  Quantum manifestations of isoperiodic stable structures (QISSs) have a
crucial role in the current behavior of quantum dissipative ratchets. In this
context, the simple shape of the ISSs has been conjectured to be an almost
exclusive feature of the classical system. This has drastic consequences for
many properties of the directed currents, the most important one being that it
imposes a significant reduction in their maximum values, thus affecting the
attainable efficiency at the quantum level. In this work we prove this
conjecture by means of comprehensive numerical explorations and statistical
analysis of the quantum states. We are able to describe the quantum parameter
space of a paradigmatic system for different values of $\hbar_{\rm eff}$ in
great detail. Moreover, thanks to this we provide evidence on a mechanism that
we call parametric tunneling by which the sharp classical borders of the
regions in parameter space become blurred in the quantum counterpart. We expect
this to be a common property of generic dissipative quantum systems.
