@article {1425,
title = {Quantum Algorithms Using the Curvelet Transform},
journal = {Proc. ACM Symposium on Theory of Computing (STOC)},
year = {2009},
month = {2009/10/28},
pages = {391-400},
abstract = { The curvelet transform is a directional wavelet transform over R^n, which is
used to analyze functions that have singularities along smooth surfaces (Candes
and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I
give an efficient implementation of a quantum curvelet transform, together with
two applications: a single-shot measurement procedure for approximately finding
the center of a ball in R^n, given a quantum-sample over the ball; and, a
quantum algorithm for finding the center of a radial function over R^n, given
oracle access to the function. I conjecture that these algorithms succeed with
constant probability, using one quantum-sample and O(1) oracle queries,
respectively, independent of the dimension n -- this can be interpreted as a
quantum speed-up. To support this conjecture, I prove rigorous bounds on the
distribution of probability mass for the continuous curvelet transform. This
shows that the above algorithms work in an idealized "continuous" model.
},
url = {http://arxiv.org/abs/0810.4968v2},
author = {Yi-Kai Liu}
}