@Sqrl, what you're basically describing is "evolutionary computing". Neural networks are a form of evolutionary computing, but it's actually a specific way of doing things (by having multiple "paths" between the input and the output, and strengthening or weakening the weighting of these paths based on multiple trials, named so because it mimics the way the brain learns, but obviously on a much simpler scale) rather than describing the concept. Another form of evolutionary computing you may have heard of is "genetic algorithms", which have a similar goal but mimic natural selection rather than human learning.
@OP. You seem to have a deep misunderstanding of what a quantum computer actually is. It's not just an evolutionary step in computers where everything is more powerful, but it's a completely different direction for computers. Think of it like the Wii compared to other consoles. Regular computers will keep getting more and more powerful, but a quantum computer is not more powerful than a regular computer. What it is is a completely different way of looking at how computers work (ie, we're not even talking about 1 and 0 any more). Now in the real world a quantum computer may not be any more powerful than a real computer, but for some tasks (mainly, many NP problems) it will be much better.
One famous (and an incredibly important, and very real danger) example is the factorisation of very large numbers. Factorisation is an NP problem, it has exponential complexity, every time you add a single bit to the number you are factorising, the amount of time taken to solve the problem doubles. Therefore when the numbers get very large, the amount of time required to solve the problem enters the billions of years. Even as computers get more powerful exponentially, the size of the numbers they can factorise in a small amount of time (say, a year) only increases bit by bit)
This is of course incredibly important because the RSA algorithm relies on the intractability of factorising large numbers, yet there is an algorithm for quantum computers which can factorise in polynomial time. 1024 bit keys should last until the end of RSA's life because the second a decently powered quantum computer comes out, RSA, and I believe, all other current forms of public key cryptography, will be completely useless, which is a huge problem because the entire secure internet world relies on it.
What you will find though, is that while some things will become faster with quantum computers, the main benefit will be that problems we couldn't solve before will now become more solvable. You may find, as Sqrl pointed out, that evolutionary computing may be a viable solution for creating AI players, but don't expect to see photorealistic graphics due to "th4 pow4 of th4 quantum!!1". Of course, the only thing that's going to stop us having photorealistic graphics in 20 years from regular computer advancements will be the designers, but I expect by then all graphics will be procedurally generated.
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