Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 13th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something <a href="https://ncatlab.org/nlab/revision/su%282%29-anyon/1">v1</a>, <a href="https://ncatlab.org/nlab/show/su%282%29-anyon">current</a>

   starting something

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 17th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * Ryan Simeon, *Universality of Fibonacci anyons in topological quantum computing* (2021) $[$[pdf](https://homes.psd.uchicago.edu/~sethi/Teaching/P243-W2021/Final%20Papers/Simeon-PHYS243_final.pdf)$]$ <a href="https://ncatlab.org/nlab/revision/diff/su%282%29-anyon/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/su%282%29-anyon/9">v9</a>, <a href="https://ncatlab.org/nlab/show/su%282%29-anyon">current</a>

   added pointer to:

   • Ryan Simeon, Universality of Fibonacci anyons in topological quantum computing (2021) $[$pdf$]$

   diff, v9, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 26th 2022
   • (edited Aug 26th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave expanded and updated ([here](https://ncatlab.org/nlab/show/su(2)-anyon#NonRealizationOfMZZInNanowires)) the list of references with (non-)retracted claims of (non-)detection of MZMs in nanowires, and their commentary/criticism. <a href="https://ncatlab.org/nlab/revision/diff/su%282%29-anyon/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/su%282%29-anyon/12">v12</a>, <a href="https://ncatlab.org/nlab/show/su%282%29-anyon">current</a>

   have expanded and updated (here) the list of references with (non-)retracted claims of (non-)detection of MZMs in nanowires, and their commentary/criticism.

   diff, v12, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 28th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added the original references proposing the existence and search for "Majorana zero modes" in nanowires: * [[Alexei Kitaev]], *Unpaired Majorana fermions in quantum wires*, Physics-Uspekhi, **44** 10S (2001) 131-136 &lbrack;[doi:10.1070/1063-7869/44/10S/S29](https://iopscience.iop.org/article/10.1070/1063-7869/44/10S/S29)&rbrack; * Roman M. Lutchyn, Jay D. Sau, [[Sankar Das Sarma]], *Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures*, Phys. Rev. Lett. **105** (2010) 077001 &lbrack;[doi:10.1103/PhysRevLett.105.077001](https://doi.org/10.1103/PhysRevLett.105.077001)&rbrack; * Yuval Oreg, Gil Refael, and Felix von Oppen, *Helical Liquids and Majorana Bound States in Quantum Wires*, Phys. Rev. Lett. **105** (2010) 177002 &lbrack;[doi:10.1103/PhysRevLett.105.177002](https://doi.org/10.1103/PhysRevLett.105.177002)&rbrack; Though at this point this may be mostly of historical interest. In any case, I think I should split off an entry *[[Majorana zero mode]]*, in order not to overburden the entry here with that story. <a href="https://ncatlab.org/nlab/revision/diff/su%282%29-anyon/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/su%282%29-anyon/15">v15</a>, <a href="https://ncatlab.org/nlab/show/su%282%29-anyon">current</a>

   I have added the original references proposing the existence and search for “Majorana zero modes” in nanowires:

   • Alexei Kitaev, Unpaired Majorana fermions in quantum wires, Physics-Uspekhi, 44 10S (2001) 131-136 [doi:10.1070/1063-7869/44/10S/S29]

   • Roman M. Lutchyn, Jay D. Sau, Sankar Das Sarma, Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures, Phys. Rev. Lett. 105 (2010) 077001 [doi:10.1103/PhysRevLett.105.077001]

   • Yuval Oreg, Gil Refael, and Felix von Oppen, Helical Liquids and Majorana Bound States in Quantum Wires, Phys. Rev. Lett. 105 (2010) 177002 [doi:10.1103/PhysRevLett.105.177002]

   Though at this point this may be mostly of historical interest. In any case, I think I should split off an entry Majorana zero mode, in order not to overburden the entry here with that story.

   diff, v15, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeFeb 26th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the following pointer for the result that $su(2)$-anyons provide universal quantum gates not only at level $k=3$ (which is the result always mentioned) but for all higher $k$, too: * [[Nikita Kolganov]], [[Sergey Mironov]], [[Andrey Morozov]], *Large $k$ topological quantum computer*, Nuclear Physics B **987** (2023) 116072 &lbrack;[arXiv:2105.03980](https://arxiv.org/abs/2105.03980), [doi:10.1016/j.nuclphysb.2023.116072](https://doi.org/10.1016/j.nuclphysb.2023.116072)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/su%282%29-anyon/20">diff</a>, <a href="https://ncatlab.org/nlab/revision/su%282%29-anyon/20">v20</a>, <a href="https://ncatlab.org/nlab/show/su%282%29-anyon">current</a>

   added the following pointer for the result that $su(2)$-anyons provide universal quantum gates not only at level $k=3$ (which is the result always mentioned) but for all higher $k$, too:

   • Nikita Kolganov, Sergey Mironov, Andrey Morozov, Large $k$ topological quantum computer, Nuclear Physics B 987 (2023) 116072 [arXiv:2105.03980, doi:10.1016/j.nuclphysb.2023.116072]

   diff, v20, current