  Quantum walk has been regarded as a primitive to universal quantum
computation. By using the operations required to describe the single particle
discrete-time quantum walk on a position space we demonstrate the realization
of the universal set of quantum gates on two- and three-qubit systems. The idea
is to utilize the effective Hilbert space of the single qubit and the position
space on which it evolves in order to realize multi-qubit states and universal
set of quantum gates on them. Realization of many non-trivial gates and
engineering arbitrary states is simpler in the proposed quantum walk model when
compared to the circuit based model of computation. We will also discuss the
scalability of the model and some propositions for using lesser number of
qubits in realizing larger qubit systems.
