Continuous Quantum Computation
Final technical rept., Jun 2001-Sep 2006
COLUMBIA UNIV NEW YORK DEPT OF COMPUTER SCIENCE
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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.
- Numerical Mathematics
- Quantum Theory and Relativity