Quantum Lattice Representation of Dark Solitons

Abstract

The nonlinear Schrodinger (NLS) equation in a self-defocusing Kerr medium supports dark solitons. Moreover the mean field description of a dilute Bose-Einstein condensate (BEC) is described by the Gross-Pitaevskii equation, which for a highly anisotropic (cigar-shaped) magnetic trap reduces to a one-dimensional (1D) cubic NLS- in an external potential. A quantum lattice algorithm is developed for the dark solitons. Simulations are presented for both black (stationary) solitons as well as (moving) dark solitons. Collisions of dark solitons are compared with the exact analytic solutions and coupled dark-bright vector solitons are examined. The quantum algorithm requires 2 qubits per scalar field at each spatial node. The unitary collision operator quantum mechanically entangles the on-site qubits, and this transitory entanglement is spread throughout the lattice by the streaming operators. These algorithms are suitable for a Type-II quantum computers, with wave function collapse induced by quantum measurements required to determine the coupling potentials.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2004
Accession Number
ADA446479

Entities

People

  • George Vahala
  • Jeffrey Yepez
  • Linda Vahala

Organizations

  • College of William & Mary

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Algorithms
  • Amplitude
  • Bose Einstein Condensates
  • Collisions
  • Computations
  • Couplings
  • Equations
  • Mathematics
  • Physics
  • Quantum Information
  • Scattering
  • Schrodinger Equation
  • Sequences
  • Stationary
  • Wave Functions

Fields of Study

  • Physics

Readers

  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.

Technology Areas

  • Quantum Computing