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Moore's law states that computer power doubles in every 18 months (more formally: "the number of transistors in a dense integrated circuit doubles about every two years."). Statistics suggest that this observation should be correct, but aren't quantum computers much more powerful than just double-powered classical computers? More interesting question is, is there even a way to improve the power of quantum computers?

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marked as duplicate by Sanchayan Dutta, glS, MEE the setup wizard, Discrete lizard, DaftWullie Jun 17 '18 at 17:05

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but aren't quantum computers much more powerful than just double-powered classical computers?

Yes. A universal quantum computer with only 100 qubits (12.5 quantum bytes) can find the ground state of a matrix with $2^{200} = 10^{60}$ elements. Assuming Moore's Law could continue forever (which is not true due to physical limitations), it would take longer than the age of the universe (13.5 billion years) for the "doubling of transistors every 18 months" to bring classical computers to what a quantum computer with one quantum gigabyte can do, for certain problems.

More interesting question is, is there even a way to improve the power of quantum computers?

There have been proposals for exploiting certain types of phenomena that would lead to devices even more powerful than quantum computers, but in all cases quantum computers would be a special case of such devices (just like classical computers are a special case of quantum computers, they are quantum computers that just only use classical gates and inputs that are not in any superposition). It is hard enough to build a quantum computer, so building the more generalized devices would be even harder.

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Moore's law is not a fundamental law of the nature. It is just a heuristic mentioned by Moore to show the growing importance of computer technology. You should never take it granted and there is nothing wrong if the actual trend doesn't follow Moore's law.

Secondly, Quantum computers give speed up in only certain kinds of computations. You cannot expect it to give exponential speed up for every classical algorithm. So it is inappropriate to compare a QC with a Classical computer. Classical computers are going to stay even after QC become commercially viable.

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    $\begingroup$ I think Moore's law might be the result a complex interaction of various non-technological, mainly economical effects, too. Like this: the need to have faster CPUs, the invested stock into the CPU development, the length of the timeline until a CPU plan becomes actually manufactured CPUs in the stores, and so on. $\endgroup$ – peterh Jun 17 '18 at 12:29
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The quantum equivalent of Moore's Law is Rose's Law which states that "the number of qubits in a scalable quantum computing architecture should double every year."

The prediction was made by Geordie Rose of D-Wave circa 2003. See D-Wave's Future of Hardware, this article or this amazing answer for more info.

My understanding is that a quantum computer can make $2^n$ computations per step where n is the number of qubits. With the number of qubits doubling every year this means the computational power of quantum computers will accelerate very quickly.

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