Do any decision problems exist outside NP and NP-Hard?

What will be some applications of commodotised quantum computers? (or any 'trivialisation' of NP-hard problems)?

Imagine, hypothetically, if we were to build computers that could solve even the most complex NP-hard problems. This imaginary computer would be so fast that even the exponential slow-down of NP-hard problems doesn't become apparent (a kind of oracle machine (http://en.wikipedia.org/wiki/Oracle_machine)). If we were to develop this technology, what could we do with such immense power? What will be some of the applications of inconceivably rapid computation, post-singularity? Also, from a technical standpoint, how would the trivialisation of the travelling-salesman problem allow us to build Turing-test passing machines?
Answer:

Cryptography breaking. After quantum computers become popular, passwords and security as we know it will no longer be effective.

Dan Zhang at Quora Visit the source

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