{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T15:48:53Z","timestamp":1778255333501,"version":"3.51.4"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T00:00:00Z","timestamp":1732665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"European Union - NextGenerationEU - Italian PNRR","award":["CN00000013 - CUP B83C22002940006"],"award-info":[{"award-number":["CN00000013 - CUP B83C22002940006"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2024,12]]},"DOI":"10.1007\/s42484-024-00224-6","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T06:41:16Z","timestamp":1732689676000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Quantum latent diffusion models"],"prefix":"10.1007","volume":"6","author":[{"given":"Francesca","family":"De\u00a0Falco","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Ceschini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Sebastianelli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bertrand","family":"Le\u00a0Saux","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Massimo","family":"Panella","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"issue":"6","key":"224_CR1","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1038\/s43588-021-00084-1","volume":"1","author":"A Abbas","year":"2021","unstructured":"Abbas A, Sutter D, Zoufal C, Lucchi A, Figalli A, Woerner S (2021) The power of quantum neural networks. Nat Comput Sci 1(6):403\u2013409. https:\/\/doi.org\/10.1038\/s43588-021-00084-1","journal-title":"Nat Comput Sci"},{"issue":"7949","key":"224_CR2","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1038\/s41586-022-05434-1","volume":"614","author":"R Acharya","year":"2023","unstructured":"Acharya R, Aleiner I et al (2023) Suppressing quantum errors by scaling a surface code logical qubit. Nature 614(7949):676\u2013681","journal-title":"Nature"},{"issue":"2","key":"224_CR3","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s10994-012-5316-5","volume":"90","author":"E A\u00efmeur","year":"2013","unstructured":"A\u00efmeur E, Brassard G, Gambs S (2013) Quantum speed-up for unsupervised learning. Mach Learn 90(2):261\u2013287. https:\/\/doi.org\/10.1007\/s10994-012-5316-5","journal-title":"Mach Learn"},{"issue":"4","key":"224_CR4","doi-asserted-by":"publisher","first-page":"043001","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. Quantum Sci Technol 4(4):043001. https:\/\/doi.org\/10.1088\/2058-9565\/ab4eb5","journal-title":"Quantum Sci Technol"},{"key":"224_CR5","unstructured":"Bergholm V, Izaac J et al (2022) PennyLane: automatic differentiation of hybrid quantum-classical computations"},{"key":"224_CR6","unstructured":"Betzalel E, Penso C, Navon A, Fetaya E (2022) A study on the evaluation of generative models"},{"issue":"6412","key":"224_CR7","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1126\/science.aar3106","volume":"362","author":"S Bravyi","year":"2018","unstructured":"Bravyi S, Gosset D, K\u00f6nig R (2018) Quantum advantage with shallow circuits. Science 362(6412):308\u2013311. https:\/\/doi.org\/10.1126\/science.aar3106","journal-title":"Science"},{"issue":"10","key":"224_CR8","doi-asserted-by":"publisher","first-page":"1040","DOI":"10.1038\/s41567-020-0948-z","volume":"16","author":"S Bravyi","year":"2020","unstructured":"Bravyi S, Gosset D, K\u00f6nig R, Tomamichel M (2020) Quantum advantage with noisy shallow circuits. Nat Phys 16(10):1040\u20131045. https:\/\/doi.org\/10.1038\/s41567-020-0948-z","journal-title":"Nat Phys"},{"key":"224_CR9","doi-asserted-by":"crossref","unstructured":"Cacioppo A, Colantonio L, Bordoni S, Giagu S (2023) Quantum diffusion models","DOI":"10.21203\/rs.3.rs-3688288\/v1"},{"issue":"4","key":"224_CR10","doi-asserted-by":"publisher","first-page":"045005","DOI":"10.1103\/RevModPhys.95.045005","volume":"95","author":"Z Cai","year":"2023","unstructured":"Cai Z, Babbush R, Benjamin SC, Endo S, Huggins WJ, Li Y, McClean JR, O\u2019Brien TE (2023) Quantum error mitigation. Rev Mod Phys 95(4):045005","journal-title":"Rev Mod Phys"},{"issue":"9","key":"224_CR11","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1038\/s42254-021-00348-9","volume":"3","author":"M Cerezo","year":"2021","unstructured":"Cerezo M, Arrasmith A, Babbush R, Benjamin SC, Endo S, Fujii K, McClean JR, Mitarai K, Yuan X, Cincio L, Coles PJ (2021) Variational quantum algorithms. Nature Reviews. Physics 3(9):625\u2013644. https:\/\/doi.org\/10.1038\/s42254-021-00348-9","journal-title":"Physics"},{"key":"224_CR12","unstructured":"Chang SY, Thanasilp S, Saux BL, Vallecorsa S, Grossi M (2024) Latent style-based quantum GAN for high-quality image generation. arXiv:2406.02668"},{"key":"224_CR13","doi-asserted-by":"crossref","unstructured":"Choi J, Lee J, Shin C, Kim S, Kim H, Yoon S (2022) Perception prioritized training of diffusion models","DOI":"10.1109\/CVPR52688.2022.01118"},{"issue":"70","key":"224_CR14","doi-asserted-by":"publisher","first-page":"4101","DOI":"10.21105\/joss.04101","volume":"7","author":"NS Detlefsen","year":"2022","unstructured":"Detlefsen NS, Borovec J, Schock J, Jha AH, Koker T, Liello LD, Stancl D, Quan C, Grechkin M, Falcon W (2022) Torchmetrics - measuring reproducibility in pytorch. J Open Source Softw 7(70):4101. https:\/\/doi.org\/10.21105\/joss.04101","journal-title":"J Open Source Softw"},{"key":"224_CR15","doi-asserted-by":"crossref","unstructured":"Du Y, Hsieh M-H, Liu T, Tao D (2020) Expressive power of parametrized quantum circuits. Phys Rev Res 2(3):033125","DOI":"10.1103\/PhysRevResearch.2.033125"},{"key":"224_CR16","unstructured":"Farhi E, Neven H (2018) Classification with quantum neural networks on near term processors"},{"issue":"3","key":"224_CR17","doi-asserted-by":"publisher","first-page":"032324","DOI":"10.1103\/PhysRevA.86.032324","volume":"86","author":"AG Fowler","year":"2012","unstructured":"Fowler AG, Mariantoni M, Martinis JM, Cleland AN (2012) Surface codes: towards practical large-scale quantum computation. Phys Rev A 86(3):032324","journal-title":"Phys Rev A"},{"key":"224_CR18","volume-title":"Advances in Neural Information Processing Systems","author":"I Goodfellow","year":"2014","unstructured":"Goodfellow I, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2014) Generative adversarial nets. In: Ghahramani Z, Welling M, Cortes C, Lawrence N, Weinberger KQ (eds) Advances in Neural Information Processing Systems, vol 27. Curran Associates Inc, NY, USA"},{"issue":"6","key":"224_CR19","doi-asserted-by":"publisher","first-page":"067001","DOI":"10.1103\/PhysRevApplied.21.067001","volume":"21","author":"Y Gujju","year":"2024","unstructured":"Gujju Y, Matsuo A, Raymond R (2024) Quantum machine learning on near-term quantum devices: current state of supervised and unsupervised techniques for real-world applications. Phys Rev Appl 21(6):067001","journal-title":"Phys Rev Appl"},{"issue":"4","key":"224_CR20","doi-asserted-by":"publisher","first-page":"040313","DOI":"10.1103\/PRXQuantum.3.040313","volume":"3","author":"Y Guo","year":"2022","unstructured":"Guo Y, Yang S (2022) Quantum error mitigation via matrix product operators. PRX Quantum 3(4):040313","journal-title":"PRX Quantum"},{"key":"224_CR21","unstructured":"Heek J, Levskaya A, Oliver A, Ritter M, Rondepierre B, Steiner A, Zee M (2023) Flax: a neural network library and ecosystem for JAX. http:\/\/github.com\/google\/flax"},{"key":"224_CR22","doi-asserted-by":"crossref","unstructured":"Helber P, Bischke B, Dengel A, Borth D (2017) EuroSAT: a novel dataset and deep learning benchmark for land use and land cover classification","DOI":"10.1109\/IGARSS.2018.8519248"},{"key":"224_CR23","volume-title":"Advances in Neural Information Processing Systems","author":"M Heusel","year":"2017","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. In: Guyon I, Luxburg UV, Bengio S, Wallach H, Fergus R, Vishwanathan S, Garnett R (eds) Advances in Neural Information Processing Systems, vol 30. Curran Associates Inc, NY, USA"},{"key":"224_CR24","doi-asserted-by":"crossref","unstructured":"He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: Proceedings of the IEEE conference on Computer Vision and Pattern Recognition (CVPR)","DOI":"10.1109\/CVPR.2016.90"},{"key":"224_CR25","unstructured":"Ho J, Jain A, Abbeel P (2020) Denoising diffusion probabilistic models. In: Larochelle H, Ranzato M, Hadsell R, Balcan MF, Lin H (eds) Advances in Neural Information Processing Systems, vol 33. Curran Associates Inc, NY, USA, pp 6840\u20136851"},{"key":"224_CR26","doi-asserted-by":"publisher","unstructured":"Huang H-L, Du Y, Gong M, Zhao Y, Wu Y, Wang C, Li S, Liang F, Lin J, Xu Y, Yang R, Liu T, Hsieh M-H, Deng H, Rong H, Peng C-Z, Lu C-Y, Chen Y-A, Tao D, Zhu X, Pan J-W (2021) Experimental quantum generative adversarial networks for image generation. Phys Rev Appl 16(2):. https:\/\/doi.org\/10.1103\/physrevapplied.16.024051","DOI":"10.1103\/physrevapplied.16.024051"},{"key":"224_CR27","doi-asserted-by":"publisher","unstructured":"Incudini M, Grossi M, Ceschini A, Mandarino A, Panella M, Vallecorsa S, Windridge D (2023) Resource saving via ensemble techniques for quantum neural networks. Quantum Mach Intell 5(2):. https:\/\/doi.org\/10.1007\/s42484-023-00126-z","DOI":"10.1007\/s42484-023-00126-z"},{"key":"224_CR28","doi-asserted-by":"crossref","unstructured":"Johri S, Debnath S, Mocherla A, Singh A, Prakash A, Kim J, Kerenidis I (2021) Nearest centroid classification on a trapped ion quantum computer. Npj Quantum Inf","DOI":"10.1038\/s41534-021-00456-5"},{"key":"224_CR29","unstructured":"Kingma DP, Ba J (2014) Adam: a method for stochastic optimization. arXiv:1412.6980"},{"key":"224_CR30","unstructured":"LeCun Y, Cortes C, Burges C (2010) MNIST handwritten digit database. ATT Labs [Online]. Available: http:\/\/yann.lecun.com\/exdb\/mnist"},{"issue":"9","key":"224_CR31","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1038\/nphys3029","volume":"10","author":"S Lloyd","year":"2014","unstructured":"Lloyd S, Mohseni M, Rebentrost P (2014) Quantum principal component analysis. Nat Phys 10(9):631\u2013633","journal-title":"Nat Phys"},{"key":"224_CR32","doi-asserted-by":"crossref","unstructured":"Parigi M, Martina S, Caruso F (2023) Quantum-noise-driven generative diffusion models","DOI":"10.1002\/qute.202300401"},{"issue":"7","key":"224_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3464420","volume":"54","author":"S Resch","year":"2021","unstructured":"Resch S, Karpuzcu UR (2021) Benchmarking quantum computers and the impact of quantum noise. ACM Comput Surv (CSUR) 54(7):1\u201335","journal-title":"ACM Comput Surv (CSUR)"},{"key":"224_CR34","doi-asserted-by":"crossref","unstructured":"Rombach R, Blattmann A, Lorenz D, Esser P, Ommer B (2021) High-resolution image synthesis with latent diffusion models. 2022 IEEE\/CVF conference on Computer Vision and Pattern Recognition (CVPR), pp 10674\u201310685","DOI":"10.1109\/CVPR52688.2022.01042"},{"key":"224_CR35","volume-title":"Advances in Neural Information Processing Systems","author":"T Salimans","year":"2016","unstructured":"Salimans T, Goodfellow I, Zaremba W, Cheung V, Radford A, Chen X, Chen X (2016) Improved techniques for training GANs. In: Lee D, Sugiyama M, Luxburg U, Guyon I, Garnett R (eds) Advances in Neural Information Processing Systems, vol 29. Curran Associates Inc, NY, USA"},{"key":"224_CR36","doi-asserted-by":"publisher","unstructured":"Scala F, Ceschini A, Panella M, Gerace D (2023) A general approach to dropout in quantum neural networks. Adv Quantum Technol. n\/a(n\/a):2300220. https:\/\/doi.org\/10.1002\/qute.202300220. Early access","DOI":"10.1002\/qute.202300220"},{"issue":"6","key":"224_CR37","doi-asserted-by":"publisher","first-page":"60002","DOI":"10.1209\/0295-5075\/119\/60002","volume":"119","author":"M Schuld","year":"2017","unstructured":"Schuld M, Fingerhuth M, Petruccione F (2017) Implementing a distance-based classifier with a quantum interference circuit. EPL (Europhys Lett) 119(6):60002. https:\/\/doi.org\/10.1209\/0295-5075\/119\/60002","journal-title":"EPL (Europhys Lett)"},{"key":"224_CR38","unstructured":"Sohl-Dickstein J, Weiss E, Maheswaranathan N, Ganguli S (2015) Deep unsupervised learning using nonequilibrium thermodynamics. In: Bach F, Blei D (eds) Proceedings of the 32nd international conference on machine learning. Proceedings of Machine Learning Research, vol 37, pp 2256\u20132265. PMLR, Lille, France. https:\/\/proceedings.mlr.press\/v37\/sohl-dickstein15.html"},{"key":"224_CR39","doi-asserted-by":"crossref","unstructured":"Tsang SL, West MT, Erfani SM, Usman M (2022) Hybrid quantum\u2013classical generative adversarial network for high-resolution image generation. IEEE Trans Quantum Eng 4:1\u201319","DOI":"10.1109\/TQE.2023.3319319"},{"key":"224_CR40","unstructured":"Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser L, Polosukhin I (2023) Attention is all you need"},{"key":"224_CR41","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.22331\/q-2024-03-14-1287","volume":"8","author":"S Wang","year":"2024","unstructured":"Wang S, Czarnik P, Arrasmith A, Cerezo M, Cincio L, Coles PJ (2024) Can error mitigation improve trainability of noisy variational quantum algorithms? Quantum 8:1287","journal-title":"Quantum"},{"issue":"5","key":"224_CR42","doi-asserted-by":"publisher","first-page":"050505","DOI":"10.1103\/PhysRevLett.109.050505","volume":"109","author":"N Wiebe","year":"2012","unstructured":"Wiebe N, Braun D, Lloyd S (2012) Quantum algorithm for data fitting. Phys Rev Lett 109(5):050505","journal-title":"Phys Rev Lett"},{"key":"224_CR43","unstructured":"Xiao H, Rasul K, Vollgraf R (2017) Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms. CoRR. arXiv:1708.07747"},{"key":"224_CR44","doi-asserted-by":"crossref","unstructured":"Yao X-W, Wang H, Liao Z, Chen M-C, Pan J, Li J, Zhang K, Lin X, Wang Z, Luo Z et al (2017) Quantum image processing and its application to edge detection: theory and experiment. Phys Rev X 7(3):031041","DOI":"10.1103\/PhysRevX.7.031041"},{"key":"224_CR45","unstructured":"Yu Z, Chen Q, Jiao Y, Li Y, Lu X, Wang X, Yang JZ (2023) Provable advantage of parameterized quantum circuit in function approximation. arXiv:2310.07528"},{"key":"224_CR46","unstructured":"Zaman K, Ahmed T, Kashif M, Hanif MA, Marchisio A, Shafique M (2024) Studying the impact of quantum-specific hyperparameters on hybrid quantum-classical neural networks"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00224-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-024-00224-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-024-00224-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T16:15:49Z","timestamp":1734970549000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-024-00224-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,27]]},"references-count":46,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["224"],"URL":"https:\/\/doi.org\/10.1007\/s42484-024-00224-6","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,27]]},"assertion":[{"value":"15 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 November 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2024","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 declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"85"}}