Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bipartite unitary gates and billiard dynamics in the Weyl chamber   Long time behavior of a unitary quantum gate $U$, acting sequentially on two
subsystems of dimension $N$ each, is investigated. We derive an expression
describing an arbitrary iteration of a two-qubit gate making use of a link to
the dynamics of a free particle in a $3D$ billiard. Due to ergodicity of such a
dynamics an average along a trajectory $V^t$ stemming from a generic two-qubit
gate $V$ in the canonical form tends for a large $t$ to the average over an
ensemble of random unitary gates distributed according to the flat measure in
the Weyl chamber - the minimal $3D$ set containing points from all orbits of
locally equivalent gates. Furthermore, we show that for a large dimension $N$
the mean entanglement entropy averaged along a generic trajectory coincides
with the average over the ensemble of random unitary matrices distributed
according to the Haar measure on $U(N^2)$.

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The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con