Comment by jiggawatts
3 months ago
> 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.
> there's strong reasons to believe that energy is required to represent all information in the physical universe
You simply do not need to believe this. The universe doesn't need to be "stored" somewhere.
> 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.
Quantum computing does not believe this. It is a theorem that you can only get n bits out of n qubits, and quantum computing speedups do not rely otherwise.
Noise is hard, but error correction is a mathematically sound response.
> The universe doesn't need to be "stored" somewhere.
Information that can have any effect on anything physical must have an energy associated with it, because that's basically the definition of energy: the property of physical systems that can cause change over time. No energy, no change in state. These are practically axioms.
Information that has zero energy can have only zero effect on observables in (our) universe.
> It is a theorem that you can only get n bits out of n qubits, and quantum computing speedups do not rely otherwise.
I'm pretty sure you've misunderstood something somewhere, because the 2^n states represented by n qubits is mentioned in practically all QC materials.