Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spatial search by continuous-time quantum walks on crystal lattices   We consider the problem of searching a general $d$-dimensional lattice of $N$
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 behaviour near a Dirac point, we develop
algorithms that solve the problem in a time of $O(\sqrt N)$ for $d>2$ and
$O(\sqrt N \log N)$ in $d=2$. 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
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg