 
Summary: THEORY OF COMPUTING, Volume 1 (2005), pp. 4779
http://www.theoryofcomputing.org
Quantum Search of Spatial Regions
Scott Aaronson Andris Ambainis
Received: June 13, 2004; published: June ?, 2005.
Abstract: Can Grover's algorithm speed up search of a physical regionfor example a
2D grid of size
n ×
n? The problem is that
n time seems to be needed for each
query, just to move amplitude across the grid. Here we show that this problem can be sur
mounted, refuting a claim to the contrary by Benioff. In particular, we show how to search
a ddimensional hypercube in time O(
n) for d 3, or O(
nlog5/2
