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Abstract: We give the first example of faster transport with a quantum walk on aninherently directed graph, on the directed line with a variable number ofself-loops at each vertex. These self-loops can be thought of as adding anumber of small dimensions. This is a discrete time quantum walk using theFourier transform coin, where the walk proceeds a distance $\Theta1$ inconstant time compared to $\Theta1-n$ classically, independent of the numberof these small dimensions. The analysis proceeds by reducing this walk to awalk with a two dimensional coin.



Author: Stephan Hoyer, David A. Meyer

Source: https://arxiv.org/







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