{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:19:49Z","timestamp":1757618389306,"version":"3.44.0"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T00:00:00Z","timestamp":1750982400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T00:00:00Z","timestamp":1750982400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the key Scientific Research Foundation of Anhui Provincial Education Department","award":["No.2023AH050481","No.2023AH050481","No.2023AH050481","No.2023AH050481"],"award-info":[{"award-number":["No.2023AH050481","No.2023AH050481","No.2023AH050481","No.2023AH050481"]}]},{"name":"the Quality Engineering Project of Anhui Provincial Education Department","award":["No.2023zygzts036","No.2023zygzts036"],"award-info":[{"award-number":["No.2023zygzts036","No.2023zygzts036"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-04821-7","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T01:48:58Z","timestamp":1750988938000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Image classification with hybrid quantum-classical neural networks under qubit flip noise"],"prefix":"10.1007","volume":"24","author":[{"given":"Ya-Qi","family":"Ling","sequence":"first","affiliation":[]},{"given":"Jun-Hu","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Li-Hua","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Cheng-Yun","family":"Ding","sequence":"additional","affiliation":[]},{"given":"Hui-Lei","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,27]]},"reference":[{"key":"4821_CR1","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1140\/epjs\/s11734-021-00061-9","volume":"230","author":"A Khrennikov","year":"2021","unstructured":"Khrennikov, A.: Roots of quantum computing supremacy: superposition, entanglement, or complementarity? Eur. Phys. J. Spec. Top. 230, 1053 (2021). https:\/\/doi.org\/10.1140\/epjs\/s11734-021-00061-9","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"4821_CR2","doi-asserted-by":"publisher","first-page":"1762","DOI":"10.1007\/s10701-020-00319-7","volume":"50","author":"A Khrennikov","year":"2020","unstructured":"Khrennikov, A.: Quantum versus classical entanglement: eliminating the issue of quantum nonlocality. Found. Phys. 50, 1762 (2020). https:\/\/doi.org\/10.1007\/s10701-020-00319-7","journal-title":"Found. Phys."},{"key":"4821_CR3","unstructured":"Caraiman, S., Manta, V.: Image processing using quantum computing. In: 2012 16th international conference on system theory, control and computing. pp. 1 - 6 (2012)"},{"key":"4821_CR4","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ad2aef","volume":"5","author":"S Arsenii","year":"2024","unstructured":"Arsenii, S., Alexandr, S., Asel, S., et al.: Quantum machine learning for image classification. Mach. Learn.: Sci. Technol. 5, 015040 (2024). https:\/\/doi.org\/10.1088\/2632-2153\/ad2aef","journal-title":"Mach. Learn.: Sci. Technol."},{"key":"4821_CR5","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s42484-021-00061-x","volume":"4","author":"T Hur","year":"2022","unstructured":"Hur, T., Kim, L., Park, D.K.: Quantum convolutional neural network for classical data classification. Quantum Mach. Intell. 4, 3 (2022). https:\/\/doi.org\/10.1007\/s42484-021-00061-x","journal-title":"Quantum Mach. Intell."},{"key":"4821_CR6","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/s42484-022-00093-x","volume":"5","author":"S Das","year":"2023","unstructured":"Das, S., Zhang, J., Martina, S., et al.: Quantum pattern recognition on real quantum processing units. Quantum Mach. Intell. 5, 16 (2023). https:\/\/doi.org\/10.1007\/s42484-022-00093-x","journal-title":"Quantum Mach. Intell."},{"key":"4821_CR7","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.neucom.2023.01.049","volume":"525","author":"W Lin","year":"2023","unstructured":"Lin, W., Liu, H.W., Xu, J., et al.: Quantum machine learning in medical image analysis: a survey. Neurocomputing 525, 42\u201353 (2023). https:\/\/doi.org\/10.1016\/j.neucom.2023.01.049","journal-title":"Neurocomputing"},{"key":"4821_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.optcom.2023.129993","volume":"550","author":"L-H Gong","year":"2024","unstructured":"Gong, L.-H., Pei, J.-J., Zhang, T.F., et al.: Quantum convolutional neural network based on variational quantum circuits. Opt. Commun. 550, 129993 (2024). https:\/\/doi.org\/10.1016\/j.optcom.2023.129993","journal-title":"Opt. Commun."},{"key":"4821_CR9","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/s42484-022-00083-z","volume":"4","author":"A Assouel","year":"2022","unstructured":"Assouel, A., Jacquier, A., Kondratyev, A.: A quantum generative adversarial network for distributions. Quantum Mach. Intell. 4, 28 (2022). https:\/\/doi.org\/10.1007\/s42484-022-00083-z","journal-title":"Quantum Mach. Intell."},{"key":"4821_CR10","doi-asserted-by":"publisher","first-page":"3371","DOI":"10.5555\/1756006","volume":"11","author":"P Vincent","year":"2010","unstructured":"Vincent, P., Larochelle, H., Lajoie, I., et al.: Stacked denoising autoencoders: learning useful representations in a deep network with a local denoising criterion. J. Mach. Learn. Res. 11, 3371 (2010). https:\/\/doi.org\/10.5555\/1756006","journal-title":"J. Mach. Learn. Res."},{"key":"4821_CR11","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., Sun, J.: Deep Residual Learning for Image Recognition. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition . pp. 770 - 778 (2016)","DOI":"10.1109\/CVPR.2016.90"},{"key":"4821_CR12","unstructured":"Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., Polosukhin, I.: Attention is all you need (2023). http:\/\/arxiv.org\/abs\/1706.03762"},{"key":"4821_CR13","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/0925-2312(93)90006-O","volume":"5","author":"S Amari","year":"1993","unstructured":"Amari, S.: Backpropagation and stochastic gradient descent method. Neurocomputing 5, 185 (1993)","journal-title":"Neurocomputing"},{"key":"4821_CR14","unstructured":"Wei, M., Schwab, D. J.: How noise affects the hessian spectrum in overparameterized neural networks (2019). http:\/\/arxiv.org\/abs\/1910.00195"},{"key":"4821_CR15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.107.170502","volume":"107","author":"A Streltsov","year":"2011","unstructured":"Streltsov, A., Kampermann, H., Bru, D.: Behavior of quantum correlations under local noise. Phys. Rev. Lett. 107, 170502 (2011). https:\/\/doi.org\/10.1103\/PhysRevLett.107.170502","journal-title":"Phys. Rev. Lett."},{"key":"4821_CR16","doi-asserted-by":"publisher","first-page":"79","DOI":"10.22331\/q-2018-08-06-79","volume":"2","author":"J Preskill","year":"2018","unstructured":"Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018). https:\/\/doi.org\/10.22331\/q-2018-08-06-79","journal-title":"Quantum"},{"key":"4821_CR17","doi-asserted-by":"crossref","unstructured":"Liang, Z., Wang, Z., Yang, J., Yang, L., Xiong, J., Shi, Y., Jiang, W.: Can noise on qubits be learned in quantum neural network? A case study on QuantumFlow (2021). http:\/\/arxiv.org\/abs\/2109.03430","DOI":"10.1109\/ICCAD51958.2021.9643470"},{"key":"4821_CR18","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/2438\/1\/012093","volume":"2438","author":"K Borras","year":"2023","unstructured":"Borras, K., Chang, S.Y., Funcke, L., Grossi, M., Hartung, T., Jansen, K., Kruecker, D., K\u00fchn, S., Rehm, F., T\u00fcys\u00fcz, C., Vallecorsa, S.: Impact of quantum noise on the training of quantum Generative Adversarial Networks. J. Phys: Conf. Ser. 2438, 012093 (2023). https:\/\/doi.org\/10.1088\/1742-6596\/2438\/1\/012093","journal-title":"J. Phys: Conf. Ser."},{"key":"4821_CR19","doi-asserted-by":"crossref","unstructured":"Escudero, E.T., Alamo, D.A., G\u00f3mez, O.M., Bringas, P.G.: Assessing the impact of noise on quantum neural networks: An experimental analysis. Presented at the, Cham (2023)","DOI":"10.1007\/978-3-031-40725-3_27"},{"key":"4821_CR20","doi-asserted-by":"publisher","first-page":"157","DOI":"10.3390\/e25010157","volume":"25","author":"C-Y Zhang","year":"2023","unstructured":"Zhang, C.-Y., Zheng, Z.-J., Fei, S.-M., Feng, M.: Dynamics of quantum networks in noisy environments. Entropy-Switz. 25, 157 (2023). https:\/\/doi.org\/10.3390\/e25010157","journal-title":"Entropy-Switz."},{"key":"4821_CR21","first-page":"1383","volume":"21","author":"MR Elman","year":"2020","unstructured":"Elman, M.R., Minnier, J., Chang, X., et al.: Noise accumulation in high dimensional classification and total signal index. J. Mach. Learn. Res. 21, 1383 (2020)","journal-title":"J. Mach. Learn. Res."},{"key":"4821_CR22","doi-asserted-by":"publisher","first-page":"6961","DOI":"10.1038\/s41467-021-27045-6","volume":"12","author":"S Wang","year":"2021","unstructured":"Wang, S., Fontana, E., Cerezo, M., et al.: Noise-induced barren plateaus in variational quantum algorithms. Nat. Commun. 12, 6961 (2021). https:\/\/doi.org\/10.1038\/s41467-021-27045-6","journal-title":"Nat. Commun."},{"key":"4821_CR23","unstructured":"Akhalwaya, I. Y., Ubaru, S., Clarkson, K. L., Squillante, M. S., Jejjala, V., He, Y.-H., Naidoo, K., Kalantzis, V., Horesh, L.: Topological data analysis on noisy quantum computers (2024). http:\/\/arxiv.org\/abs\/2209.09371"},{"key":"4821_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.92.062309","volume":"92","author":"P Webster","year":"2015","unstructured":"Webster, P., Bartlett, S.D., Poulin, D.: Reducing the overhead for quantum computation when noise is biased. Phys. Rev. A 92, 062309 (2015). https:\/\/doi.org\/10.1103\/PhysRevA.92.062309","journal-title":"Phys. Rev. A"},{"key":"4821_CR25","doi-asserted-by":"publisher","DOI":"10.1103\/Phys.Rev.Lett.127.270502","volume":"127","author":"M Urbanek","year":"2021","unstructured":"Urbanek, M., Nachman, B., Pascuzzi, V.R., et al.: Mitigating depolarizing noise on quantum computers with noise-estimation circuits. Phys. Rev. Lett. 127, 270502 (2021). https:\/\/doi.org\/10.1103\/Phys.Rev.Lett.127.270502","journal-title":"Phys. Rev. Lett."},{"key":"4821_CR26","doi-asserted-by":"publisher","first-page":"6077","DOI":"10.1038\/s41598-024-52485-7","volume":"14","author":"Y Hama","year":"2024","unstructured":"Hama, Y., Nishi, H.: Quantum error mitigation via quantum-noise-effect circuit groups. Sci. Rep. 14, 6077 (2024). https:\/\/doi.org\/10.1038\/s41598-024-52485-7","journal-title":"Sci. Rep."},{"key":"4821_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.15.034026","volume":"15","author":"J Sun","year":"2021","unstructured":"Sun, J., Yuan, X., Tsunoda, T., et al.: Mitigating realistic noise in practical noisy intermediate-scale quantum devices. Phys. Rev. Applied. 15, 034026 (2021). https:\/\/doi.org\/10.1103\/PhysRevApplied.15.034026","journal-title":"Phys. Rev. Applied."},{"key":"4821_CR28","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ac2a5e","volume":"23","author":"L Wang","year":"2021","unstructured":"Wang, L., Sun, Y., Zhang, X.: Quantum deep transfer learning. New J. Phys. 23, 103010 (2021)","journal-title":"New J. Phys."},{"key":"4821_CR29","doi-asserted-by":"publisher","DOI":"10.3389\/fphy.2021.755139","volume":"9","author":"M Alam","year":"2022","unstructured":"Alam, M., Ghosh, S.: QNet: a scalable and noise-resilient quantum neural network architecture for noisy intermediate-scale quantum computers. Front. Phys. 9, 755139 (2022)","journal-title":"Front. Phys."},{"key":"4821_CR30","doi-asserted-by":"publisher","first-page":"9223","DOI":"10.1109\/JSTARS.2023.3316306","volume":"16","author":"S Otgonbaatar","year":"2023","unstructured":"Otgonbaatar, S., Schwarz, G., Datcu, M., Kranzlm\u00fcller, D.: Quantum transfer learning for real-world, small, and high-dimensional remotely sensed datasets. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 16, 9223 (2023). https:\/\/doi.org\/10.1109\/JSTARS.2023.3316306","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"4821_CR31","doi-asserted-by":"publisher","first-page":"340","DOI":"10.22331\/q-2020-10-09-340","volume":"4","author":"A Mari","year":"2020","unstructured":"Mari, A., Bromley, T.R., Izaac, J., et al.: Transfer learning in hybrid classical-quantum neural networks. Quantum 4, 340 (2020). https:\/\/doi.org\/10.22331\/q-2020-10-09-340","journal-title":"Quantum"},{"key":"4821_CR32","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1162\/neco.1989.1.4.541","volume":"1","author":"Y LeCun","year":"1989","unstructured":"LeCun, Y., Boser, B., Denker, J.S., et al.: Backpropagation applied to handwritten zip code recognition. Neural Comput. 1, 541 (1989)","journal-title":"Neural Comput."},{"key":"4821_CR33","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1145\/3065386","volume":"60","author":"A Krizhevsky","year":"2017","unstructured":"Krizhevsky, A., Sutskever, I., Hinton, G.E.: ImageNet classification with deep convolutional neural networks. Commun. ACM 60, 84 (2017). https:\/\/doi.org\/10.1145\/3065386","journal-title":"Commun. ACM"},{"key":"4821_CR34","unstructured":"Boureau, Y.-L., Ponce, J., Lecun, Y.: A theoretical analysis of feature pooling in visual recognition. Presented at the ICML 2010 - Proceedings, 27th International Conference on Machine Learning November 6 (2010)"},{"key":"4821_CR35","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/s11128-024-04530-7","volume":"23","author":"C-Y Ding","year":"2024","unstructured":"Ding, C.-Y., Liu, W.-F., Zhang, L.-H.: Fusion of atomic W-like states in cavity QED systems. Quantum Inf. Process. 23, 319 (2024). https:\/\/doi.org\/10.1007\/s11128-024-04530-7","journal-title":"Quantum Inf. Process."},{"key":"4821_CR36","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/s11128-023-04072-4","volume":"22","author":"S Sadana","year":"2023","unstructured":"Sadana, S., Maccone, L., Sinha, U.: Noise analysis for the Sorkin and Peres tests performed on a quantum computer. Quantum Inf. Process. 22, 317 (2023). https:\/\/doi.org\/10.1007\/s11128-023-04072-4","journal-title":"Quantum Inf. Process."},{"key":"4821_CR37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.127.110505","volume":"127","author":"X-M Hu","year":"2021","unstructured":"Hu, X.-M., Zhang, C., Guo, Y., et al.: Pathways for entanglement-based quantum communication in the face of high noise. Phys. Rev. Lett. 127, 110505 (2021). https:\/\/doi.org\/10.1103\/PhysRevLett.127.110505","journal-title":"Phys. Rev. Lett."},{"key":"4821_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42484-021-00038-w","volume":"3","author":"T Hubregtsen","year":"2021","unstructured":"Hubregtsen, T., Pichlmeier, J., Stecher, P., et al.: Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility, and entangling capability. Quantum Mach. Intell. 3, 1 (2021)","journal-title":"Quantum Mach. Intell."},{"key":"4821_CR39","doi-asserted-by":"publisher","first-page":"677","DOI":"10.22331\/q-2022-03-30-677","volume":"6","author":"D Wierichs","year":"2022","unstructured":"Wierichs, D., Izaac, J., Wang, C., et al.: General parameter-shift rules for quantum gradients. Quantum 6, 677 (2022). https:\/\/doi.org\/10.22331\/q-2022-03-30-677","journal-title":"Quantum"},{"key":"4821_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/s11433-021-1734-3","volume":"64","author":"J Liu","year":"2021","unstructured":"Liu, J., Lim, K.H., Wood, K.L., et al.: Hybrid quantum-classical convolutional neural networks. Sci. China Phys. Mech. Astron. 64, 290311 (2021). https:\/\/doi.org\/10.1007\/s11433-021-1734-3","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"4821_CR41","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10773-024-05669-w","volume":"63","author":"Y-Q Ling","year":"2024","unstructured":"Ling, Y.-Q., Zhang, J.-H., Zhang, L.-H., et al.: Image classification using hybrid classical-quantum neutral networks. Int. J. Theor. Phys. 63, 125 (2024). https:\/\/doi.org\/10.1007\/s10773-024-05669-w","journal-title":"Int. J. Theor. Phys."},{"key":"4821_CR42","unstructured":"Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition (2015). http:\/\/arxiv.org\/abs\/1409.1556"},{"key":"4821_CR43","unstructured":"Wang, X., Lin, B., Liu, D., Xu, C.: Efficient transfer learning in diffusion models via adversarial noise (2023). http:\/\/arxiv.org\/abs\/2308.11948"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04821-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04821-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04821-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T22:48:14Z","timestamp":1757198894000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04821-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,27]]},"references-count":43,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["4821"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04821-7","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2025,6,27]]},"assertion":[{"value":"3 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"197"}}