  Simulations of one quantum system by an other has an implication in
realization of quantum machine that can imitate any quantum system and solve
problems that are not accessible to classical computers. One of the approach to
engineer quantum simulations is to discretize the space-time degree of freedom
in quantum dynamics and define the quantum cellular automata (QCA), a local
unitary update rule on a lattice. Different models of QCA are constructed using
set of conditions which are not unique and are not always in implementable
configuration on any other system. Dirac Cellular Automata (DCA) is one such
model constructed for Dirac Hamiltonian (DH) in free quantum field theory.
Here, starting from a split-step discrete-time quantum walk (QW) which is
uniquely defined for experimental implementation, we recover the DCA along with
all the fine oscillations in position space and bridge the missing connection
between DH-DCA-QW. We will present the contribution of the parameters resulting
in the fine oscillations on the Zitterbewegung frequency and entanglement. The
tuneability of the evolution parameters demonstrated in experimental
implementation of QW will establish it as an efficient tool to design quantum
simulator and approach quantum field theory from principles of quantum
information theory.
