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timtyler comments on Bloggingheads: Yudkowsky and Aaronson talk about AI and Many-worlds - Less Wrong
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It's a purely theoretical counterfactual about the combination of Moore's law and Grover's algorithm.
Moore's law says that the computer becomes twice as efficient in 18 months. Grover's algorithm says that the time taken by a quantum computer to solve SAT is the square root of the time required by a classical computer. Thus in 18 months, Moore's law of hardware should make the quantum computer 4 times as fast.
Well, I can see what math was done. The problem is the false assertion. I learned in math classes that if you accept one false thing, you can prove everything, and consequently your understanding of the difference between what's true and what's not dwindles to zero. You can't just believe one false thing.
If we actually "switched to quantum computers" it isn't clear we would get an exponential trajectory at all - due to the proximity of physical limits. If we did get an exponential trajectory, I can see no coherent reason for thinking the doubling time would relate to that of classical computers - because the technology is quite different. Currently, quantum computers grow mostly by adding qubits - not by the shrinking in component size that drives Moore's law in classical computers. That increases their quantum-parallelism, but doesn't affect their speed.