{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T22:31:38Z","timestamp":1777501898771,"version":"3.51.4"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T00:00:00Z","timestamp":1674000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Mach. Intell."],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s42484-022-00091-z","type":"journal-article","created":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T10:02:56Z","timestamp":1674036176000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Non-IID quantum federated learning with one-shot communication complexity"],"prefix":"10.1007","volume":"5","author":[{"given":"Haimeng","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,18]]},"reference":[{"key":"91_CR1","doi-asserted-by":"publisher","first-page":"3457","DOI":"10.1103\/PhysRevA.52.3457","volume":"52","author":"A Barenco","year":"1995","unstructured":"Barenco A, Bennett CH, Cleve R, DiVincenzo DP, Margolus N, Shor P, Sleator T, Smolin JA, Weinfurter H (1995) Elementary gates for quantum computation. Phys Review A 52:3457","journal-title":"Phys Review A"},{"key":"91_CR2","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1038\/nature23474","volume":"549","author":"J Biamonte","year":"2017","unstructured":"Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S (2017) Quantum machine learning. Nature 549:195","journal-title":"Nature"},{"key":"91_CR3","volume-title":"Pattern recognition and machine learning (information science and statistics)","author":"CM Bishop","year":"2006","unstructured":"Bishop CM (2006) Pattern recognition and machine learning (information science and statistics). Springer-Verlag, Berlin"},{"key":"91_CR4","unstructured":"Bradbury J, Frostig R, Hawkins P, Johnson MJ, Leary C, Maclaurin D, Necula G, Paszke A, VanderPlas J, Wanderman-Milne S, Zhang Q (2018) JAX: composable transformations of Python+NumPy programs"},{"key":"91_CR5","doi-asserted-by":"crossref","unstructured":"Broadbent A, Fitzsimons J, Kashefi E (2009) Universal blind quantum computation. In: 2009 50th annual IEEE symposium on foundations of computer science, IEEE, pp 517\u2013526","DOI":"10.1109\/FOCS.2009.36"},{"key":"91_CR6","doi-asserted-by":"publisher","first-page":"460","DOI":"10.3390\/e23040460","volume":"23","author":"SY-C Chen","year":"2021","unstructured":"Chen SY-C, Yoo S (2021) Federated quantum machine learning. Entropy 23:460","journal-title":"Entropy"},{"key":"91_CR7","doi-asserted-by":"crossref","unstructured":"Chehimi M, Saad W (2022) Quantum federated learning with quantum data. In: ICASSP 2022-2022 IEEE international conference on acoustics, speech and signal processing (ICASSP), IEEE, pp 8617\u20138621","DOI":"10.1109\/ICASSP43922.2022.9746622"},{"key":"91_CR8","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1063\/PT.3.4164","volume":"72","author":"S Das Sarma","year":"2019","unstructured":"Das Sarma S, Deng D-L, Duan L-M (2019) Machine learning meets quantum physics. Phys Today 72:48","journal-title":"Phys Today"},{"key":"91_CR9","doi-asserted-by":"publisher","first-page":"eaat9004","DOI":"10.1126\/sciadv.aat9004","volume":"4","author":"X Gao","year":"2018","unstructured":"Gao X, Zhang Z-Y, Duan L-M (2018) A quantum machine learning algorithm based on generative models. Sci Adv 4:eaat9004","journal-title":"Sci Adv"},{"key":"91_CR10","first-page":"16937","volume":"33","author":"J Geiping","year":"2020","unstructured":"Geiping J, Bauermeister H, Dr\u00f6ge H, Moeller M (2020) Inverting gradients-how easy is it to break privacy in federated learning? Adv Neural Inf Process Syst 33:16937","journal-title":"Adv Neural Inf Process Syst"},{"key":"91_CR11","doi-asserted-by":"publisher","first-page":"160501","DOI":"10.1103\/PhysRevLett.100.160501","volume":"100","author":"V Giovannetti","year":"2008","unstructured":"Giovannetti V, Lloyd S, Maccone L (2008a) Quantum random access memory. Phys Rev Lett 100:160501","journal-title":"Phys Rev Lett"},{"key":"91_CR12","doi-asserted-by":"publisher","first-page":"052310","DOI":"10.1103\/PhysRevA.78.052310","volume":"78","author":"V Giovannetti","year":"2008","unstructured":"Giovannetti V, Lloyd S, Maccone L (2008b) Architectures for a quantum random access memory. Phys Rev A 78:052310","journal-title":"Phys Rev A"},{"key":"91_CR13","doi-asserted-by":"publisher","first-page":"044002","DOI":"10.7566\/JPSJ.90.044002","volume":"90","author":"FA Gonz\u00e1lez","year":"2021","unstructured":"Gonz\u00e1lez FA, Vargas-Calder\u00f3n V, Vinck-Posada H (2021) Classification with quantum measurements. J Phys Soc Jpn 90:044002. https:\/\/doi.org\/10.7566\/JPSJ.90.044002","journal-title":"J Phys Soc Jpn"},{"key":"91_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s42484-022-00079-9","volume":"4","author":"FA Gonz\u00e1lez","year":"2022","unstructured":"Gonz\u00e1lez FA, Gallego A, Toledo-Cort\u00e9s S, Vargas-Calder\u00f3n V (2022) Learning with density matrices and random features. Quantum Mach Intell 4:1","journal-title":"Quantum Mach Intell"},{"key":"91_CR15","unstructured":"Goodfellow I, Bengio Y, Courville A (2016) Deep Learning. (MIT Press). http:\/\/www.deeplearningbook.org"},{"key":"91_CR16","unstructured":"Guha N, Talwalkar A, Smith V (2019) One-shot federated learning. arXiv:1902.11175"},{"key":"91_CR17","doi-asserted-by":"publisher","first-page":"150502","DOI":"10.1103\/PhysRevLett.103.150502","volume":"103","author":"AW Harrow","year":"2009","unstructured":"Harrow AW, Hassidim A, Lloyd S (2009) Quantum algorithm for linear systems of equations. Phys Rev Lett 103:150502","journal-title":"Phys Rev Lett"},{"key":"91_CR18","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1038\/s41586-019-0980-2","volume":"567","author":"V Havl\u00ed\u010dek","year":"2019","unstructured":"Havl\u00ed\u010dek V, C\u00f3rcoles AD, Temme K, Harrow AW, Kandala A, Chow JM, Gambetta JM (2019) Supervised learning with quantum-enhanced feature spaces. Nature 567:209","journal-title":"Nature"},{"key":"91_CR19","unstructured":"Hsieh K, Phanishayee A, Mutlu O, Gibbons P (2020) The non-iid data quagmire of decentralized machine learning. In: International conference on machine learning, PMLR, pp 4387\u20134398"},{"key":"91_CR20","doi-asserted-by":"publisher","first-page":"eabk3333","DOI":"10.1126\/science.abk3333","volume":"377","author":"H-Y Huang","year":"2022","unstructured":"Huang H-Y, Kueng R, Torlai G, Albert VV, Preskill J (2022) Provably efficient machine learning for quantum many-body problems. Science 377:eabk3333","journal-title":"Science"},{"key":"91_CR21","doi-asserted-by":"publisher","first-page":"1050","DOI":"10.1038\/s41567-020-0932-7","volume":"16","author":"H-Y Huang","year":"2020","unstructured":"Huang H-Y, Kueng R, Preskill J (2020) Predicting many properties of a quantum system from very few measurements. Nature Phys 16:1050","journal-title":"Nature Phys"},{"key":"91_CR22","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1162\/neco.1991.3.1.79","volume":"3","author":"RA Jacobs","year":"1991","unstructured":"Jacobs RA, Jordan MI, Nowlan SJ, Hinton GE (1991) Adaptive mixtures of local experts. Neural Comput 3:79","journal-title":"Neural Comput"},{"key":"91_CR23","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1162\/neco.1994.6.2.181","volume":"6","author":"MI Jordan","year":"1994","unstructured":"Jordan MI, Jacobs RA (1994) Hierarchical mixtures of experts and the em algorithm. Neural Comput 6:181","journal-title":"Neural Comput"},{"key":"91_CR24","doi-asserted-by":"crossref","unstructured":"Kasturi A, Ellore AR, Hota C (2020) Fusion learning: a one shot federated learning. In: International conference on computational science, Springer, pp 424\u2013436","DOI":"10.1007\/978-3-030-50420-5_31"},{"key":"91_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s42400-021-00077-7","volume":"4","author":"A Khraisat","year":"2021","unstructured":"Khraisat A, Alazab A (2021) A critical review of intrusion detection systems in the internet of things: techniques, deployment strategy, validation strategy, attacks, public datasets and challenges. Cybersecurity 4:1","journal-title":"Cybersecurity"},{"key":"91_CR26","unstructured":"Kingma DP, Ba J (2017) Adam: A method for stochastic optimization. arXiv:1412.6980"},{"key":"91_CR27","unstructured":"Kone\u010dny\u0300 J, McMahan HB, Yu FX, Richt\u00e1rik P, Suresh AT, Bacon D (2016) Federated learning: strategies for improving communication efficiency. arXiv:1610.05492"},{"key":"91_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41534-018-0113-z","volume":"5","author":"R LaRose","year":"2019","unstructured":"LaRose R, Tikku A, O\u2019Neel-Judy \u00c9, Cincio L, Coles PJ (2019) Variational quantum state diagonalization. Quantum Inf 5:1","journal-title":"Quantum Inf"},{"key":"91_CR29","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1016\/j.ins.2014.03.035","volume":"273","author":"H-S Li","year":"2014","unstructured":"Li H-S, Zhu Q, Li M-C, Ian H, et al. (2014) Multidimensional color image storage, retrieval, and compression based on quantum amplitudes and phases. Inf Sci 273:212","journal-title":"Inf Sci"},{"key":"91_CR30","doi-asserted-by":"publisher","first-page":"150503","DOI":"10.1103\/PhysRevLett.118.150503","volume":"118","author":"J Li","year":"2017","unstructured":"Li J, Yang X, Peng X, Sun C-P (2017) Hybrid quantum-classical approach to quantum optimal control. Phys Rev Lett 118:150503","journal-title":"Phys Rev Lett"},{"key":"91_CR31","doi-asserted-by":"crossref","unstructured":"Li W, Deng D-L (2021) Recent advances for quantum classifiers. Sci China Phys Mech Astron 65","DOI":"10.1007\/s11433-021-1793-6"},{"key":"91_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11433-021-1753-3","volume":"64","author":"W Li","year":"2021","unstructured":"Li W, Lu S, Deng D-L (2021a) Quantum federated learning through blind quantum computing. Sci China Phys Mech Astron 64:1","journal-title":"Sci China Phys Mech Astron"},{"key":"91_CR33","doi-asserted-by":"crossref","unstructured":"Li H-S, Fan P, Peng H, Song S, Long G-L (2021b) Multilevel 2-d quantum wavelet transforms. IEEE Transactions on Cybernetics","DOI":"10.1109\/TCYB.2021.3049509"},{"key":"91_CR34","doi-asserted-by":"publisher","first-page":"062324","DOI":"10.1103\/PhysRevA.98.062324","volume":"98","author":"J-G Liu","year":"2018","unstructured":"Liu J-G, Wang L (2018) Differentiable learning of quantum circuit born machines. Phys Rev A 98:062324","journal-title":"Phys Rev A"},{"key":"91_CR35","doi-asserted-by":"crossref","unstructured":"Liu J, Tang Y, Zhao H, Wang X, Li F, Zhang J (2022) Cps attack detection under limited local information in cyber security: a multi-node multi-class classification ensemble approach. arXiv:2209.00170","DOI":"10.1145\/3585520"},{"key":"91_CR36","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. Nature Phys 10:631","journal-title":"Nature Phys"},{"key":"91_CR37","doi-asserted-by":"publisher","first-page":"040502","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 121:040502","journal-title":"Phys Rev Lett"},{"key":"91_CR38","doi-asserted-by":"publisher","first-page":"014303","DOI":"10.1103\/PhysRevA.64.014303","volume":"64","author":"G-L Long","year":"2001","unstructured":"Long G-L, Sun Y (2001) Efficient scheme for initializing a quantum register with an arbitrary superposed state. Phys Rev A 64:014303","journal-title":"Phys Rev A"},{"key":"91_CR39","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10462-012-9338-y","volume":"42","author":"S Masoudnia","year":"2014","unstructured":"Masoudnia S, Ebrahimpour R (2014) Mixture of experts: a literature survey. Artif Intell Rev 42:275","journal-title":"Artif Intell Rev"},{"key":"91_CR40","unstructured":"McMahan B, Moore E, Ramage D, Hampson S, Arcas BAy (2017) Communication-efficient learning of deep networks from decentralized data. In: Singh A, Zhu J (eds) Proceedings of the 20th international conference on artificial intelligence and statistics, proceedings of machine learning research, vol 54. PMLR, pp. 1273\u20131282"},{"key":"91_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-018-07090-4","volume":"9","author":"JR McClean","year":"2018","unstructured":"McClean JR, Boixo S, Smelyanskiy VN, Babbush R, Neven H (2018) Barren plateaus in quantum neural network training landscapes. Nature Commun 9:1","journal-title":"Nature Commun"},{"key":"91_CR42","doi-asserted-by":"publisher","first-page":"032309","DOI":"10.1103\/PhysRevA.98.032309","volume":"98","author":"K Mitarai","year":"2018","unstructured":"Mitarai K, Negoro M, Kitagawa M, Fujii K (2018) Quantum circuit learning. Phys Rev A 98:032309","journal-title":"Phys Rev A"},{"key":"91_CR43","unstructured":"Nielsen MA, Chuang IL (2010) Quantum Computation and Quantum Information. (Cambridge University Press)"},{"key":"91_CR44","doi-asserted-by":"publisher","first-page":"032302","DOI":"10.1103\/PhysRevA.83.032302","volume":"83","author":"M Plesch","year":"2011","unstructured":"Plesch M, Brukner \u010c (2011) Quantum-state preparation with universal gate decompositions. Phys Rev A 83:032302","journal-title":"Phys Rev A"},{"key":"91_CR45","doi-asserted-by":"publisher","first-page":"130503","DOI":"10.1103\/PhysRevLett.113.130503","volume":"113","author":"P Rebentrost","year":"2014","unstructured":"Rebentrost P, Mohseni M, Lloyd S (2014) Quantum support vector machine for big data classification. Phys Rev Lett 113:130503","journal-title":"Phys Rev Lett"},{"key":"91_CR46","unstructured":"Rezende D, Mohamed S (2015) Variational inference with normalizing flows. In: International conference on machine learning, PMLR, pp 1530\u20131538"},{"key":"91_CR47","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41746-020-00323-1","volume":"3","author":"N Rieke","year":"2020","unstructured":"Rieke N, Hancox J, Li W, Milletari F, Roth HR, Albarqouni S, Bakas S, Galtier MN, Landman BA, Maier-Hein K, et al. (2020) The future of digital health with federated learning. NPJ Digit Med 3:1","journal-title":"NPJ Digit Med"},{"key":"91_CR48","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1023\/A:1026543900054","volume":"40","author":"Y Rubner","year":"2000","unstructured":"Rubner Y, Tomasi C, Guibas LJ (2000) The earth mover\u2019s distance as a metric for image retrieval. Int J Comput Vis 40:99","journal-title":"Int J Comput Vis"},{"key":"91_CR49","doi-asserted-by":"publisher","first-page":"e1249","DOI":"10.1002\/widm.1249","volume":"8","author":"O Sagi","year":"2018","unstructured":"Sagi O, Rokach L (2018) Ensemble learning: a survey. Wiley Interdiscip Rev Data Min Knowl Discov 8:e1249","journal-title":"Wiley Interdiscip Rev Data Min Knowl Discov"},{"key":"91_CR50","first-page":"189","volume":"22","author":"S Salehkaleybar","year":"2021","unstructured":"Salehkaleybar S, Sharif-Nassab A, Golestani SJ (2021) One-shot federated learning: theoretical limits and algorithms to achieve them. J Mach Learn Res 22:189","journal-title":"J Mach Learn Res"},{"key":"91_CR51","doi-asserted-by":"publisher","first-page":"040504","DOI":"10.1103\/PhysRevLett.122.040504","volume":"122","author":"M Schuld","year":"2019","unstructured":"Schuld M, Killoran N (2019) Quantum machine learning in feature hilbert spaces. Phys Rev Lett 122:040504","journal-title":"Phys Rev Lett"},{"key":"91_CR52","unstructured":"Swart JM (2020) Introduction to quantum probability. http:\/\/staff.utia.cas.cz\/swart\/lecture_notes\/qua20_04_27.pdf. Accessed: July 1 2022"},{"key":"91_CR53","doi-asserted-by":"crossref","unstructured":"Xia Q, Li Q (2021) Quantumfed: a federated learning framework for collaborative quantum training. In: 2021 IEEE global communications conference (GLOBECOM). IEEE, pp 1\u20136","DOI":"10.1109\/GLOBECOM46510.2021.9685012"},{"key":"91_CR54","doi-asserted-by":"publisher","first-page":"110502","DOI":"10.1103\/PhysRevLett.126.110502","volume":"126","author":"T Xin","year":"2021","unstructured":"Xin T, Che L, Xi C, Singh A, Nie X, Li J, Dong Y, Lu D (2021) Experimental quantum principal component analysis via parametrized quantum circuits. Phys Rev Lett 126:110502","journal-title":"Phys Rev Lett"},{"key":"91_CR55","unstructured":"Yun WJ, Kim JP, Jung S, Park J, Bennis M, Kim J (2022) Slimmable quantum federated learning. arXiv:2207.10221"},{"key":"91_CR56","doi-asserted-by":"crossref","unstructured":"Zhang S-X, Allcock J, Wan Z-Q, Liu S, Sun J, Yu H, Yang X-H, Qiu J, Ye Z, Chen Y-Q, et al. (2022) Tensorcircuit: a quantum software framework for the nisq era. arXiv:2205.10091","DOI":"10.22331\/q-2023-02-02-912"},{"key":"91_CR57","unstructured":"Zhao Y, Li M, Lai L, Suda N, Civin D, Chandra V (2018) Federated learning with non-iid data. arXiv:1806.00582"},{"key":"91_CR58","unstructured":"Zhou Y, Pu G, Ma X, Li X, Wu D (2020) Distilled one-shot federated learning. arXiv:2009.07999"},{"key":"91_CR59","doi-asserted-by":"crossref","unstructured":"Zhou Z-H (2021) Machine learning. Springer Nature","DOI":"10.1007\/978-981-15-1967-3"},{"key":"91_CR60","unstructured":"Zhu L, Liu Z, Han S (2019) Deep leakage from gradients. Adv Neural Inf Process Syst 32"}],"container-title":["Quantum Machine Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-022-00091-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s42484-022-00091-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s42484-022-00091-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T07:28:02Z","timestamp":1687159682000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s42484-022-00091-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,18]]},"references-count":60,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["91"],"URL":"https:\/\/doi.org\/10.1007\/s42484-022-00091-z","relation":{},"ISSN":["2524-4906","2524-4914"],"issn-type":[{"value":"2524-4906","type":"print"},{"value":"2524-4914","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,18]]},"assertion":[{"value":"25 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2023","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 author declares no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Competing interests"}}],"article-number":"3"}}