# 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.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Quantum Theory and Relativity