Quantum approximation I. embeddings of finite-dimensional Lp spaces

Journal of Complexity

Volumn 20, Issue 1, 2004, Pages 5-26

  Heinrich, Stefan ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1242322161     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jco.2003.08.002     Document Type: Article

References (26)

1. D. Aharonov, Quantum computation - a review, in: D. Stauffer (Ed.), Annual Review of Computational Physics, Vol. VI, World Scientific, Singapore, 1998; see also http://arXiv.org/abs/quant-ph/9812037.
2. R. Beals, H. Buhrman, R. Cleve, M. Mosca, R. de Wolf, Quantum lower bounds by polynomials, Proceedings of 39th IEEE FOCS, 1998, pp. 352-361; see also http://arXiv.org/abs/quant-ph/9802049.
3. G. Brassard, P. Høyer, M. Mosca, A. Tapp, Quantum amplitude amplification and estimation, 2000; see http://arXiv.org/abs/quant-ph/0005055.
4. A. Ekert, P. Hayden, H. Inamori, Basic concepts in quantum computation, 2000; see http://arXiv.org/abs/quant-ph/0011013.
5. L. Grover, A framework for fast quantum mechanical algorithms, Proceedings of the 30th Annual ACM Symposium on the Theory of Computing, ACM Press, New York, 1998, pp. 53-62; see also http://arXiv.org/abs/quant-ph/9711043.
6. J. Gruska, Quantum Computing, McGraw-Hill, London, 1999.
7. 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. 123-171.
8. S. Heinrich, Quantum summation with an application to integration, J. Complexity 18 (2002) 1-50; see also http://arXiv.org/abs/quant-ph/0105116.
9. S. Heinrich, From Monte Carlo to quantum computation, in: K. Entacher, W.Ch. Schmid, A. Uhl (Guest Eds.), Proceedings of the Third IMACS Seminar on Monte Carlo Methods MCM2001, Salzburg, Special Issue of Mathematics and Computers in Simulation, Vol. 62, 2003, pp. 219-230.
10. S. Heinrich, Quantum integration in Sobolev classes, J. Complexity 19 (2003) 19-42; see also http://arXiv.org/abs/quant-ph/0112153.
11. S. Heinrich, Quantum Approximation II. Sobolev Embeddings, J. Complexity, to appear; see also http://arXiv.org/abs/quant-ph/0305031.
12. S. Heinrich, M. Kwas, H. Woźniakowski. Quantum Boolean summation with repetitions in the worst-average setting, to appear in: H. Niederreiter (Ed.), Monte Carlo and Quasi-Monte Carlo Methods 2002. Springer-Verlag, 2004.
13. 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.
14. S. Heinrich, E. Novak, On a problem in quantum summation, J. Complexity 19 (2003) 1-18; see also http://arXiv.org/abs/quant-ph/0109038.
15. M. Kwas, H. Woźniakowski, Sharp error bounds on quantum Boolean summation in various settings, 2003; http://arXiv.org/abs/quant-ph/0303049.
16. 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.
17. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
18. E. Novak, Deterministic and Stochastic Error Bounds in Numerical Analysis, Lecture Notes in Mathematics, Vol. 1349, Springer, Berlin, 1988.
19. E. Novak, Quantum complexity of integration, J. Complexity 17 (2001) 2-16; see also http://arXiv.org/abs/quant-ph/0008124.
20. E. Novak, I.H. Sloan, H. Woźniakovvski, Tractability of approximation for weighted Korobov spaces on classical and quantum computers, Found. Comput. Math., to appear; see also http://arXiv.org/abs/quant-ph/0206023.
21. A. Pietsch, Eigenvalues and s-Numbers, Cambridge University Press, Cambridge, 1987.
22. A.O. Pittenger, Introduction to Quantum Computing Algorithms, Birkhäuser, Boston, 1999.
23. D. Pollard, Convergence of Stochastic Processes, Springer, New York. 1984.
24. P.W. Shor, Introduction to quantum algorithms, 2000; see http://arXiv.org/abs/quant-ph/0005003.
25. J.F. Traub, G.W. Wasilkowski, H. Woźniakowski, Information-Based Complexity, Academic Press, New York, 1988.
26. J.F. Traub, H. Woźniakowski, Path integration on a quantum computer, 2001; see http://arXiv.org/abs/quant-ph/0109113.