Comment by jiggawatts

> complex Hilbert space in 2^n dimensions

A very simple argument is that there's strong reasons to believe that energy is required to represent all information in the physical universe. You can't have "states" without mass/energy storing that state somewhere.

2^n is clearly super-linear in 'n', so as you scale to many particles, the equations suggest that you'd need a ludicrously huge state space, which requires a matching amount of energy to store. Clearly, this is not what happens, increasing the mass/energy of a system 10x doesn't result in 2^10 = 1024x as much mass/energy. You get 10x, plus or minus a correction for binding energy, GR, or whatever.

Quantum Computing is firmly based on pretending that this isn't how it is, that somehow you can squeeze 2^n bits of information out of a system with 'n' parts to it.

The ever increasing difficulties with noise, etc... indicate that no, there's no free lunch here, no matter how long we stand in the queue with an empty tray.