Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General structures of reversible and quantum gates   The most general structure (in matrix form) of a single-qubit gate is
presented. Subsequently, used that to obtain a set of conditions for testing
(a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not
decomposable into two single qubit gates and (b) whether a given single qubit
gate is self-inverse? Relevance of the results reported here is discussed in
the context of optimization of reversible and quantum circuits, especially for
the optimization of quantum cost. A systematic procedure is developed for the
identification of the non-decomposable 2-qubit gates. Such a non-decomposable
2-qubit gate along with all possible single qubit gates form a universal
quantum gate library. Further, some possible applications of the present work
are also discussed.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph