Continuous quantum computation: Difference between revisions

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over the last few years there have been numerous papers studying the complexity of quantum algorithms solving continuous problems. The approximation of multivariate integrals and functions, the solution of initial value problems, the Sturm-Liouville eigenvalue problem are just a few examples. More details can be found in the papers below and the references therein:

*Bessen, A. J. (2005), A lower bound for phase estimation, Physical Review A, 71(4), 042313. Also http://arXiv.org/quant-ph/0412008.

042313*Heinrich, S. (2002), Quantum Summation with an Application to Integration, J. Complexity, 18(1), 1–50. Also http://arXiv.org/quant-ph/04120080105116.

*Heinrich, S. (2003), Quantum integration in Sobolev spaces, J. Complexity, 19, 19–42. *Heinrich, S. (2004), Quantum Approximation I. Embeddings of Finite Dimensional <math>L_p</math> Spaces, J. Complexity, 20, 5–26. Also http://arXiv.org/quant-ph/0305030.

*Heinrich, S. (2002), Quantum Summation with an Application to Integration, J. Complexity,

18*Heinrich, S. (12004), 1–50Quantum Approximation II. Sobolev Embeddings, J. Complexity, 20, 27–45. Also http://arXiv.org/quant-ph/01051160305031.

*Jaksch, P. and Papageorgiou, A. (2003), Eigenvector approximation leading to exponential speedup of quantum eigenvalue calculation, Phys. Rev. Lett., 91, 257902. Also http://arXiv.org/quant-ph/0308016.

*Heinrich, S. (2003), Quantum integration in Sobolev spaces, J. Complexity, 19, 19–42.

*Kacewicz, B. Z. (2004), Randomized and quantum solution of initial value problems, to appear in J. Complexity.

*Heinrich, S. (2004), Quantum Approximation I. Embeddings of Finite Dimensional Lp

*Kwas, M., Complexity of multivariate Feynman-Kac Path Integration in Randomized and Quantum Settingssettings, 2004, LANL preprint quant-ph/0410134

Spaces, J. Complexity, 20, 5–26. Also http://arXiv.org/quant-ph/0305030.

Heinrich*Novak, SE. (20042001), Quantum Approximationcomplexity II.of Sobolev Embeddingsintegration, J. Complexity, 17, 2–16. Also http://arXiv.org/quant-ph/0008124.

*Novak, E., Sloan, I. H., and Wozniakowski, H., Tractability of Approximation for Weighted Korobovorobov Spaces on Classical and Quantum Computers, Journal of Foundations of Computational Mathematics, 4, 121-156, 2004. Also http://arXiv.org/quant-ph/0206023

20, 27–45. Also http://arXiv.org/quant-ph/0305031.

*Papageorgiou, A. and Wo´zniakowski, H. (2005), Classical and Quantum Complexity of the Sturm-Liouville Eigenvalue Problem, Quantum Information Processing, 4, 87–127. Also http://arXiv.org/quant-ph/0502054.

Jaksch, P. and Papageorgiou, A. (2003), Eigenvector approximation leading to exponential

*Traub, J. F. and Wo´zniakowski, H. (2002), Path integration on a quantum computer, Quantum Information Processing, 1(5), 365–388, 2002. Also http://arXiv.org/quantph/0109113.

speedup of quantum eigenvalue calculation, Phys. Rev. Lett., 91, 257902. Also

*Wo´zniakowski, H. (2006), The Quantum Setting with Randomized Queries for Continuous Problems, Quantum Information Processing, 5(2), 83–130. Also http://arXiv.org/quant-ph/060196.

http://arXiv.org/quant-ph/0308016.

*Kacewicz, B. Z. (2004), Randomized and quantum solution of initial value problems, to

appear in J. Complexity.

*Kwas, M., Complexity of multivariate Feynman-Kac Path Integration in Randomized and Quantum Settings, 2004, LANL preprint quant-ph/0410134

*Novak, E. (2001), Quantum complexity of integration, J. Complexity, 17, 2–16. Also

http://arXiv.org/quant-ph/0008124.

*Novak, E., Sloan, I. H., and Wozniakowski, H., Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers, Journal of Foundations of Computational Mathematics, 4, 121-156, 2004. Also http://arXiv.org/quant-ph/0206023

*Papageorgiou, A. and Wo´zniakowski, H. (2005), Classical and Quantum Complexity of

teh Sturm-Liouville Eigenvalue Problem, Quantum Information Processing, 4, 87–127.

Also http://arXiv.org/quant-ph/0502054.

*Traub, J. F. and Wo´zniakowski, H. (2002), Path integration on a quantum computer,

Quantum Information Processing, 1(5), 365–388, 2002. Also http://arXiv.org/quantph/

0109113.

*Wo´zniakowski, H. (2006), The Quantum Setting with Randomized Queries for

Continuous Problems, Quantum Information Processing, 5(2), 83–130. Also

http://arXiv.org/quant-ph/060196.

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