Computers are entropy engines. For example, when they decompose a large number into its prime factors, the entropy of these factors is lower than that of the original number. The third law of thermodynamics states that total entropy tends to increase, so the computer must be converting low entropy energy into a high entropy form, such as heat, in order to perform this operation.
The promise of quantum computers is that as the number of bits rise, their computational power to perform such calculations rises exponentially – if only the quantum state could be kept from decaying.
But as noted above, energy must be supplied to the core components that actually carry out the computation. As the computational power of the system rises exponentially with the number of bits, the amount of energy that must be pumped through and converted to heat, also rises exponentially.
But the quantum state is intrinsically fragile and is destroyed by heat. The third law of thermodynamics shows itself by exponentially narrowing the band within which quantum coherence is maintained and so makes it exponentially costlier in terms of energy input to preserve. This problem is fundamentally intractable. Since there are no stabilizing/cooling mechanisms that scale exponentially with the bit count, quantum computers will never grow much more powerful than they are today.
I therefore do not believe they will ever be more than expensive toys. Specifically, I predict that no quantum processor will ever exceed the performance of a mid-range desktop CPU such as the i5-6600K for a task such as factoring large numbers.
