Randomized and quantum algorithms yeild a speed-up for initial-value problems

Journal of Complexity

Volumn 20, Issue 6, 2004, Pages 821-834

  Kacewicz, Bolesław ^a  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

Initial value problems; Quantum algorithms; Randomized algorithms

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; INTEGRATION; NUMERICAL ANALYSIS; ORDINARY DIFFERENTIAL EQUATIONS; RANDOM PROCESSES;

QUANTUM ALGORITHMS; RANDOMIZED ALGORITHMS;

INITIAL VALUE PROBLEMS;

EID: 10244234121     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jco.2004.05.002     Document Type: Article

References (14)

1. G. Brassard, P. HØoyer, M. Mosca, A. Tapp, Quantum amplitude amplification and estimation, Technical Report, 2000; http://arXiv.org/abs/quant-ph/0005055.
2. L. Grover, A fast quantum mechanical algorithm for database search, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, ACM Press, New York, 1996, pp. 212-219; see also http://arXiv.org/abs/quant-ph/9605043.
3. S. Heinrich, Quantum summation with an application to integration, J. Complexity 18 (2002) 1-50.
4. p spaces, J. Complexity 20 (2004) 5-26 see also http://arXiv.org/abs/quant-ph/0305030.
5. S. Heinrich, Quantum approximation II. Sobolev embeddings, J. Complexity 20 (2004) 27-45 see also http://arXiv.org/abs/quant-ph/0305031.
6. 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. 50-62 see also http://arXiv.org/abs/quant-ph/0105114.
7. B. Kacewicz, How to increase the order to get minimal-error algorithms for systems of ODEs, Numer. Math. 45 (1984) 93-104.
8. B. Kacewicz, Minimum asymptotic error of algorithms for solving ODE, J. Complexity 4 (1988) 373-389.
9. B. Kacewicz, On sequential and parallel solution of initial value problems, J. Complexity 6 (1990) 136-148.
10. A. Nayak, F. Wu, The quantum query complexity of approximating the median and related statistics, STOC, May 1999, pp. 384-393; see also http://arXiv.org/abs/quant-ph/9804066.
11. E. Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis, in: Lecture Notes in Mathematics, Vol. 1349, Springer, Berlin, 1988.
12. E. Novak, Quantum complexity of integration, J. Complexity 17 (2001) 2-16 see also http://arXiv.org/abs/quant-ph/0008124.
13. P.W. Shor, Algorithms for quantum computation: discrete logarithms and factoring, Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124-134, IEEE Computer Society Press, Los Alamitos, CA; see also http://arXiv.org/abs/quant-ph/9508027.
14. J.F. Traub, H. Wońiakowski, Path integration on a quantum computer, 2001; Technical Report, http://arXiv.org/abs/quant-ph/0109113.