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Quantum Lattice-Gas Model For The Diffusion Equation

Author

Listed:
  • JEFFREY YEPEZ

    (Air Force Research Laboratory, Hanscom Field, Massachusetts 01731, USA)

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.

Suggested Citation

  • Jeffrey Yepez, 2001. "Quantum Lattice-Gas Model For The Diffusion Equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(09), pages 1285-1303.
    • Handle: RePEc:wsi:ijmpcx:v:12:y:2001:i:09:n:s0129183101002656
    DOI: 10.1142/S0129183101002656
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