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13

The first thing to do is to think topologically: make sure you understand why a coffee cup is the same thing topologically as a donut. Now, imagine we swap two identical particles, and do it again, so that we are back where we started. Apply this topological thinking to the paths taken by the particles: it is the same as doing nothing. Here I show a ...


9

You are right, it does look like the Wikipedia page needs work, so I will have to update it. But for now I will answer all five questions: 1) What do they mean by "much less restricted than fermions and bosons? The exchange of two fermions or bosons is restricted by: $|\psi_1\psi_2\rangle = \pm|\psi_2\psi_1\rangle$. The "$+$" corresponds to bosons and ...


6

It depends what you mean by the 'existence' of anyons. One way is to engineer a Hamiltonian which leads to quasiparticles (or other defects) that have anyonic statistics. This will require the Hamiltonian to be implemented, the system to be cooled to sufficiently near the ground state, the anyons to be manipulated, etc. So there's a lot to be done, and I ...


5

The Toric code is an error correcting code. The distance of the code (I.e. the number of local operations required to convert one logical state into an orthogonal one) is equal to $N$, where the Toric code is defined on an $N\times N$ grid. One of the places that the performance of the Toric code really wins out is that although it is only distance $N$, the ...


5

Are there other instances of topological QC that do not use anyons? No, that's basically by definition. That said, there are different ways that one could use topological systems in order to achieve quantum computation. In the version you're talking about, you use these anyon pairs to define qubits, and braid them around each other to create quantum gates. ...


4

The only two quasi-particle quanta for which I know there to be active research in quantum computing are phonons and anyons. Phonons: That state-of-the-art is given my answer here: Phononic Quantum Computing Anyons: Synthesizing the first anyonic qubit is still an outstanding goal, but major milestones have been discussed very recently. This paper was the ...


3

The spin-statistics theorem requires a particle's wave function to acquire the same phase when it is rotated by an angle of $2 \pi$ about itself and when exchanged with an identical (indistinguishable) particle. For example, a fermion acquires a phase of $-1$ both in exchange and self-rotation. Thus, when we think of an anyon as a flux-charge entity, we ...


1

Microsoft has invested huge resources into engineering topological qubits. Their approach is based on topological Majorana states, which occur at the edges of a topological superconducting chain or at interfaces between such chains. For those who see these words for the first time, a quick mental representation is supplied by a ribbon, which can be twisted a ...


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