Summary: Quantum Search of Spatial Regions (Extended Abstract) #
Scott Aaronson +
University of California, Berkeley
Andris Ambainis #
University of Latvia
Abstract
Can Grover's quantum search algorithm speed up
search of a physical region---for 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 Benio#.
In particular, we show how to search a d­dimensional
hypercube in time O( # n) for d # 3, or O( # n log 3 n)
for d = 2. More generally, we introduce a model of
quantum query complexity on graphs, motivated by fun­
damental physical limits on information storage, par­
ticularly the holographic principle from black hole ther­
modynamics. Our results in this model include almost­
tight upper and lower bounds for many search tasks;

Source: Aaronson, Scott - Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)

Collections: Physics; Computer Technologies and Information Sciences