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15

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 ...


11

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 ...


7

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. ...


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 ...


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 ...


4

You may be confusing two uses of the word "base". One definition of "base" has to do with how many digits are used to represent a number. For example, base two uses the digits 0 and 1, and the number five is written as 101 in base two. But in quantum mechanics there is another use of the word "base" which has to do with basis vectors for a vector space. This ...


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 ...


3

The preferred basis problem is essentially something from the many worlds interpretation: If we are to interpret a superposition as representing many universes, what basis should we choose? Since this comes from the foundations of QM, this aspect of your question is perhaps better suited to the physics stack exchange. Is there a preferred basis for a ...


3

This is not the first time that there is found 'experimental proof' of (non-Abelian) anyons. Note also that the article does not use the word proof but rather evidence - that's why I also used the quotation marks above. Back in 2012 there supposedly was found the first experimental evidence of Majorana bound states by an observation of the zero bias peak. I ...


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 ...


1

I'm not sure if you count adiabatic quantum computing as fringe, but there was a paper using 4 NMR qubits to implement a adiabatic analogue to HHL which allowed them to invert an 8x8 operator with 98.4% fidelity which got put on arXiv a couple weeks ago. I thought that was pretty neat.


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