# From Monte Carlo to Quantum Computation

- Published: 23 Dec 2001

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[1] D. Aharonov (1998): Quantum computation - a review. In: Annual Review of Computational Physics, World Scientific, volume VI, ed. Dietrich Stauffer, see also http://arXiv.org/abs/quant-ph/9812037.

[3] R. Beals, H. Buhrman, R. Cleve, M. Mosca, and R. de Wolf (1998): Quantum lower bounds by polynomials. Proceedings of 39th IEEE FOCS, 352-361, see also http://arXiv.org/abs/quant-ph/9802049. [OpenAIRE]

[4] M. Boyer, P. Brassard, P. Høyer, and A. Tapp (1998): Tight bounds on quantum searching. Fortschritte der Physik 46, 493 - 505, see also http://arXiv.org/abs/quant-ph/9605034.

[5] G. Brassard, P. Høyer, M. Mosca, and A. Tapp (2000): Quantum amplitude amplification and estimation. Technical report, http://arXiv.org/abs/quantph/0005055. [OpenAIRE]

[6] G. Brassard, P. Høyer, and A. Tapp (1998): Quantum counting. Lect. Notes in Comp. Science 1443, 820 - 831, see also http://arXiv.org/abs/quant-ph/9805082.

[7] D. Deutsch (1985): Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond., Ser. A 400, 97-117.

[8] A. Ekert, P. Hayden, and H. Inamori (2000): Basic concepts in quantum computation. See http://arXiv.org/abs/quant-ph/0011013. [OpenAIRE]

[9] R. Feynman (1982): Simulating physics with computers. Int. J. Theor. Phys. 21, 467-488.

[10] L. Grover (1996): A fast quantum mechanical algorithm for database search. Proc. 28 Annual ACM Symp. on the Theory of Computing, 212-219, ACM Press New York. See also http://arXiv.org/abs/quant-ph/9605043. [OpenAIRE]

[11] L. Grover (1998): A framework for fast quantum mechanical algorithms. Proc. 30 Annual ACM Symp. on the Theory of Computing, 53-62, ACM Press New York. See also http://arXiv.org/abs/quant-ph/9711043.

[12] J. Gruska (1999): Quantum Computing. McGraw-Hill, London.

[13] S. Heinrich (1993): Random approximation in numerical analysis. In: K. D. Bierstedt, A. Pietsch, W. M. Ruess, and D. Vogt, editors, Functional Analysis, 123 - 171, Marcel Dekker.

[14] S. Heinrich (2001): Quantum summation with an application to integration. Journal of Complexity (to appear). See also http://arXiv.org/abs/quantph/0105116.

[15] S. Heinrich (2001): Quantum integration in Sobolev classes (in preparation).

[16] S. Heinrich and E. Novak (2001a): Optimal summation and integration by deterministic, randomized, and quantum algorithms. In: K.-T. Fang, F. J. Hickernell, and H. Niederreiter, editors, Monte Carlo and QuasiMonte Carlo Methods 2000, Springer-Verlag, Berlin (to appear), see also http://arXiv.org/abs/quant-ph/0105114.

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