The quantum computers are much much faster than the classical. For example, if we work with N bits, our computers need to do 2^N "readings".  The quantum computers need only one reading.

About the scope of quantum mechanics, no one can say. Every day the scientists descover new things. Perhaps, our notion about the reality will be changed.

Quantum computing has relevance in solving a few urgent problems, and in particular one that is associated with finding efficient ways of  mitigating the contribution of fossil fuel emissions to global warming trends. Carbon capture and sequestration has been identified as a viable route  to mitigating carbon dioxide emissions. But computational challenges still exist in determining the exact  force fields using high-level quantum chemical calculations in specific material systems. It is hoped that the  parallelism afforded by quantum computers may one day help determine the material system with the optimum force fields needed to stop current warming trends.  Another obvious application is the development of quantum cryptographic tools to prevent hacking and spying activities. Lastly, the use of quantum technologies in medical robotic systems promises to be an exciting interdisciplinary field of research involving quantum physicists and medical scientists.

Though the quantum computer is still elusive, the commercial products of quantum key distribution are already available in the international market.

At first, we should actually HAVE a quantum computer of reasonable size. Unless one struggles with the factorisation of nubers in the range of 10-100 (see however a not scalable(?) approach in Phys. Rev. Lett. 98, 120502 (2007)) we are not in the position to ask for valuable applications first.

There will certainly be several in case we should finally succeed in building a quantum computing device. The huge parallelisation is already something which gives a hughe advantage. Having a nonzero probability of success(!), the result could afterwards easily be verifyed, if it is a problem in NP.

Only at the moment, people are not pushed hardly towards thinking about possible solutions, as an existence of this device would certainly do (see however the remarks made by Alagu Thilgam).

The opposite direction is far more developed: quantum cryptography, since it works already quite some time (see also here the answer by Alagu).

As far as your question about quantum mechanics is concerned: quantum mechanicsis the theory of choice still, not an option, for any modern practical problem, and we are more about to enter this field even more, seeing the development and Moore's law. Think about modern *classical* computers where the essential elements (memory and CPU) are about to leave the "classical" regime in quantum mechanics, and then every single element was to be treated quantum mechanical: so far, e.g. electrical currents through such an element is treated as if it was a classical quantity .

We are on the cusp of a new era of computing, with Google, IBM and other tech companies using a theory launched by Einstein to build machines capable of solving seemingly impossible tasks.

Quantum computing certainly sounds like the future. It’s the technology of choice for sci-fi film-makers who want their artificial intelligence networks to have unlimited potential. But,the question is what is it really about, and what might it do? One of the possible answer that it might change the way we think about computers, the way how they works and might bring with it new algorithms and careers. They are surely to revolutionize the future of computing.