Type-II Quantum Algorithms for Solitons

Abstract

There are many problems of scientific interest that are not tractable on any foreseeable classical computer. Quantum computers have the potential of exploiting non-classical features like quantum entanglement and phase coherence which can exponentially speed-up the computational algorithm. Quantum algorithms have been developed to study the evolution of solitons in the Korteveg-de Vries equation and the Nonlinear Schrodinger equation. These nonlinear equations have known exact analytic solutions to which the quantum algorithm solutions have been compared - with excellent agreement. Vector soliton propagation down birefringment media have also been considered as well as soliton turbulence and the corresponding power spectra. It has been found that two on-site qubits per spatial node is sufficient to model a scalar continuum field. The particular choice and sequence of unitary collision and streaming operators dictate the final continuum form of the partial differential equation.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2004
Accession Number
ADA420618

Entities

People

  • George Vahala

Organizations

  • College of William & Mary

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Collisions
  • Differential Equations
  • Equations
  • Functions (Mathematics)
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Phase Transformations
  • Polarization
  • Power Spectra
  • Quantum Algorithms
  • Quantum Computers
  • Quantum Computing
  • Real Variables
  • Schrodinger Equation
  • Sequences

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Quantum Computing