Area Computation Utilizing The Quantum Curvelet Transform
Open Access
Author:
Petersen, Evan Scot
Area of Honors:
Computer Engineering
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Sean Hallgren, Thesis Supervisor Sean Hallgren, Thesis Supervisor Lee David Coraor, Thesis Honors Advisor
Keywords:
Quantum Computing Curvelet Transform Area Finding
Abstract:
In the past year, a lower bound was placed on the complexity of calculating the volume of an object by a randomized algorithm. Here, I take the first steps to show reason to believe a quantum computer may be able to break that lower bound through use of a quantum algorithm utilizing Yi-Kai Liu’s quantum curvelet transform. To do that, I take on a simpler, easier version of the problem and show reason to believe that a quantum computer could solve this in constant time through the use of various simulations of the algorithm at work. I also show some attempts to make alternative versions of the quantum curvelet transform and the problems associated with these particular methods. This paper also reinforces the work of Dr. Liu on his algorithms in the continuous case by demonstrating something similar to what he conjectured should work in the discrete case.
