Author(s)

Shinji Hamada¹, Hideo Sekino^1,2,3

¹Toyohashi University of Technology, Toyohashi, Japan.
²Stony Brook University, New York, USA.
³Tokyo Institute of Technology, Tokyo, Japan.

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.

Nonlinear Quantum Cellular Automaton, QCA, Quantum Walk, Linear Fractional Map, Advection-Diffusion Equation, Burgers Equation, Porous-Medium Equation, Soliton

Hamada, S. and Sekino, H. (2016) Solution of Nonlinear Advection-Diffusion Equations via Linear Fractional Map Type Nonlinear QCA. Journal of Quantum Information Science, 6, 263-295. doi: 10.4236/jqis.2016.64017.