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Abstract: I introduce a new type of continuous-time quantum walk on graphs called thequantum snake walk, the basis states of which are fixed-length paths snakesin the underlying graph. First I analyze the quantum snake walk on the line,and I show that, even though most states stay localized throughout theevolution, there are specific states which most likely move on the line as wavepackets with momentum inversely proportional to the length of the snake. Next Idiscuss how an algorithm based on the quantum snake walk might potentially beable to solve an extended version of the glued trees problem which asks to finda path connecting both roots of the glued trees graph. No efficient quantumalgorithm solving this problem is known yet.



Author: Ansis Rosmanis

Source: https://arxiv.org/







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