Re: What's the application?
The classic example of where classical computers don't work too well is called The Travelling Salesman problem - ie what's the most efficient route to visit all the cities. Some quantum computers could calculate all possible paths *simultaneously*.
No! The class of algorithms efficiently computable by Quantum Computers (i.e. BQP) does NOT include NP-hard or even NP-complete problems.
Some scientists doubt if quantum error rates can be reduced sufficiently, but it's too big a prize to not reach towards.
Yes indeed: The Future of Quantum Computing (Hope this goes through, sometimes Forum Control™ takes a dislike links to Quanta Mag, I suppose it's on the list of the false-newsy sites somehow)