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Science 24 February 2006:
Vol. 311. no. 5764, pp. 1133 - 1135
DOI: 10.1126/science.1121541
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Reports

Quantum Computation as Geometry

Michael A. Nielsen,* Mark R. Dowling, Mile Gu, Andrew C. Doherty

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.

School of Physical Sciences, The University of Queensland, Queensland 4072, Australia.

* To whom correspondence should be addressed. E-mail: nielsen{at}physics.uq.edu.au

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THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
Quantum Phase Extraction in Isospectral Electronic Nanostructures.
C. R. Moon, L. S. Mattos, B. K. Foster, G. Zeltzer, W. Ko, and H. C. Manoharan (2008)
Science 319, 782-787
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Science. ISSN 0036-8075 (print), 1095-9203 (online)