%0 Journal Article
%T Quantum Computation as Geometry
%A Michael A. Nielsen
%A Mark R. Dowling
%A Mile Gu
%A Andrew C. Doherty
%J Physics
%D 2006
%I arXiv
%R 10.1126/science.1121541
%X Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. 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.
%U http://arxiv.org/abs/quant-ph/0603161v2