Abstract
We consider the problem of searching a general -dimensional lattice of vertices for a single marked item using a continuous-time quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behavior near a Dirac point, we develop algorithms that solve the problem in a time of for and in . In particular, we show that such algorithms exist even for hypercubic lattices in any dimension. Unlike previous continuous-time quantum walk algorithms on hypercubic lattices in low dimensions, our approach does not use external memory.
4 More- Received 14 March 2014
DOI:https://doi.org/10.1103/PhysRevA.89.052337
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