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JoshuaZ comments on One last roll of the dice - Less Wrong Discussion
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Oh. Lubos Motl. Considering he seems to spend his time doing things like telling Scott Aaronson that Scott doesn't understand quantum mechanics, I don't think Motl's opinion should actually have much weight in this sort of context.
Quantum topological computers are more robust than old-fashioned quantum computers, but they aren't that more robust and they have their own host of issues. People likely aren't looking into this because a) it seems only marginally more reasonable than the more common version of microtubules doing quantum computation and b) it isn't clear how one would go about testing any such idea.
In the article I linked, Lubos is expressing a common opinion about the merit of such formulas. It's a deeper issue than just Lubos being opinionated.
If I had bothered to write a paper, back when I was thinking about anyons in microtubules, we would know a lot more by now about the merits of that idea and how to test it. There would have been a response and a dialogue. But I let it go and no-one else took it up on the theoretical level.
Do you have any suggested method for testing the microtubule claim?
From my perspective, first you should just try to find a biophysically plausible model which contains anyons. Then you can test it, e.g. by examining optical and electrical properties of the microtubule.
People measure such properties already, so we may already have relevant data, even evidence. There is a guy in Japan (Anirban Bandyopadhyay) who claims to have measured all sorts of striking electrical properties of the microtubule. When he talks about theory, I just shake my head, but that doesn't tell us whether his data is good or bad.