Accession Number:

ADA465614

Title:

Continuous Quantum Computation

Descriptive Note:

Final technical rept., Jun 2001-Sep 2006

Corporate Author:

COLUMBIA UNIV NEW YORK DEPT OF COMPUTER SCIENCE

Personal Author(s):

Report Date:

2007-03-01

Pagination or Media Count:

31.0

Abstract:

The focus of this research was on developing quantum algorithms for continuous problems, complexity analysis of these algorithms, and their simulation and implementation. Continuous problems are a focus because much of physics, chemistry, and engineering depends on continuous mathematical formulations such as partial differential equations, path integration, approximation, and high-dimensional integration. New algorithms and quantum speedups were obtained for a number of important problems such as path integration, eigenvalues of Hermitian operators, Feynman-Kac path integration, high-dimensional approximation, and the Sturm-Liouville eigenvalue problem. The simulation and implementation part of the project included simulation of the quantum summation algorithm, implementation of the quantum Bakers map, NMR implementation of a quantum lattice gas, application of a Loschmidt echo, single spin measurement, and experiments in solid-state simulation.

Subject Categories:

  • Numerical Mathematics
  • Quantum Theory and Relativity

Distribution Statement:

APPROVED FOR PUBLIC RELEASE