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The first line of the Wikipedia article on Moore's law states that

Moore's law is the observation that the number of transistors in a dense integrated circuit doubles about every two years

As scientists groan on about running into the physical limits of Moore's law, another bunch of scientists[or the media?] seems to feel like they can keep up the trend by leveraging characteristics of quantum computers.

However, a quantum computer doesn't use transistors in the same way that a traditional computer does, and adding another qubit, according to my knowledge, can double the computational power of the computer!

For that reason, is it time to restate Moore's law in such a way that it can take into account computational power as an abstract concept, and not necessarily a physical one?

Does it even make sense to ask that question?

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Quantum computers are interesting, but I don't think the primary motivation for quantum computers has anything to do with Moore's law. You might want to double-check where you got that impression from. Quantum computers -- if possible -- will be faster for some narrow set of problems, but by no means for all problems. See Why and how is a quantum computer faster than a regular computer? and Is it proven that quantum computation is no better at solving NP complete problems than classical computation?.

It's not really accurate to say that adding another qubit doubles the computational power of the computer. I suspect you might be falling for a common misconception about quantum computing (that they "try all possible combinations..."). See The Limits of Quantum by Scott Aaronson for some explanation.

I don't think there is any need to restate Moore's law. It is a rough rule of thumb about classical computers. It doesn't claim to say anything about quantum computers or computational power in general.

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