*raises hand*
Uhm...excuse me, but doesn't the act of observation of a "quantum system" usually involve a transfer of energy into the system, a laser pulse for example? In that case, the result would be simple perturbation, in which the excess energy is transferred to the various excited states of the system, whose linear combination would be equal to the previous energy plus the additional perturbative energy. As such, the growth of your plant would be dependent entirely on incident light in addition to whatever energy was present initially, assuming the system lacks the ability to radiate the excess energy out. Since visible light has on average 3.6E-17 J/photon, it would require 2.5E33 photons to attain 1kg of matter (assuming perfect energy-matter conversion as per E=mc2 and more importantly the ability to store the energy in defiance of that pesky second law of thermo). Since the frequency (that's photons/second) is approximately 5E16 hz, this would require 4.6E16 seconds, or approximately 1.5 billion years. That's incidentally assuming we use a laser to avoid wasting any photons due to the usual dispersion effect. We could, of course, accumulate multiple such lasers. If we were to, for example, align a million lasers so that they would all hit the plant, it would still take over 1500 years. And keep in mind, this is only for a single kg of matter, and I honestly do not know what form that would take on. I'd guess you could make subatomic particles via nucleosynthesis, but that would also take tremendous amounts of temperature, and even then you'd only have the simplest elements. You would then need an atom smasher to convert a tiny fraction of those into the higher order elements needed for your research projects. That would, of course, require additional energy for operation and storage. So...we're talking timespans on the order of the age of the universe, and a power source equivalent to your average supermassive black hole to make enough raw material for the completion of whatever it is you're trying to research.
But hey...this is still more believable and much less annoying than the planet mining bullocks. Not to mention this would be no less impossible than piloting your little ship through the center of a blue giant for some idiotic reasons (like the guy commanding the ship being drunk). Or for that matter a single probe launched vertically through the atmosphere of a gas giant surviving despite a) immense heat caused by friction, and b) the crushing gravity, and indeed mining what I can only presume to be methane or metallic hydrogen. See, this is why I can no longer enjoy a good sci-fi game...
(Yes, the comic was brilliant. Thank you for making my day a little more bearable!)