  The ground state of the bilayer Kitaev model with the Heisenberg-type
interlayer exchange interaction is investigated by means of the exact
diagonalization. Calculating the ground-state energy, local quantity defined on
each plaquette, and dynamical spin structure factor, we obtain results
suggesting the existence of a quantum phase transition between the Kitaev
quantum spin liquid (QSL) and dimer singlet states when the interlayer coupling
is antiferromagnetic. On the other hand, increasing the ferromagnetic
interlayer coupling, there exists no singularity in the physical quantities,
suggesting that the $S=1/2$ Kitaev QSL state realized in each layer
adiabatically connects to another QSL state realized in the $S=1$ Kitaev model.
Thermodynamic properties are also studied by means of the thermal pure quantum
state method.
