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.
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?
Eliezer Yudkowsky and Scott Aaronson - Percontations: Artificial Intelligence and Quantum Mechanics
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