  Quantum walks play an important role for developing quantum algorithms and
quantum simulations. Here we present one dimensional three-state quantum
walk(lazy quantum walk) and show its equivalence for circuit realization in
ternary quantum logic for the first of its kind. Using an appropriate logical
mapping of the position space on which a walker evolves onto the multi-qutrit
states, we present efficient quantum circuits considering the nearest neighbour
position space for the implementation of lazy quantum walks in one-dimensional
position space in ternary quantum system. We also address scalability in terms
of $n$-qutrit ternary system with example circuits for a three qutrit state
space.
