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My basic understanding of topological quantum computing is that it makes use of anyons which are particles satisfying the following rule under wave-function swap:

$$ |\psi_1 \psi_2\rangle = e^{i \theta} |\psi_2 \psi_1\rangle$$

We recognize the specific cases of boson for $\theta=0$ and fermions for $\theta=\pi$.

Now, Microsoft wants to do topological quantum computing with Majorana particles which are Fermions.

If the point is to use anyons, why is it so important to use Majorana particle? After all this is just a Fermion: couldn't electrons also do the job?

I feel like there is some subtelty here. Namely, somewhat that, yes, Majorana particles are fermions, but quantum computing based on Majorana particle still somewhat uses non-trivial anyons (i.e. that are neither fermions or bosons).

Peter-Jan
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Marco Fellous-Asiani
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It is the exact same answer as to your previous question - thier topological nature. The point to use Majorana particles stems from the fact that they are defined by the topology of the Hamiltonian (or: the physical system), thus are robust in the same sort of manner that topological codes are.

They also have the nice features that they are thier own anti particles, which makes is possibile do define Clifford operator on them.

David Dentelski
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