Simulation of the diffusion equation on a type-II quantum computer
G. P. Berman, Alexandr Alexandrovich Ezhov, D. I. Kamenev, Jeffrey Yepez · Physical Review A · 2002
A lattice-gas algorithm for the one-dimensional diffusion equation is realized using radio frequency pulses in a one-dimensional spin system. The model is a large array of quantum two-qubit nodes interconnected by the nearest-neighbor classical communication channels. We present a quantum protocol for implementation of the quantum collision operator and a method for initialization and reinitialization of quantum states. Numerical simulations of the quantum-classical dynamics are in good agreement with the analytic solution for the diffusion equation.