  Quantum walks are not only algorithmic tools for quantum computation but also
not trivial models which describe various physical processes. The paper
compares one-dimensional version of the free particle Dirac equation with
discrete time quantum walk (DTQW). We show that the discretized Dirac equation
when compared with DTQW results in interesting relations. It is also shown that
two relativistic effects associated with the Dirac equation, namely
Zitterbewegung (quivering motion) and Klein's paradox, are present in DTQW,
which can be implemented within non-relativistic quantum mechanics.
