printable pdf
比利时vs摩洛哥足彩 ,
university of california san diego

****************************

quantum computation seminar

yi-kai liu

institute for quantum information, caltech

towards quantum algorithms using the curvelet transform

abstract:

the curvelet transform is a directional wavelet transform, introduced by candes and donoho (2002). i will present some preliminary results on curvelet-based quantum algorithms. first, the quantum curvelet transform can be implemented efficiently, for a simple class of ``haar curvelets," and possibly for other curvelets as well. next, consider the following example. given a state that is a uniform superposition over a ball in $\mathbb{r}^n$, we compute the (continuous) curvelet transform. we then measure the state, and observe a scale $a$, direction $\theta$ and location $b$. with significant probability, $a$ is small (corresponding to a fine-scale element), and $b$ and $\theta$ determine a line that passes close to the center of the ball. this suggests an interesting quantum algorithm for finding the center of a radial function. however, there remain some technical obstacles in carrying this result over to the discrete setting, and in designing a suitable mother curvelet that can be implemented efficiently.

host: david meyer

july 24, 2008

12:30 pm

ap&m 7218

****************************