Quantum Lattice-Gas Model for the Diffusion Equation

Abstract

Presented is a factorized quantum lattice-gas algorithm to model the diffusion equation. It is a minimal model with two qubits per node of a one-dimensional lattice and it is suitable for implementation on a large array of small quantum computers interconnected by nearest-neighbor classical communication channels. The quantum lattice-gas system is described at the mesoscopic scale by a lattice-Boltzmann equation whose collision term is unconditionally stable and obeys the principle of detailed balance. An analytical treatment of the model is given to predict a macroscopic effective field theory. The numerical simulations are in excellent agreement with the analytical results. In particular, numerical' simulations confirm the value of the analytically calculated diffusion constant. The algorithm is time-explicit with numerical convergence that is first-order accurate in time and second-order accurate in space.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2001
Accession Number
ADA444279

Entities

People

  • J. Yepez

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force Research Laboratories
  • Algorithms
  • Boltzmann Equation
  • Collisions
  • Computers
  • Convergence
  • Differential Equations
  • Diffusion
  • Dynamics
  • Equations
  • Quantum Algorithms
  • Quantum Computers
  • Quantum Computing
  • Quantum Information Science
  • Quantum States
  • Simulations

Readers

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

Technology Areas

  • Quantum Computing
  • Space