{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T04:00:06Z","timestamp":1773201606881,"version":"3.50.1"},"reference-count":31,"publisher":"Elsevier BV","issue":"3-6","license":[{"start":{"date-parts":[[2003,3,1]],"date-time":"2003-03-01T00:00:00Z","timestamp":1046476800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2003,3]]},"DOI":"10.1016\/s0378-4754(02)00239-2","type":"journal-article","created":{"date-parts":[[2003,3,4]],"date-time":"2003-03-04T16:29:22Z","timestamp":1046795362000},"page":"219-230","source":"Crossref","is-referenced-by-count":9,"title":["From Monte Carlo to quantum computation"],"prefix":"10.1016","volume":"62","author":[{"given":"Stefan","family":"Heinrich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0378-4754(02)00239-2_BIB1","unstructured":"D. Aharonov, Quantum computation\u2014a review, in: Annual Review of Computational Physics, vol. VI, World Scientific, Dietrich Stauffer, 1998; see also http:\/\/arxiv.org\/abs\/quant-ph\/9812037."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB2","unstructured":"D.S. Abrams, C.P. Williams, Fast quantum algorithms for numerical integrals and stochastic processes, Technical report, 1999; see also http:\/\/arxiv.org\/abs\/quant-ph\/9908083."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB3","doi-asserted-by":"crossref","unstructured":"R. Beals, H. Buhrman, R. Cleve, M. Mosca, R. de Wolf, Quantum lower bounds by polynomials, in: Proceedings of 39th IEEE FOCS, 1998, pp. 352\u2013361; see also http:\/\/arxiv.org\/abs\/quant-ph\/9802049.","DOI":"10.1109\/SFCS.1998.743485"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB4","doi-asserted-by":"crossref","unstructured":"M. Boyer, P. Brassard, P. H\u00f8yer, A. Tapp, Tight bounds on quantum searching, Fortschritte Phys. 46 (1998) 493\u2013505; see also http:\/\/arxiv.org\/abs\/quant-ph\/9605034.","DOI":"10.1002\/(SICI)1521-3978(199806)46:4\/5<493::AID-PROP493>3.0.CO;2-P"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB5","unstructured":"G. Brassard, P.H\u00f8yer, M. Mosca, A. Tapp, Quantum amplitude amplification and estimation, Technical report, 2000; see also http:\/\/arxiv.org\/abs\/quant-ph\/0005055."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB6","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1098\/rspa.1985.0070","article-title":"Quantum theory, the Church\u2013Turing principle and the universal quantum computer","volume":"400","author":"Deutsch","year":"1985","journal-title":"Proc. R. Soc. London Ser. A"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB7","doi-asserted-by":"crossref","unstructured":"A. Ekert, P. Hayden, H. Inamori, Basic concepts in quantum computation, 2000; see also http:\/\/arxiv.org\/abs\/quant-ph\/0011013.","DOI":"10.1142\/9789812811264_0016"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB8","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF02650179","article-title":"Simulating physics with computers","volume":"21","author":"Feynman","year":"1982","journal-title":"Int. J. Theor. Phys."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB9","doi-asserted-by":"crossref","unstructured":"L. Grover, A fast quantum mechanical algorithm for database search, in: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, ACM Press, New York, 1996, pp. 212\u2013219; see also http:\/\/arxiv.org\/abs\/quant-ph\/9605043.","DOI":"10.1145\/237814.237866"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB10","unstructured":"J. Gruska, Quantum Computing, McGraw-Hill, London, 1999."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB11","unstructured":"S. Heinrich, Random approximation in numerical analysis, In: K.D. Bierstedt, A. Pietsch, W. M. Ruess, D. Vogt (Eds.), Functional Analysis, Marcel Dekker, New York, 1993, pp. 123\u2013171."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB12","doi-asserted-by":"crossref","unstructured":"S. Heinrich, Quantum summation with an application to integration, J. Complexity 18 (2002) 1\u201350; see also http:\/\/arxiv.org\/abs\/quant-ph\/0105116.","DOI":"10.1006\/jcom.2001.0629"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB13","unstructured":"S. Heinrich, Quantum integration in Sobolev classes, J. Complexity, 2002, in press; see also http:\/\/arxiv.org\/abs\/quant-ph\/0112153."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB14","doi-asserted-by":"crossref","unstructured":"S. Heinrich, E. Novak, Optimal summation and integration by deterministic, randomized, and quantum algorithms, In: K.-T. Fang, F.J. Hickernell, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2000, Springer, Berlin, 2002, pp. 50\u201362; see also http:\/\/arxiv.org\/abs\/quant-ph\/0105114.","DOI":"10.1007\/978-3-642-56046-0_4"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB15","unstructured":"S. Heinrich, E. Novak, On a problem in quantum summation. J. Complexity, 2002, in press; see also http:\/\/arxiv.org\/abs\/quant-ph\/0109038."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB16","unstructured":"Y.I. Manin, Computable and uncomputable, Sovetskoye Radio, Moscow, 1980 (in Russian)."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB17","unstructured":"Y.I. Manin, Classical computing, quantum computing, and Shor\u2019s factoring algorithm, 1999; see also http:\/\/arxiv.org\/abs\/quant-ph\/9903008."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB18","doi-asserted-by":"crossref","unstructured":"A. Nayak, F. Wu, The quantum query complexity of approximating the median and related statistics, STOC, May 1999, pp. 384\u2013393; see also http:\/\/arxiv.org\/abs\/quant-ph\/9804066.","DOI":"10.1145\/301250.301349"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB19","unstructured":"M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB20","doi-asserted-by":"crossref","unstructured":"E. Novak, Deterministic and stochastic error bounds in numerical analysis, Lecture Notes Math. 1349 (1988).","DOI":"10.1007\/BFb0079792"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB21","doi-asserted-by":"crossref","unstructured":"E. Novak, Quantum complexity of integration, J. Complexity 17 (2001) 2\u201316; see also http:\/\/arxiv.org\/abs\/quant-ph\/0008124.","DOI":"10.1006\/jcom.2000.0566"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB22","doi-asserted-by":"crossref","unstructured":"A.O. Pittenger, Introduction to Quantum Computing Algorithms, Birkh\u00e4user, Boston, 1999.","DOI":"10.1007\/978-1-4612-1390-1"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB23","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/0022-314X(80)90084-0","article-title":"Probabilistic algorithm for testing primality","volume":"12","author":"Rabin","year":"1980","journal-title":"J. Number Theor."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB24","doi-asserted-by":"crossref","unstructured":"P.W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 124\u2013134; see also http:\/\/arxiv.org\/abs\/quant-ph\/9508027.","DOI":"10.1109\/SFCS.1994.365700"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB25","unstructured":"P.W. Shor, Introduction to quantum algorithms, 2000; see also http:\/\/arxiv.org\/abs\/quant-ph\/0005003."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB26","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1137\/0206006","article-title":"A fast Monte Carlo test for primality","volume":"6","author":"Solovay","year":"1977","journal-title":"SIAM J. Comput."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB27","unstructured":"J.F. Traub, H. Wo\u017aniakowski, Path integration on a quantum computer, 2001; see also http:\/\/arxiv.org\/abs\/quant-ph\/0109113."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB28","unstructured":"J.F. Traub, G.W. Wasilkowski, H. Wo\u017aniakowski, Information-Based Complexity, Academic Press, New York, 1988."},{"key":"10.1016\/S0378-4754(02)00239-2_BIB29","doi-asserted-by":"crossref","unstructured":"G. Brassard, P. H\u00f8yer, A. Tapp, Quantum counting, Lecture Notes Comput. Sci. 1443 (1998) 820\u2013831; see also http:\/\/arxiv.org\/abs\/quant-ph\/9805082.","DOI":"10.1007\/BFb0055105"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB30","doi-asserted-by":"crossref","unstructured":"L. Grover, A framework for fast quantum mechanical algorithms, in: Proceedings of the 30th Annual ACM Symposium on the Theory of Computing, ACM Press, New York, 1998, pp. 53\u201362; see also http:\/\/arxiv.org\/abs\/quant-ph\/9711043.","DOI":"10.1145\/276698.276712"},{"key":"10.1016\/S0378-4754(02)00239-2_BIB31","doi-asserted-by":"crossref","unstructured":"P.W. Shor, Quantum computing, Documenta Math. ICM I (1998) 467\u2013486.","DOI":"10.4171\/dms\/1-1\/16"}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475402002392?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475402002392?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2023,4,25]],"date-time":"2023-04-25T21:32:22Z","timestamp":1682458342000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475402002392"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":31,"journal-issue":{"issue":"3-6","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["S0378475402002392"],"URL":"https:\/\/doi.org\/10.1016\/s0378-4754(02)00239-2","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2003,3]]}}}