Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time and Space Efficient Quantum Algorithms for Detecting Cycles and
  Testing Bipartiteness   We study space and time efficient quantum algorithms for two graph problems
-- deciding whether an $n$-vertex graph is a forest, and whether it is
bipartite. Via a reduction to the s-t connectivity problem, we describe quantum
algorithms for deciding both properties in $\tilde{O}(n^{3/2})$ time and using
$O(\log n)$ classical and quantum bits of storage in the adjacency matrix
model. We then present quantum algorithms for deciding the two properties in
the adjacency array model, which run in time $\tilde{O}(n\sqrt{d_m})$ and also
require $O(\log n)$ space, where $d_m$ is the maximum degree of any vertex in
the input graph.

19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th