  We study the level statistics of an interacting multi-qubit system, namely
the kicked Ising spin chain, in the regime of quantum chaos. Long range
quasi-energy level statistics show effects analogous to the ones observed in
semi-classical systems due to the presence of classical periodic orbits, while
short range level statistics display perfect statistical agreement with random
matrix theory. Even though our system possesses no classical limit, our result
suggest existence of an important non-universal system specific behavior at
short time scale, which clearly goes beyond finite size effects in random
matrix theory.
