Assume the number of quantum gate-ops per second doubles every 18 months. Assume SAT is O(2^n) on a classical computer and O(2^(n/2)) by Grover's. Then the maximum feasible problem size on a classical computer increases by 1 every 18 months, and on a quantum computer increases by 2. No factors of anything involved.
Alternately, if you measure a fixed problem size, then by assumption speed doubles for both.
So where does 4x come from?
It just comes from treating classical computers as the correct measuring stick. It would be more precise to refer, as you do, to 18 months as the add one time than the doubling time. But if you do call it the doubling time, then for quantum computers, it becomes the 4x time. Of course, it's not uniform--it doesn't apply to problems in P.
Eliezer Yudkowsky and Scott Aaronson - Percontations: Artificial Intelligence and Quantum Mechanics
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