Quantum Computing Stack Exchange
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Questions tagged [topological-quantum-computing]

Topological quantum computing is a theoretical quantum computing model that employs two-dimensional quasiparticles called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions).

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

I have been trying to get a basic idea of what anyons are for the past couple of days. However, the online articles (including Wikipedia) seem unusually vague and impenetrable as far as explaining topological quantum computing and anyons goes. The…
Sanchayan Dutta
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What is the status of confirming the existence of anyons?

In a comment on my answer to the question: What exactly are anyons and how are they relevant to topological quantum computing? I was asked to give specific examples of occurrence of anyons in nature. I've spent 3 days searching, but every article…
user1271772 No more free time
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How does topological quantum computing differ from other models of quantum computing?

I've heard the term Topological Quantum Computer a few times now and know that it is equivalent to quantum computers using circuits with respect to some polynomial-time reduction. However, it is totally unclear to me how such a quantum computer…
dtell
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Reference that explains how to read 3d topological diagrams for surface code computations

I like making diagrams to describe computations. For the surface code, an excellent tool is 3d topological diagrams. Here is an example diagram (made by me in SketchUp): The basic idea is that white boundaries are places where Z observable chains…
Craig Gidney
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Is Gil Kalai's argument against topological quantum computers sound?

In a lecture, recorded on Youtube, Gil Kalai presents a 'deduction' for why topological quantum computers will not work. The interesting part is that he claims this is a stronger argument than the argument against fault tolerant computing in…
Discrete lizard
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Are there connections between long-range entanglement and topological quantum computation?

Long-range entanglement is characterized by topological order (some kinds of global entanglement properties), and the "modern" definition of topological order is the ground state of the system cannot be prepared by a constant-depth circuit from a…
Yupan Liu
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Are there any other companies besides Microsoft pursuing topological QC?

Also, why is Microsoft placing such an emphasis on topological qubits when most other companies seem to be focusing on other qubit technologies? I know topological qubits could handle noise far better than other systems, so they are appealing, but…
jman
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Topological Circuit Simulator

Does something like Quirk exist for topological (eg. braided) circuits? Alternatively, any ideas on how @CraigGidney is getting these circuits (or something similar)?
user820789
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How does the size of a toric code torus affect its ability to protect qubits?

The Toric code Hamiltonian is: $\sum_{x,y}\left( \prod_{i\in p(x,y)} Z_{ixy} + \prod_{i\in v(x,y)} X_{ixy} \right),$ where the $v$ and $p$ are defined according to this picture (courtesy of James Wooton's contribution to Wikipedia): At the moment…
user1271772 No more free time
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Correspondence between the Topological model and Quantum Circuit model

For example, given the $R$ & $F$ gates and Toric codes for a given problem, how to convert this code into the conventional circuit model and vice versa. From the literature developed, it seems that they tackle fairly different kinds of problems for…
user5438
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Why is it helpful to use Majorana particle in topological quantum computing (they are just Fermions?!)

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…
Marco Fellous-Asiani
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Origin of braiding in measurement-only TQC

I have a technical question on the "measurement-only"-proposal for topological quantum computation on anyons. First some background: Background. While it has become a common idea that topological quantum gates could be implemented by braiding…
Urs Schreiber
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Does this experimental discovery of anyons enables the topological quantum computer (e.g. Microsoft) to become a reality?

Microsoft has its own agenda regarding quantum computer - it is topological quantum computer being invented by the team lead by Michael Freedman https://www.microsoft.com/en-us/research/project/topological-quantum-computing/ While this idea is very…
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What is the correspondence between adiabatic phase and a topological phase?

In the adiabatic model, we have a system acquiring a Berry phase due to cyclic slow periodic evolution under a Hamiltonian. While in the topological phases, we talk about systems such as anyons which acquire fractional phases under permutation or…
Siddhant Singh
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Anyon alternatives in topological quantum computing

A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons. -Wikipedia Are there other instances of topological quantum computing models that do not use anyons? Are there alternative…
user820789
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