Quantum Computation as Geometry
Abstract
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.
 Publication:

Science
 Pub Date:
 February 2006
 DOI:
 10.1126/science.1121541
 arXiv:
 arXiv:quantph/0603161
 Bibcode:
 2006Sci...311.1133N
 Keywords:

 PHYSICS;
 Quantum Physics
 EPrint:
 13 Pages, 1 Figure