{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T11:48:42Z","timestamp":1774352922146,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T00:00:00Z","timestamp":1771891200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T00:00:00Z","timestamp":1771891200000},"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 Inf Process"],"DOI":"10.1007\/s11128-026-05094-4","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T10:54:55Z","timestamp":1771930495000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropy-based framework for quantum algorithm robustness: discriminating noise channel impacts on Shor\u2019s period finding and establishing critical performance thresholds"],"prefix":"10.1007","volume":"25","author":[{"given":"Suresh Kumar","family":"Samarla","sequence":"first","affiliation":[]},{"given":"P.","family":"Maragathavalli","sequence":"additional","affiliation":[]},{"given":"P. D. S. S. Lakshmi","family":"Kumari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,24]]},"reference":[{"key":"5094_CR1","doi-asserted-by":"publisher","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124\u2013134 (1994). https:\/\/doi.org\/10.1109\/SFCS.1994.365700","DOI":"10.1109\/SFCS.1994.365700"},{"issue":"6866","key":"5094_CR2","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1038\/414883a","volume":"414","author":"LMK Vandersypen","year":"2001","unstructured":"Vandersypen, L.M.K., Steffen, M., Breyta, G., Yannoni, C.S., Sherwood, M.H., Chuang, I.L.: Experimental realization of shor\u2019s quantum factoring algorithm using nuclear magnetic resonance. Nature 414(6866), 883\u2013887 (2001). https:\/\/doi.org\/10.1038\/414883a","journal-title":"Nature"},{"issue":"11","key":"5094_CR3","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1038\/nphoton.2012.259","volume":"6","author":"E Martin-Lopez","year":"2012","unstructured":"Martin-Lopez, E., Laing, A., Lawson, T., Alvarez, R., Zhou, X.-Q., O\u2019Brien, J.L.: Experimental realization of shor\u2019s quantum factoring algorithm using qubit recycling. Nat. Photon. 6(11), 773\u2013776 (2012). https:\/\/doi.org\/10.1038\/nphoton.2012.259","journal-title":"Nat. Photon."},{"key":"5094_CR4","doi-asserted-by":"publisher","unstructured":"Fowler, A.G.: Time-optimal quantum computation. arXiv preprint (2012) https:\/\/doi.org\/10.48550\/arXiv.1210.4626 . arXiv:1210.4626 [quant-ph]","DOI":"10.48550\/arXiv.1210.4626"},{"key":"5094_CR5","doi-asserted-by":"publisher","first-page":"433","DOI":"10.22331\/q-2021-04-15-433","volume":"5","author":"C Gidney","year":"2021","unstructured":"Gidney, C., Ekeraa, M.: How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum 5, 433 (2021). https:\/\/doi.org\/10.22331\/q-2021-04-15-433","journal-title":"Quantum"},{"issue":"4","key":"5094_CR6","first-page":"317","volume":"3","author":"J Proos","year":"2003","unstructured":"Proos, J., Zalka, C.: Shor\u2019s discrete logarithm quantum algorithm for elliptic curves. Quantum Inf. Comput. 3(4), 317\u2013344 (2003)","journal-title":"Quantum Inf. Comput."},{"issue":"2","key":"5094_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-021-03391-8","volume":"21","author":"M Ekeraa","year":"2022","unstructured":"Ekeraa, M.: On the success probability of quantum order finding. Quantum Inf. Process. 21(2), 1\u201339 (2022). https:\/\/doi.org\/10.1007\/s11128-021-03391-8. arXiv:2109.08041","journal-title":"Quantum Inf. Process."},{"issue":"7779","key":"5094_CR8","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1038\/s41586-019-1666-5","volume":"574","author":"F Arute","year":"2019","unstructured":"Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G.S.L., Buell, D.A., et al.: Quantum supremacy using a programmable superconducting processor. Nature 574(7779), 505\u2013510 (2019). https:\/\/doi.org\/10.1038\/s41586-019-1666-5","journal-title":"Nature"},{"key":"5094_CR9","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition, (2010). https:\/\/www.cambridge.org\/9781107002173"},{"issue":"11","key":"5094_CR10","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s11128-023-04149-0","volume":"22","author":"T-L Huang","year":"2023","unstructured":"Huang, T.-L., Wu, Y.-Z., Ni, M., Wang, S., Ye, Y.-J.: Effect of quantum noise on the performance of shor\u2019s algorithm. Quantum Inf. Process. 22(11), 399 (2023). https:\/\/doi.org\/10.1007\/s11128-023-04149-0","journal-title":"Quantum Inf. Process."},{"issue":"1\u20132","key":"5094_CR11","doi-asserted-by":"publisher","first-page":"97","DOI":"10.2478\/qic-2025-0006","volume":"25","author":"L Gyongyosi","year":"2025","unstructured":"Gyongyosi, L., Imre, S.: Networked quantum services. Quantum Inf. Comput. 25(1\u20132), 97\u2013140 (2025). https:\/\/doi.org\/10.2478\/qic-2025-0006","journal-title":"Quantum Inf. Comput."},{"issue":"11","key":"5094_CR12","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1145\/3524455","volume":"65","author":"R Van Meter","year":"2022","unstructured":"Van Meter, R., Dakic, B.: Advances in the quantum internet. Commun. ACM 65(11), 66\u201375 (2022). https:\/\/doi.org\/10.1145\/3524455","journal-title":"Commun. ACM"},{"issue":"1","key":"5094_CR13","doi-asserted-by":"publisher","first-page":"1149","DOI":"10.1109\/COMST.2017.2786748","volume":"20","author":"L Gyongyosi","year":"2018","unstructured":"Gyongyosi, L., Imre, S., Nguyen, H.T.: A survey on quantum channel capacities. IEEE Commun. Surv. Tutor. 20(1), 1149\u20131205 (2018). https:\/\/doi.org\/10.1109\/COMST.2017.2786748","journal-title":"IEEE Commun. Surv. Tutor."},{"issue":"1","key":"5094_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41598-020-76728-5","volume":"10","author":"TS Humble","year":"2020","unstructured":"Humble, T.S., Gottesman, D., Kawakami, E., Monroe, C., Rieffel, E.G., Smith, R.S., Van Meter, R.: Scalable distributed gate-model quantum computers. Sci. Rep. 10(1), 1\u201315 (2020). https:\/\/doi.org\/10.1038\/s41598-020-76728-5","journal-title":"Sci. Rep."},{"issue":"9","key":"5094_CR15","doi-asserted-by":"publisher","first-page":"1196","DOI":"10.3390\/e24091196","volume":"24","author":"I Tajti","year":"2022","unstructured":"Tajti, I., Gyongyosi, L.: Adaptive problem solving dynamics in gate-model quantum computers. Entropy 24(9), 1196 (2022). https:\/\/doi.org\/10.3390\/e24091196","journal-title":"Entropy"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05094-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-026-05094-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05094-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T09:55:31Z","timestamp":1774346131000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-026-05094-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,24]]},"references-count":15,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["5094"],"URL":"https:\/\/doi.org\/10.1007\/s11128-026-05094-4","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,24]]},"assertion":[{"value":"29 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2026","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 that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable. This manuscript does not contain data from any individual person.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"Not applicable. The study does not involve human participants or animal experiments.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}}],"article-number":"85"}}