It explains one of the most remarkable known applications of quantum computers: to search an N-item search space, they only need to examine the search space roughly the square root of N times.
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Hardware, at least it used to. Not hand-wave ;-).
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Heh. Indeed. I glanced briefly at that piece when it came out; it looks substantially weaker than the best criticism. The best critical discussion I know of was between Aram Harrow (pro) and Gil Kalai (con) and a tonne of expert commenters (pro and con) on Dick Lipton's blog.
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Homework?
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Back in my day, we had to build our own (wire-wrapped) single board computer, program the boot ROM, prove it worked. Hence my sound motto: "hardware or gtfo".
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