[ncmncm]

Not a belief: it is a definition. If somebody comes up with something useful that doesn't fit, this becomes "classical" computation, and the new kind gets an adjective -- say, "quantum", that's catchy -- and then they both get to be computation.

Defining what you can't prove isn't a dodge. It's the foundation of all rigorous thinking. You can only prove anything within the bounds of a formalism, and anything is impossible only within that formalism. Thus in Einstein Lorentz space, going faster than light is impossible. Out here, it's true only if E-L is right about that. (And we know it's not right about everything, but still maybe -- probably -- about that.)

[tialaramex]

Quantum computers aren't doing anything that you couldn't do with a Turing machine. You can get a perfectly nice emulator that will run all Quantum computer algorithms on your Turing machine today. They'll just be annoyingly slow.

There are some machines that don't exist which are categorically more capable than a Turing machine, such as Clock Doubling Machines, (which get to do an infinite amount of Turing computation in finite time) but those don't exist at all so while philosophers can insist upon debating them it won't do you any practical good.