Quantum computers provide exponential speedup relative to classical computers. However, it is empirical fact that increasing of number of qubits makes the the computer harder and harder to keep working (decoherence, decreasing energy level separation, longer relaxation times ... ). To do that you have to go to lower temperatures and better shielding form environment perturbation and higher precision of manufacturing.
I would like to know if there are some fundamental rules of nature which connects this parameters with number of qubits, a least for adiabatic quantum computers and quantum annealing, which seems to be most practical.
- Eg. if required temperature (reps. $\beta=1/T$ ) would scale also exponentially with number of qubits ( because energy difference between levels would scale exponentially as well ), it would effectively make the computer performance scaling just linearly with advances in cooling and shielding technology.
- perhaps, there can be fundamental limit which at the end connect relaxation time to number of qubits, in such a way that increasing number of qubits would require exponential increase of relaxation time ( i.e. if energy level separation is exponentially decreased than period of quantum beating between them takes proportionally longer). This would mean that processing performance measured in number of examined qubit configurations per time would be actually limited by some constant.
there is some interesting movie about practical adiabatic quantum computing which can be good introduction into practical issues.