{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T12:48:12Z","timestamp":1753274892850,"version":"3.37.3"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2024,11,6]],"date-time":"2024-11-06T00:00:00Z","timestamp":1730851200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,11,6]],"date-time":"2024-11-06T00:00:00Z","timestamp":1730851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62373078"],"award-info":[{"award-number":["62373078"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-024-04581-w","type":"journal-article","created":{"date-parts":[[2024,11,6]],"date-time":"2024-11-06T16:04:18Z","timestamp":1730909058000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Towards an efficient implementation of Dempster\u2013Shafer: $$\\alpha $$-junction fusion rules on quantum circuits"],"prefix":"10.1007","volume":"23","author":[{"given":"Linxuan","family":"Li","sequence":"first","affiliation":[]},{"given":"Qianli","family":"Zhou","sequence":"additional","affiliation":[]},{"given":"Zhen","family":"Li","sequence":"additional","affiliation":[]},{"given":"Yong","family":"Deng","sequence":"additional","affiliation":[]},{"given":"\u00c9loi","family":"Boss\u00e9","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,11,6]]},"reference":[{"key":"4581_CR1","doi-asserted-by":"crossref","unstructured":"Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. In: Classic Works of the Dempster-Shafer Theory of Belief Functions, pp. 57\u201372. Springer, Berlin (2008)","DOI":"10.1007\/978-3-540-44792-4_3"},{"key":"4581_CR2","doi-asserted-by":"publisher","DOI":"10.1515\/9780691214696","volume-title":"A Mathematical Theory of Evidence","author":"G Shafer","year":"1976","unstructured":"Shafer, G.: A Mathematical Theory of Evidence, vol. 42. Princeton University Press, Princeton (1976)"},{"key":"4581_CR3","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2024.109034","volume":"490","author":"Y Wang","year":"2024","unstructured":"Wang, Y., Li, Z., Deng, Y.: A new orthogonal sum in random permutation set. Fuzzy Sets Syst 490, 109034 (2024). https:\/\/doi.org\/10.1016\/j.fss.2024.109034","journal-title":"Fuzzy Sets Syst"},{"key":"4581_CR4","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1016\/j.inffus.2022.08.030","volume":"89","author":"X Deng","year":"2023","unstructured":"Deng, X., Xue, S., Jiang, W.: A novel quantum model of mass function for uncertain information fusion. Inf Fusion 89, 619\u2013631 (2023)","journal-title":"Inf Fusion"},{"key":"4581_CR5","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.109680","volume":"255","author":"L Fei","year":"2022","unstructured":"Fei, L., Wang, Y.: An optimization model for rescuer assignments under an uncertain environment by using Dempster\u2013Shafer theory. Knowl. Based Syst. 255, 109680 (2022)","journal-title":"Knowl. Based Syst."},{"key":"4581_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2024.110474","author":"H Wang","year":"2024","unstructured":"Wang, H., Abdin, A.F., Fang, Y.-P., Puchinger, J., Zio, E.: Coordinating dynamic traffic-power systems under decentralized and centralized decision environments. Comput. Ind. Eng. (2024). https:\/\/doi.org\/10.1016\/j.cie.2024.110474","journal-title":"Comput. Ind. Eng."},{"key":"4581_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2023.114388","volume":"178","author":"T Zhao","year":"2024","unstructured":"Zhao, T., Li, Z., Deng, Y.: Linearity in Deng entropy. Chaos Solitons Fractals 178, 114388 (2024). https:\/\/doi.org\/10.1016\/j.chaos.2023.114388","journal-title":"Chaos Solitons Fractals"},{"key":"4581_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2024.114976","volume":"184","author":"T Zhan","year":"2024","unstructured":"Zhan, T., Zhou, J., Li, Z., Deng, Y.: Generalized information entropy and generalized information dimension. Chaos Solitons Fractals 184, 114976 (2024)","journal-title":"Chaos Solitons Fractals"},{"key":"4581_CR9","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.ins.2023.03.059","volume":"633","author":"L Pan","year":"2023","unstructured":"Pan, L., Gao, X.: Evidential Markov decision-making model based on belief entropy to predict interference effects. Inf. Sci. 633, 10\u201326 (2023)","journal-title":"Inf. Sci."},{"key":"4581_CR10","doi-asserted-by":"publisher","unstructured":"Deng, J., Deng, Y., Yang, J.-B.: Random permutation set reasoning. In: IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 1\u201312 (2024). https:\/\/doi.org\/10.1109\/TPAMI.2024.3438349","DOI":"10.1109\/TPAMI.2024.3438349"},{"issue":"9","key":"4581_CR11","doi-asserted-by":"publisher","DOI":"10.1063\/5.0220154","volume":"34","author":"J Zhou","year":"2024","unstructured":"Zhou, J., Li, Z., Deng, Y.: Random walk in random permutation set theory. Chaos Interdiscip. J. Nonlinear Sci. 34(9), 093137 (2024). https:\/\/doi.org\/10.1063\/5.0220154","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"issue":"8","key":"4581_CR12","doi-asserted-by":"publisher","first-page":"4772","DOI":"10.1109\/TSMC.2024.3389464","volume":"54","author":"Z Zhang","year":"2024","unstructured":"Zhang, Z., Liu, Z., Tian, H., Martin, A.: Mixed-type imputation for missing data credal classification via quality matrices. IEEE Trans. Syst. Man. Cybern. Syst. 54(8), 4772\u20134785 (2024). https:\/\/doi.org\/10.1109\/TSMC.2024.3389464","journal-title":"IEEE Trans. Syst. Man. Cybern. Syst."},{"key":"4581_CR13","doi-asserted-by":"publisher","unstructured":"Huang, L., Fan, J., Liew, A.W.-C.: Integration of multikinds imputation with covariance adaptation based on evidence theory. In: IEEE Transactions on Neural Networks and Learning Systems, pp. 1\u201315 (2024). https:\/\/doi.org\/10.1109\/TNNLS.2024.3412371","DOI":"10.1109\/TNNLS.2024.3412371"},{"key":"4581_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TIM.2024.3443349","volume":"73","author":"L Huang","year":"2024","unstructured":"Huang, L., Liu, G.: Convolutional feature aggregation network with self-supervised learning and decision fusion for sar target recognition. IEEE Trans. Instrum. Meas. 73, 1\u201314 (2024). https:\/\/doi.org\/10.1109\/TIM.2024.3443349","journal-title":"IEEE Trans. Instrum. Meas."},{"issue":"3","key":"4581_CR15","doi-asserted-by":"publisher","first-page":"2097","DOI":"10.1109\/TWC.2023.3295382","volume":"23","author":"J Wang","year":"2024","unstructured":"Wang, J., Jiang, C., Kuang, L., Han, R.: Satellite multi-beam collaborative scheduling in satellite aviation communications. IEEE Trans. Wirel. Commun. 23(3), 2097\u20132111 (2024). https:\/\/doi.org\/10.1109\/TWC.2023.3295382","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"5","key":"4581_CR16","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1109\/MCOM.001.2100850","volume":"60","author":"J Wang","year":"2022","unstructured":"Wang, J., Jiang, C., Kuang, L.: High-mobility satellite-uav communications: Challenges, solutions, and future research trends. IEEE Commun. Mag. 60(5), 38\u201343 (2022). https:\/\/doi.org\/10.1109\/MCOM.001.2100850","journal-title":"IEEE Commun. Mag."},{"issue":"1\u20132","key":"4581_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0888-613X(02)00066-X","volume":"31","author":"P Smets","year":"2002","unstructured":"Smets, P.: The application of the matrix calculus to belief functions. Int. J. Approx. Reason. 31(1\u20132), 1\u201330 (2002)","journal-title":"Int. J. Approx. Reason."},{"issue":"7280","key":"4581_CR18","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1038\/463441a","volume":"463","author":"E Knill","year":"2010","unstructured":"Knill, E.: Quantum computing. Nature 463(7280), 441\u2013443 (2010)","journal-title":"Nature"},{"issue":"2","key":"4581_CR19","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"PW Shor","year":"1999","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303\u2013332 (1999)","journal-title":"SIAM Rev."},{"key":"4581_CR20","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"issue":"15","key":"4581_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.103.150502","volume":"103","author":"AW Harrow","year":"2009","unstructured":"Harrow, A.W., Hassidim, A., Lloyd, S.: Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103(15), 150502 (2009)","journal-title":"Phys. Rev. Lett."},{"key":"4581_CR22","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)","journal-title":"Quantum"},{"issue":"9","key":"4581_CR23","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, S.C., Endo, S., Fujii, K., McClean, J.R., Mitarai, K., Yuan, X., Cincio, L., et al.: Variational quantum algorithms. Nat. Rev. Phys. 3(9), 625\u2013644 (2021)","journal-title":"Nat. Rev. Phys."},{"key":"4581_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2022.08.003","volume":"986","author":"J Tilly","year":"2022","unstructured":"Tilly, J., Chen, H., Cao, S., Picozzi, D., Setia, K., Li, Y., Grant, E., Wossnig, L., Rungger, I., Booth, G.H., et al.: The variational quantum eigensolver: a review of methods and best practices. Phys. Rep. 986, 1\u2013128 (2022)","journal-title":"Phys. Rep."},{"key":"4581_CR25","doi-asserted-by":"publisher","first-page":"899","DOI":"10.22331\/q-2023-01-19-899","volume":"7","author":"C Lyu","year":"2023","unstructured":"Lyu, C., Xu, X., Yung, M.-H., Bayat, A.: Symmetry enhanced variational quantum spin eigensolver. Quantum 7, 899 (2023)","journal-title":"Quantum"},{"issue":"4","key":"4581_CR26","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.: Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4(4), 043001 (2019)","journal-title":"Quantum Sci. Technol."},{"key":"4581_CR27","doi-asserted-by":"publisher","first-page":"1188","DOI":"10.22331\/q-2023-11-22-1188","volume":"7","author":"C Bravo-Prieto","year":"2023","unstructured":"Bravo-Prieto, C., LaRose, R., Cerezo, M., Subasi, Y., Cincio, L., Coles, P.J.: Variational quantum linear solver. Quantum 7, 1188 (2023)","journal-title":"Quantum"},{"issue":"7671","key":"4581_CR28","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1038\/nature23879","volume":"549","author":"A Kandala","year":"2017","unstructured":"Kandala, A., Mezzacapo, A., Temme, K., Takita, M., Brink, M., Chow, J.M., Gambetta, J.M.: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549(7671), 242\u2013246 (2017)","journal-title":"Nature"},{"key":"4581_CR29","doi-asserted-by":"publisher","first-page":"191","DOI":"10.22331\/q-2019-10-07-191","volume":"3","author":"X Yuan","year":"2019","unstructured":"Yuan, X., Endo, S., Zhao, Q., Li, Y., Benjamin, S.C.: Theory of variational quantum simulation. Quantum 3, 191 (2019)","journal-title":"Quantum"},{"issue":"3","key":"4581_CR30","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.1.033062","volume":"1","author":"KM Nakanishi","year":"2019","unstructured":"Nakanishi, K.M., Mitarai, K., Fujii, K.: Subspace-search variational quantum eigensolver for excited states. Phys. Rev. Res. 1(3), 033062 (2019)","journal-title":"Phys. Rev. Res."},{"key":"4581_CR31","unstructured":"Johnson, P.D., Romero, J., Olson, J., Cao, Y., Aspuru-Guzik, A.: Qvector: an algorithm for device-tailored quantum error correction. arXiv preprint arXiv:1711.02249 (2017)"},{"key":"4581_CR32","doi-asserted-by":"crossref","unstructured":"Resconi, G., Nikolov, B.: Tests and entity in evidence theory and quantum mechanics. In: Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569), vol. 3, pp. 1723\u20131728. IEEE (2001)","DOI":"10.1109\/NAFIPS.2001.943812"},{"issue":"8","key":"4581_CR33","doi-asserted-by":"publisher","DOI":"10.1063\/1.4891972","volume":"55","author":"A Vourdas","year":"2014","unstructured":"Vourdas, A.: Quantum probabilities as Dempster\u2013Shafer probabilities in the lattice of subspaces. J. Math. Phys. 55(8), 082107 (2014)","journal-title":"J. Math. Phys."},{"issue":"2","key":"4581_CR34","doi-asserted-by":"publisher","first-page":"2054","DOI":"10.1109\/TPAMI.2022.3167045","volume":"45","author":"F Xiao","year":"2023","unstructured":"Xiao, F., Pedrycz, W.: Negation of the quantum mass function for multisource quantum information fusion with its application to pattern classification. IEEE Trans. Pattern Anal. Mach. Intell. 45(2), 2054\u20132070 (2023). https:\/\/doi.org\/10.1109\/TPAMI.2022.3167045","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"4581_CR35","doi-asserted-by":"crossref","unstructured":"Deng, X., Jiang, W.: Quantum representation of basic probability assignments based on mixed quantum states. In: 2021 IEEE 24th International Conference on Information Fusion (FUSION), pp. 1\u20136. IEEE (2021)","DOI":"10.23919\/FUSION49465.2021.9626984"},{"issue":"11","key":"4581_CR36","doi-asserted-by":"publisher","first-page":"14329","DOI":"10.1007\/s10489-022-04181-0","volume":"53","author":"F Xiao","year":"2023","unstructured":"Xiao, F.: Generalized quantum evidence theory. Appl. Intell. 53(11), 14329\u201314344 (2023)","journal-title":"Appl. Intell."},{"key":"4581_CR37","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2023.119885","volume":"223","author":"Q Zhou","year":"2023","unstructured":"Zhou, Q., Tian, G., Deng, Y.: Bf-qc: Belief functions on quantum circuits. Expert Syst. Appl. 223, 119885 (2023). https:\/\/doi.org\/10.1016\/j.eswa.2023.119885","journal-title":"Expert Syst. Appl."},{"key":"4581_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112962","volume":"166","author":"Q Zhou","year":"2023","unstructured":"Zhou, Q., Deng, Y.: Generating sierpinski gasket from matrix calculus in Dempster\u2013Shafer theory. Chaos Solitons Fractals 166, 112962 (2023)","journal-title":"Chaos Solitons Fractals"},{"key":"4581_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.inffus.2023.102070","volume":"102","author":"H Luo","year":"2024","unstructured":"Luo, H., Zhou, Q., Li, Z., Deng, Y.: Variational quantum linear solver-based combination rules in Dempster\u2013Shafer theory. Inf. Fusion 102, 102070 (2024)","journal-title":"Inf. Fusion"},{"key":"4581_CR40","unstructured":"Pichon, F., Den\u0153ux, T.: Interpretation and computation of alpha-junctions for combining belief functions. In: 6th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA\u201909) (2009)"},{"key":"4581_CR41","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th, Anniversary Edition. Cambridge University Press, Cambridge (2010)"},{"key":"4581_CR42","unstructured":"Romero, S.V., Santos-Su\u00e1rez, J.: Paulicomposer: compute tensor products of pauli matrices efficiently. arXiv preprint arXiv:2301.00560 (2023)"},{"issue":"2","key":"4581_CR43","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s11128-023-03869-7","volume":"22","author":"IF Araujo","year":"2023","unstructured":"Araujo, I.F., Park, D.K., Ludermir, T.B., Oliveira, W.R., Petruccione, F., Silva, A.J.: Configurable sublinear circuits for quantum state preparation. Quantum Inf. Process. 22(2), 123 (2023)","journal-title":"Quantum Inf. Process."},{"key":"4581_CR44","doi-asserted-by":"crossref","unstructured":"Smets, P.: The $$\\alpha $$-junctions: combination operators applicable to belief functions. In: International Joint Conference on Qualitative and Quantitative Practical Reasoning, pp. 131\u2013153. Springer (1997)","DOI":"10.1007\/BFb0035618"},{"key":"4581_CR45","doi-asserted-by":"publisher","unstructured":"Qiskit: An open-source framework for quantum computing (2023). https:\/\/doi.org\/10.5281\/zenodo.2573505","DOI":"10.5281\/zenodo.2573505"},{"issue":"5","key":"4581_CR46","first-page":"170","volume":"43","author":"MJ Powell","year":"2007","unstructured":"Powell, M.J.: A view of algorithms for optimization without derivatives. Math. Today Bull. Inst. Math. Appl. 43(5), 170\u2013174 (2007)","journal-title":"Math. Today Bull. Inst. Math. Appl."},{"issue":"6","key":"4581_CR47","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1007\/s11128-021-03140-x","volume":"20","author":"A Pellow-Jarman","year":"2021","unstructured":"Pellow-Jarman, A., Sinayskiy, I., Pillay, A., Petruccione, F.: A comparison of various classical optimizers for a variational quantum linear solver. Quantum Inf. Process. 20(6), 202 (2021)","journal-title":"Quantum Inf. Process."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04581-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-024-04581-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04581-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T07:25:19Z","timestamp":1732865119000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-024-04581-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,6]]},"references-count":47,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["4581"],"URL":"https:\/\/doi.org\/10.1007\/s11128-024-04581-w","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2024,11,6]]},"assertion":[{"value":"26 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"374"}}