Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Complexity of Testing Group Commutativity   We consider the problem of testing the commutativity of a black-box group
specified by its k generators. The complexity (in terms of k) of this problem
was first considered by Pak, who gave a randomized algorithm involving O(k)
group operations. We construct a quite optimal quantum algorithm for this
problem whose complexity is in O (k^{2/3}). The algorithm uses and highlights
the power of the quantization method of Szegedy. For the lower bound of
Omega(k^{2/3}), we give a reduction from a special case of Element Distinctness
to our problem. Along the way, we prove the optimality of the algorithm of Pak
for the randomized model.

16
The categories of this paper are: stat
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc