  In this paper we investigate tensor modes of perturbations in the universe
governed by Loop Quantum Cosmology. We derive the equation for tensor modes and
investigate numerically effects of quantum corrections. This investigation
reveals that the region of super-adiabatic amplification of tensor modes is
smaller in comparison with the classical case. Neglecting quantum corrections
to the equation for tensor modes and holding underlying loop dynamics we study
analytically the creation of gravitons. We calculate the power spectrum of
tensor perturbations during the super-inflationary phase induced by Loop
Quantum Gravity. The main result obtained is the spectrum of gravitons,
produced in the transition from the quantum to classical regime of the
Universe. Obtained spectrum is characterized by a hard branch. The numerical
investigation shows the strong dependence of $\nu_{\text{max}}$ frequency with
respect to quantum numbers. The parameter
$\Omega_{\text{gw}}(\nu_{\text{max}})$ approaches even to $\sim 10^{-1}$ for
highest frequencies. We compare our results with recent constraints from the
Laser Interferometer Gravitational-wave Observatory (LIGO) and find that it is
possible to test the quantum effects in the early Universe.
