I know that 3-SAT problem is NP-Complete but 'they say' it can be run quit faster on a quantum machine. Could you explain what kind of performance is possible to gain using quantum computers?
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The formalities of complexity theory are based on the Turing Machine, so this means that any __solution__ to 3-SAT has the same complexity regardless of the actually machine you might implement it on. I think that we'd need to use a different method/language to describe what we really care about (speed) to account for situations where QMs can defy complexity (although I know zero about QMs...) – Elliott Mar 31 '21 at 08:21
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IIRC Grover's algorithm gets you a square-root speedup over brute force, but the status of NP versus BQP is mostly up in the air I think. – David Eisenstat Apr 02 '21 at 01:35