"Arch Comput Methods Eng"},{"key":"8172_CR9","first-page":"17022","volume":"33","author":"J Kong","year":"2020","unstructured":"Kong J, Kim J, Bae J (2020) Hifi-gan: Generative adversarial networks for efficient and high fidelity speech synthesis. Adv Neural Inf Process Syst 33:17022\u201317033","journal-title":"Adv Neural Inf Process Syst"},{"key":"8172_CR10","first-page":"1","volume":"2021","author":"C Besombes","year":"2021","unstructured":"Besombes C, Pannekoucke O, Lapeyre C, Sanderson B, Thual O (2021) Producing realistic climate data with GANs. Nonlinear Process Geophysc Discuss 2021:1\u201339","journal-title":"Nonlinear Process Geophysc Discuss"},{"key":"8172_CR11","unstructured":"Arjovsky M, Bottou L (2017) Towards principled methods for training generative adversarial networks. arXiv preprint arXiv:1701.04862"},{"key":"8172_CR12","unstructured":"Arjovsky M, Chintala S, Bottou L (2017) Wasserstein generative adversarial networks. In: International Conference on Machine Learning, pp 214\u2013223. PMLR"},{"issue":"4","key":"8172_CR13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.040502","volume":"121","author":"S Lloyd","year":"2018","unstructured":"Lloyd S, Weedbrook C (2018) Quantum generative adversarial learning. Phys Rev Lett 121(4):040502. https:\/\/doi.org\/10.1103\/PhysRevLett.121.040502","journal-title":"Phys Rev Lett"},{"key":"8172_CR14","doi-asserted-by":"publisher","unstructured":"Olivera-Atencio ML, Lamata L, Casado-Pascual J (2025) Impact of amplitude and phase damping noise on quantum reinforcement learning: challenges and opportunities. Eur Phys J Spec Top 1\u20137https:\/\/doi.org\/10.1140\/epjs\/s11734-025-01760-3","DOI":"10.1140\/epjs\/s11734-025-01760-3"},{"issue":"11","key":"8172_CR15","doi-asserted-by":"publisher","first-page":"3307","DOI":"10.1021\/acs.jcim.3c00562","volume":"63","author":"P-Y Kao","year":"2023","unstructured":"Kao P-Y, Yang Y-C, Chiang W-Y, Hsiao J-Y, Cao Y, Aliper A, Ren F, Aspuru-Guzik A, Zhavoronkov A, Hsieh M-H et al (2023) Exploring the advantages of quantum generative adversarial networks in generative chemistry. J Chem Inf Model 63(11):3307\u20133318. https:\/\/doi.org\/10.1021\/acs.jcim.3c00562","journal-title":"J Chem Inf Model"},{"key":"8172_CR16","doi-asserted-by":"publisher","unstructured":"Chu C, Skipper G, Swany M, Chen F (2023) Iqgan: robust quantum generative adversarial network for image synthesis on nisq devices. In: ICASSP 2023-2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, pp 1\u20135. https:\/\/doi.org\/10.1109\/ICASSP49357.2023.1009677","DOI":"10.1109\/ICASSP49357.2023.1009677"},{"issue":"1","key":"8172_CR17","doi-asserted-by":"publisher","first-page":"19649","DOI":"10.1038\/s41598-021-98933-6","volume":"11","author":"K Nakaji","year":"2021","unstructured":"Nakaji K, Yamamoto N (2021) Quantum semi-supervised generative adversarial network for enhanced data classification. Sci Rep 11(1):19649. https:\/\/doi.org\/10.1038\/s41598-021-98933-6","journal-title":"Sci Rep"},{"key":"8172_CR18","doi-asserted-by":"publisher","unstructured":"Stein SA, Baheri B, Chen D, Mao Y, Guan Q, Li A, Fang B, Xu S (2021) Qugan: a quantum state fidelity based generative adversarial network. In: 2021 IEEE International Conference on Quantum Computing and Engineering (QCE), IEEE, pp 71\u201381. https:\/\/doi.org\/10.1109\/QCE52317.2021.00023","DOI":"10.1109\/QCE52317.2021.00023"},{"issue":"2","key":"8172_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.16.024051","volume":"16","author":"H-L Huang","year":"2021","unstructured":"Huang H-L, Du Y, Gong M, Zhao Y, Wu Y, Wang C, Li S, Liang F, Lin J, Xu Y et al (2021) Experimental quantum generative adversarial networks for image generation. Phys Rev Appl 16(2):024051. https:\/\/doi.org\/10.1103\/PhysRevApplied.16.024051","journal-title":"Phys Rev Appl"},{"issue":"4","key":"8172_CR20","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ac0d4d","volume":"6","author":"D Herr","year":"2021","unstructured":"Herr D, Obert B, Rosenkranz M (2021) Anomaly detection with variational quantum generative adversarial networks. Quant Sci Technol 6(4):045004. https:\/\/doi.org\/10.1088\/2058-9565\/ac0d4d","journal-title":"Quant Sci Technol"},{"key":"8172_CR21","doi-asserted-by":"publisher","unstructured":"Silver D, Patel T, Cutler W, Ranjan A, Gandhi H, Tiwari D (2023) Mosaiq: quantum generative adversarial networks for image generation on nisq computers. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision, pp. 7030\u20137039. https:\/\/doi.org\/10.1109\/ICCV51070.2023.00647","DOI":"10.1109\/ICCV51070.2023.00647"},{"key":"8172_CR22","doi-asserted-by":"publisher","unstructured":"Qu Z, Shi W, Tiwari P (2023) Quantum conditional generative adversarial network based on patch method for abnormal electrocardiogram generation. Comput Biol Med 166, 107549. https:\/\/doi.org\/10.1016\/j.compbiomed.2023.107549","DOI":"10.1016\/j.compbiomed.2023.107549"},{"key":"8172_CR23","doi-asserted-by":"publisher","unstructured":"Tsang SL, West MT, Erfani SM, Usman M (2023) Hybrid quantum\u2013classical generative adversarial network for high-resolution image generation. IEEE Trans Quant Eng 4, 1\u201319https:\/\/doi.org\/10.1109\/TQE.2023.3319319","DOI":"10.1109\/TQE.2023.3319319"},{"key":"8172_CR24","doi-asserted-by":"publisher","unstructured":"Kossale Y, Airaj M, Darouichi A (2022) Mode collapse in generative adversarial networks: an overview. In: 2022 8th International Conference on Optimization and Applications (ICOA), pp 1\u20136. IEEE. https:\/\/doi.org\/10.1109\/ICOA55659.2022.9934291","DOI":"10.1109\/ICOA55659.2022.9934291"},{"issue":"2","key":"8172_CR25","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/aaea94","volume":"4","author":"W Huggins","year":"2019","unstructured":"Huggins W, Patil P, Mitchell B, Whaley KB, Stoudenmire EM (2019) Towards quantum machine learning with tensor networks. Quant Sci Technol 4(2):024001. https:\/\/doi.org\/10.1088\/2058-9565\/aaea94","journal-title":"Quant Sci Technol"},{"key":"8172_CR26","unstructured":"Chakrabarti S, Yiming H, Li T, Feizi S, Wu X (2019) Quantum wasserstein generative adversarial networks. Adv Neural Inf Process Syst 32"},{"key":"8172_CR27","doi-asserted-by":"crossref","unstructured":"Thomas AM, Youel H, Jose ST (2024) Vae-qwgan: addressing mode collapse in quantum gans via autoencoding priors. arXiv preprint arXiv:2409.10339","DOI":"10.1007\/s42484-025-00314-z"},{"key":"8172_CR28","doi-asserted-by":"publisher","unstructured":"Zhou NR, Zhang TF, Xie XW, Wu JY (2023) Hybrid quantum\u2013classical generative adversarial networks for image generation via learning discrete distribution. Signal Process Image Commun 110, 116891. https:\/\/doi.org\/10.1016\/j.image.2022.116891","DOI":"10.1016\/j.image.2022.116891"},{"issue":"4","key":"8172_CR29","doi-asserted-by":"publisher","DOI":"10.1088\/2058-9565\/ab4eb5","volume":"4","author":"M Benedetti","year":"2019","unstructured":"Benedetti M, Lloyd E, Sack S, Fiorentini M (2019) Parameterized quantum circuits as machine learning models. Quant Sci Technol 4(4):043001. https:\/\/doi.org\/10.1088\/2058-9565\/ab4eb5","journal-title":"Quant Sci Technol"},{"issue":"2","key":"8172_CR30","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/s11128-025-04665-1","volume":"24","author":"J Cunningham","year":"2025","unstructured":"Cunningham J, Zhuang J (2025) Investigating and mitigating barren plateaus in variational quantum circuits: a survey. Quant Inf Process 24(2):48. https:\/\/doi.org\/10.1007\/s11128-025-04665-1","journal-title":"Quant Inf Process"},{"issue":"1","key":"8172_CR31","doi-asserted-by":"publisher","first-page":"15886","DOI":"10.1038\/s41598-024-66394-2","volume":"14","author":"X Ding","year":"2024","unstructured":"Ding X, Song Z, Xu J, Hou Y, Yang T, Shan Z (2024) Scalable parameterized quantum circuits classifier. Sci Rep 14(1):15886. https:\/\/doi.org\/10.1038\/s41598-024-66394-2","journal-title":"Sci Rep"},{"issue":"7","key":"8172_CR32","doi-asserted-by":"publisher","first-page":"3797","DOI":"10.1109\/TIT.2014.2320500","volume":"60","author":"T Van Erven","year":"2014","unstructured":"Van Erven T, Harremos P (2014) R\u00e9nyi divergence and Kullback-Leibler divergence. IEEE Trans Inf Theory 60(7):3797\u20133820. https:\/\/doi.org\/10.1109\/TIT.2014.2320500","journal-title":"IEEE Trans Inf Theory"},{"issue":"3","key":"8172_CR33","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1007\/s00220-020-03702-7","volume":"381","author":"R Longo","year":"2021","unstructured":"Longo R, Xu F (2021) Von Neumann entropy in QFT. Commun Math Phys 381(3):1031\u20131054. https:\/\/doi.org\/10.1007\/s00220-020-03702-7","journal-title":"Commun Math Phys"},{"issue":"11","key":"8172_CR34","doi-asserted-by":"publisher","first-page":"2278","DOI":"10.1109\/5.726791","volume":"86","author":"Y Lecun","year":"1998","unstructured":"Lecun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278\u20132324. https:\/\/doi.org\/10.1109\/5.726791","journal-title":"Proc IEEE"},{"key":"8172_CR35","unstructured":"Xiao H, Rasul K, Vollgraf R (2017) Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747"},{"key":"8172_CR36","unstructured":"Heusel M, Ramsauer H, Unterthiner T, Nessler B, Hochreiter S (2017) Gans trained by a two time-scale update rule converge to a local nash equilibrium. Adv Neural Inf Process Syst 30"},{"issue":"1","key":"8172_CR37","doi-asserted-by":"publisher","first-page":"9967","DOI":"10.1038\/s41598-018-28270-8","volume":"8","author":"X Zhu","year":"2018","unstructured":"Zhu X, Su S, Fu M, Liu J, Zhu L, Yang W, Jing G, Guo Y (2018) A cosine similarity algorithm method for fast and accurate monitoring of dynamic droplet generation processes. Sci Rep 8(1):9967. https:\/\/doi.org\/10.1038\/s41598-018-28270-8","journal-title":"Sci Rep"},{"key":"8172_CR38","doi-asserted-by":"publisher","unstructured":"K\u00f6lle M, Stenzel G, Stein J, Zielinski S, Ommer B, Linnhoff-Popien C (2024) Quantum denoising diffusion models. In: 2024 IEEE International Conference on Quantum Software (QSW), IEEE, pp 88\u201398. https:\/\/doi.org\/10.1109\/QSW62656.2024.00023","DOI":"10.1109\/QSW62656.2024.00023"},{"key":"8172_CR39","doi-asserted-by":"publisher","unstructured":"Wang Z, Simoncelli EP, Bovik AC (2003) Multiscale structural similarity for image quality assessment. In: The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, vol 2, pp 1398\u201314022. https:\/\/doi.org\/10.1109\/ACSSC.2003.1292216","DOI":"10.1109\/ACSSC.2003.1292216"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-08172-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-08172-z","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-08172-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,25]],"date-time":"2025-12-25T09:42:11Z","timestamp":1766655731000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-08172-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,25]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["8172"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-08172-z","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,25]]},"assertion":[{"value":"8 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 December 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no conflict of interest to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"25"}}