  I introduce a new type of continuous-time quantum walk on graphs called the
quantum snake walk, the basis states of which are fixed-length paths (snakes)
in the underlying graph. First I analyze the quantum snake walk on the line,
and I show that, even though most states stay localized throughout the
evolution, there are specific states which most likely move on the line as wave
packets with momentum inversely proportional to the length of the snake. Next I
discuss how an algorithm based on the quantum snake walk might potentially be
able to solve an extended version of the glued trees problem which asks to find
a path connecting both roots of the glued trees graph. No efficient quantum
algorithm solving this problem is known yet.
