Classic von Neumann: "You insist that there is something a machine cannot do. If you will tell me precisely what it is that a machine cannot do, then I can always make a machine which will do just that!"
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We can use conventional computers to simulate quantum computers though. Here's an example: http://www.quantumplayground.net/#/home The problem is simulating quantum algorithms on classical computers doesn't scale well.
This is discussed in the essay. It's hard to see in the excerpt I quoted, since the work is being done by qualifiers ("simple, direct", "intractable" etc) that are explained elsewhere. http://michaelnielsen.org/blog/quantum-computing-for-everyone/ …