Quantum perpetual motion 
Perpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not.

(Source:Wikipedia)
With this definition in mind, particularly the "operates indefinitely" (I don't care about producing work), won't quantum mechanics allow perpetual motion due to energy quantization?
For example, an electron in hydrogen can be thought of as perpetual motion. It's indefinite(I think so); unlike gravitational orbits (which slowly release energy). This is due to the quantization of energy. Without it, the electron would have fallen into the nucleus.
More generally, if we energy is quantized in a system, dissipative forces of lesser magnitude cannot act on it, due to quantization. 
For example, if a block can have only an integer value of energy in Joules, then frictional forces of power $P<\frac{1 J}{\text{planck time}}$ cannot act. Or something like that.
So does quantum mechanics permit an infinitely advanced civilization to build a machine which operated indefinitely without doing work?
I'm not well versed in quantum mechanics, so I may be making a mistake here, or I may just be confused. Refer to equations if you want, but try not to use them too heavily unless the answer depends on it. It's OK if they're explained a bit.
 A: Yes, perpetual motion that does not work is possible, and has been done in a famous Soviet experiment. You put a superfluid in the interior of a macroscopic donut-shaped tube in the normal state, and let the tube spin along the donut axis, fluid plus pipe, then cool the thing down so that it becomes a superfluid. Then you stop the tube from spinning.
The superfluid will spin with no measurable loss essentially forever, even in imperfect conditions. It spun for many years without measurable loss in the actual experiment. This is quantum perpetual motion in your sense, and it doesn't require such an advanced civilization, just mid 20th century humans.
The statement that perpetual motion is impossible is nowadays always interpreted to mean energy producing machine, not a motion that does not decay by friction.
A: I guess the operative question here (no pun intended) is, what does it mean for a machine to "operate"? If you consider a particle that just sits there and doesn't do anything to be an operating machine, then yes, it is theoretically possible to build one. Just put an atom somewhere isolated and leave it there. In reality, of course, you can't do this because there's no place in space that is truly isolated, and even if you did manage to cut off a box from all external influences, you would have virtual particle pairs popping out of the vacuum. But in a theoretical empty universe with no quantum fluctuations, assuming that the constituent particles are stable, an atom would just sit there forever.
But I don't think anyone would seriously consider a static system to be a machine. That's really all that an electron in an undisturbed atom is. It's just like a particle sitting in space, except that instead of sitting at one location, it probabilistically "sits" at every location.
A: It seems that a PMM is impossible even if energy levels are quantized.
As @DavidZaslavsky pointed out, the electron example is sort of invalid, as there's no motion involved.
In QM, even if we manage to lower the effectiveness of dissipative forces to below the quantum of energy of the PMM in question, we will still have vacuum fluctuations, which can both give and take any amount of extra energy from the system at random. Now, there is a finite probability that it ends up taking all of the energy away (it can have some 'gives' interspersed as well). Note that after this it may go back in motion after recieving some energy from the surroundings). Obviously, it is no longer in motion, so in such a case, the PMM ceases to be perpetual. Since we have infinite time to consider the motion of the machine, this event becomes compulsory at some point in the infinite lifetime of the PMM. And thus, no PMM constructed on the basis of quantization of energy will work.
In fact, this seems to put an extra barrier for PMM enthusiasts. Even if you manage to remove all dissipative forces, quantum mechanics will bring the machine to an instantaneous standstill at some point in time. So it's no longer 'perpetual motion'
