  Recently, it has been demonstrated that asymptotic states of open quantum
system can undergo qualitative changes resembling pitchfork, saddle-node, and
period doubling classical bifurcations. Here, making use of the periodically
modulated open quantum dimer model, we report and investigate a quantum
Neimark-Sacker bifurcation. Its classical counterpart is the birth of a torus
(an invariant curve in the Poincar\'{e} section) due to instability of a limit
cycle (fixed point of the Poincar\'{e} map). The quantum system exhibits a
transition from unimodal to bagel shaped stroboscopic distributions, as for
Husimi representation, as for observables. The spectral properties of Floquet
map experience changes reminiscent of the classical case, a pair of complex
conjugated eigenvalues approaching a unit circle. Quantum Monte-Carlo wave
function unraveling of the Lindblad master equation yields dynamics of single
trajectories on "quantum torus" and allows for quantifying it by rotation
number. The bifurcation is sensitive to the number of quantum particles that
can also be regarded as a control parameter.
