TITLE:
Solution of Nonlinear Advection-Diffusion Equations via Linear Fractional Map Type Nonlinear QCA
AUTHORS:
Shinji Hamada, Hideo Sekino
KEYWORDS:
Nonlinear Quantum Cellular Automaton, QCA, Quantum Walk, Linear Fractional Map, Advection-Diffusion Equation, Burgers Equation, Porous-Medium Equation, Soliton
JOURNAL NAME:
Journal of Quantum Information Science,
Vol.6 No.4,
December
13,
2016
ABSTRACT: Linear fractional map type (LFMT) nonlinear QCA (NLQCA), one of the simplest reversible NLQCA is studied analytically as well as numerically. Linear advection equation or Time Dependent Schrödinger Equation (TDSE) is obtained from the continuum limit of linear QCA. Similarly it is found that some nonlinear advection-diffusion equations including inviscid Burgers equation and porous-medium equation are obtained from LFMT NLQCA.