19
votes
Accepted
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, ...
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17
votes
Accepted
How does topological quantum computing differ from other models of quantum computing?
The idea of topological quantum computing was introduced by Kitaev in this paper. The basic idea is to build a quantum computer using the properties of exotic types of particles, known as anyons.
...
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12
votes
Accepted
Is Gil Kalai's argument against topological quantum computers sound?
A topological quantum computer could be made by using an exotic phase of matter in which anyons arise as localized effects (such as quasiparticles or defects). In this case, errors typically cost ...
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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 ...
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 ...
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8
votes
Are there connections between long-range entanglement and topological quantum computation?
There were two simultaneous PRLs published by Kitaev & Preskill and Levin & Wen that I think answer your question.
These use the area law of entanglement seen by states that can be expressed ...
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7
votes
Accepted
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 ...
- 60.8k
6
votes
How does the size of a toric code torus affect its ability to protect qubits?
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 ...
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6
votes
Accepted
Why is this topological gate mentioned in Raussendorf et al. 2007 a CNOT?
There are a variety ways of showing this, depending on your prior knowledge. The simplest is to know that you can convert a braiding diagram into a ZX calculus graph by changing each ring into a ...
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6
votes
Accepted
What is the Stabilizer of a Code?
A group action of a group $G$ on a set $X$ is a map $\phi:\, G\times X \rightarrow X$ such that
$$
\phi(e,x) = x, \quad\text{and}\quad
\phi(g, \phi(h,x) ) = \phi(gh,x),
$$
for all $x\in X$ and $g,h\...
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6
votes
Accepted
Why Is This the Ground State of a Toric Code?
The crucial point it seems you are missing is to recognize that $A_s^2=1$ (for that matter, $B_p^2=1$ also) and therefore $(1+A_s)/2$ is a projector onto the $+1$ eigenspace of $A_s$. We would then ...
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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 ...
- 281
5
votes
Accepted
What is the correspondence between adiabatic phase and a topological phase?
When a quantum system, parametrized by a manifold of classical parameters, evolves along a closed path in the parameter space, its state experiences a unitary transformation, which is called a ...
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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. ...
- 281
5
votes
Accepted
Topological Circuit Simulator
Those figures were created manually with sketchup, which is a 3d modelling tool. There was no simulation involved, only careful application of known rules.
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5
votes
Topological Circuit Simulator
There is QTop which is an open-source project that can simulate but also visualize topological quantum codes.
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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 ...
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4
votes
Reference that explains how to read 3d topological diagrams for surface code computations
Here's an unfinished slide deck I have on reading these diagrams: https://docs.google.com/presentation/d/1IjZ-0W9Y22wNG5036WFnnkF5Az1Zt8jTHFTC1-e7Em4/edit?usp=sharing
- 40.8k
4
votes
Accepted
Are there any other companies besides Microsoft pursuing topological QC?
Microsoft is the only company that is trying to build a topological quantum computer. You mention that topological qubits handle noise far better than other systems, but they are also theoretical. ...
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4
votes
What is the correspondence between adiabatic phase and a topological phase?
From Wikipedia:
In physics, topological order is a kind of order in the
zero-temperature phase of matter (also known as quantum matter).
Macroscopically, topological order is defined and ...
- 60.8k
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 ...
4
votes
Accepted
Is the honeycomb code a subsystem code?
Subsystem codes have observables that commute with all measured operators. The honeycomb code as normally described has measured operators that anticommute with any possible choice of observable. It ...
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4
votes
Accepted
Are there logical operations unique to topological quantum computing?
"Are there any algorithms or logical operations which are only unique to topological quantum computing architecture?"
No.
Any "universal" quantum computer that is capable of ...
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 ...
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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 ...
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3
votes
Accepted
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)...
- 2,585
3
votes
Accepted
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 ...
- 11.4k
3
votes
Is the honeycomb code a subsystem code?
The honeycomb 'code' is not even really a code - you can't write down a gauge group that defines a (subsystem of a) subspace that defines it. It's really more a fault-tolerant circuit (which steps ...
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2
votes
How does the size of a toric code torus affect its ability to protect qubits?
The length of the loops determines the quantity called the code distance. The key fact about its effect on the function of the code is the exponential suppression of errors.
More precisely, if $d$ is ...
- 24.2k
2
votes
How does topological quantum computing differ from other models of quantum computing?
Another approach to topological quantum computing could be that of topological insulators, and the use of the 1/2 integer quantum Hall effect. These insulators have the potential to be less error-...
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