Simulating quantum Systems with cellular automata
Cellular automata-(CA) are computational structures spaciously and temporally discrete which were originally proposed by John von Neumann in the late 1940’s. They have the same computational power of Turing machines.This tool enables us to simulate a large number of different problems in distinct areas.
After the discussion proposed by Richard Feynman about the efficiency of classical computers at simulating quantum systems, different quantum computational formalisms were proposed such as quantum circuits and quantum cellular automaton-(QCA), with the purpose of simulating quantum systems.
In this seminar we will show different CA formalisms and see examples of its applications. In particular we will show how the random walk
(RW) problem can be simulated by a CA. Its continuous limit can be achieved through the Chapman-Enskog expansion.
Finally we will show, in analogous way, how the quantum walk (QW) is modelled by QCA and obtain its continouous limit.