Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster Quantum Concentration via Grover's Search   We present quantum algorithms for routing concentration assignments on full
capacity fat-and-slim concentrators, bounded fat-and-slim concentrators, and
regular fat-and-slim concentrators. Classically, the concentration assignment
takes $O(n)$ time on all these concentrators, where $n$ is the number of
inputs. Powered by Grover's quantum search algorithm, our algorithms take
$O(\sqrt{nc}\ln{c})$ time, where $c$ is the capacity of the concentrator. Thus,
our quantum algorithms are asymptotically faster than their classical
counterparts, when $c\ln^2{c}=o(n)$.In general, $c = n^\mu,$ satisfies
$c\ln^2{c}=o(n),$ implying a time complexity of $O(n^{0.5(1+ \mu )} \ln n),$
for any $\mu, 0 < \mu < 1.$

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The categories of this paper are: supr-con
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph