  In this paper we investigate one dimensional quantum walks with two-step
memory, which can be viewed as an extension of quantum walks with one-step
memory. We develop a general formula for the amplitudes of the two-step-memory
walk with Hadamard coin by using path integral approach, and numerically
simulate its process. The simulation shows that the probability distribution of
this new walk is different from that of the Hadamard quantum walk with one-step
memory, while it presents some similarities with that of the normal Hadamard
quantum walk without memory.
