  We consider a discrete-time 2-state quantum walk on the line. The state of
the quantum walker evolves according to a rule which is determined by a
coin-flip operator and a position-shift operator. In this paper we take a
3-periodic time evolution as the rule. For such a quantum walk, we get a limit
distribution which expresses the asymptotic behavior of the walker after a long
time. The limit distribution is different from that of a time-independent
quantum walk or a 2-period time-dependent quantum walk. We give some analytical
results and then consider a number of variants of our model and indicate the
result of simulations for these ones.

Quantum Physics;Probability