Continuous Quantum Computation

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 Baker's map, NMR implementation of a quantum lattice gas, application of a Loschmidt echo, single spin measurement, and experiments in solid-state simulation.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2007
Accession Number
ADA465614

Entities

People

  • Joseph F. Traub

Organizations

  • Columbia University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force Research Laboratories
  • Algorithms
  • Computational Complexity
  • Computational Science
  • Computations
  • Eigenvalues
  • Equations
  • Information Processing
  • Jet Propulsion
  • Path Integrals
  • Quantum Algorithms
  • Quantum Bits
  • Quantum Circuits
  • Quantum Computing
  • Quantum Information
  • Quantum Information Science
  • Simulations

Readers

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  • Linear Algebra
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.

Technology Areas

  • Quantum Computing