The Discrete Curvelet Transform for Quantum Algorithms

Open Access
Author:
Kerekes, Justin T
Area of Honors:
Computer Science
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Sean Hallgren, Thesis Supervisor
  • John Joseph Hannan, Honors Advisor
Keywords:
  • discrete curvelet transform
  • quantum curvelet transform
  • quantum algorithm
  • center finding
Abstract:
This thesis explores the possibility of using the discrete quantum curvelet transform on square functions in two dimensions for use in different quantum algorithms such as Yi-Kai Liu’s center finding algorithm. I verify that using the discrete curvelet transform on a uniform quantum state in two dimensions will yield a new quantum state with a better-than-uniform probability to measure the corners of the distribution.