Quantum computers evolution. Development of that time of computer will solve many problems.
In my opinion the crucial difference between classical and quantum computers is related with some particular properties that only can be achieved in the quantum regime. In a quantum computer the information is stored in physical systems that are represented by a qubit or a linear combinations of these states (spin systems, two-level systems, etc). Therefore, you can apply unitary transformations on these states (by applying microwaves, magnetic fields, etc) and translate the unitary evolution of the system (by measurement the final state) as a quantum logic gate.
The same idea can be applied in the classical limit, however, in the quantum regime you can use some "unique properties" as quantum entanglement, superposition of states (and many others), and therefore, realize many simultaneous operations at the same time. The latter implies that you can increase the speed of classical algorithms and gain a great power of calculation by manipulating quantum systems.
Maybe in the future, a quantum computer could easily solve (in some minutes or seconds) the Navier–Stokes equations for better climate predictions, the Kohn-Sham equations in DFT simulations for obtain a profound understanding of some interesting molecular structures or simply; a faster computer for our daily lives =)
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Too soon to ask such questions. Quantum computing and quantum computers are for the moment quite different things.
A keyword in the computers industry is miniaturization. For building a quantum computer, at least part of the components have to be miniaturized, e.g. components performing a certain calculus, or protocol. That's not simple. Fot instance, an elementary device, a Stern-Gerlach apparatus, only the magnets have cca. 12cm length. How to miniaturize this?
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