Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parameterization of quantum walks on cycles   This study investigate the unitary equivalence classes of quantum walks on
cycles. We show that unitary equivalence classes of quantum walks on a cycle
with $N$ vertices are parameterized by $2N$ real parameters. Moreover, the
ranges of two of the parameters are restricted, and the ranges depend on the
parity of $N$.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int