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19 votes
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What exactly are anyons and how are they relevant to topological quantum computing?

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, ...
Simon Burton's user avatar
11 votes

What exactly are anyons and how are they relevant to topological quantum computing?

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 ...
user1271772's user avatar
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9 votes

What is the status of confirming the existence of anyons?

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 ...
James Wootton's user avatar
7 votes
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Anyon alternatives in topological quantum computing

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 ...
DaftWullie's user avatar
5 votes

What is the status of confirming the existence of anyons?

A more definite claim of detection of abelian anyons appeared in 2020: H. Bartolomei et al.: "Fractional statistics in anyon collisions", Science 368, 173-177 (2020) (arXiv:2006.13157) J. ...
Urs Schreiber's user avatar
5 votes

Can you make anyons in 3 dimensions using rings?

Indeed -- in theory, at least -- anyonic statistics does not so much require the ambient space to be 2-dimensional, as it requires the anyonic defects to have co-dimension 2 (hence dimension 2 less ...
Urs Schreiber's user avatar
4 votes

Topological quantum computer and two dimensional materials

Besides nanowires, Majoranas can also be found in the center of vortices in a chiral p-wave superconductor, for instance [1]. Moving the vortices in real space or using some measurement based ...
Bruna Mendonça's user avatar
4 votes

What is the most economical and preferred basis for the qudit?

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 ...
Simon Burton's user avatar
4 votes
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Breakthroughs in quantum computing using non-standard quanta

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 ...
user1271772's user avatar
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3 votes
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What is the most economical and preferred basis for the qudit?

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 ...
James Wootton's user avatar
3 votes

Does this experimental discovery of anyons enables the topological quantum computer (e.g. Microsoft) to become a reality?

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 ...
JSdJ's user avatar
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3 votes

Can you make anyons in 3 dimensions using rings?

In 3 dimensions, you can have both point particles and loops/rings/strings (all mean the same thing). There are several known braiding processes involving these two kinds of objects: A particle can ...
Meng Cheng's user avatar
3 votes
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Topological anyonic molecule statistics

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)...
David Bar Moshe's user avatar
2 votes

Measuring Ising anyons: What is a fusion measurement?

A bit late, but some comments for the sake of posterity: Yes, the claim is that in certain systems, a pair of anyons can be brought close together -- then measuring (for instance) the energy of the ...
Sachin Valera's user avatar
1 vote
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Energy and degeneracy of the ground state and excitations of the toric code

One of the major points of the Toric code Hamiltonian is that all the terms commute, each of which as $\pm 1$ eigenvalues. So, to find the ground state, you need something that is the $+1$ eigenstate ...
DaftWullie's user avatar
1 vote
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Topological quantum computer and two dimensional materials

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 ...
Emil Prodan's user avatar
1 vote

Simulating quantum computers using anyon braiding

In the paper Simulation of topological field theories by quantum computers by Freedman, Larsen, and Wang they prove that "TQFTs cannot be used to define a model of computation stronger than the ...
schrodingers_ncat's user avatar
1 vote

Breakthroughs in quantum computing using non-standard quanta

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....
Dripto Debroy's user avatar
1 vote

What exactly are anyons and how are they relevant to topological quantum computing?

Here would be my laymen explanation. The big idea of quantum computation is that there are quantum systems which are hard to classically simulate. This means that quantum processes can be viewed as ...
Milo Moses's user avatar

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