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

One Dimensional Quantum Walks with Two-step Memory