# Majorana Fermions and Representations of the Braid Group

@article{Kauffman2017MajoranaFA, title={Majorana Fermions and Representations of the Braid Group}, author={Louis H. Kauffman}, journal={arXiv: Geometric Topology}, year={2017} }

In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this result with the Ivanov braiding associated with Majorana operators. The paper generalizes observations of Kauffman and Lomonaco and of Mo-Lin Ge to show that certain strings of… Expand

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#### References

SHOWING 1-10 OF 46 REFERENCES

Braiding and Majorana fermions

- Mathematics
- 2017

In this paper, we study unitary braid group representations associated with Majorana fermions. Majorana fermions are represented by Majorana operators, elements of a Clifford algebra. The paper… Expand

Extraspecial 2-groups and images of braid group representations

- Mathematics
- 2005

We investigate a family of (reducible) representations of the braid groups Bn corresponding to a specific solution to the Yang‐Baxter equation. The images of Bn under these representations are finite… Expand

More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation

- Physics, Computer Science
- Scientific reports
- 2015

The 3- body Hamiltonian commuting with Γ is derived by 3-body -matrix, and it is shown that the essence of the doubling degeneracy is due to . Expand

Braiding operators are universal quantum gates

- Physics
- 2004

This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change… Expand

$q$ - Deformed Spin Networks, Knot Polynomials and Anyonic Topological Quantum Computation

- Mathematics, Physics
- 2006

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups.… Expand

The Fibonacci Model and the Temperley-Lieb Algebra

- Mathematics, Physics
- 2008

We give an elementary construction of the Fibonacci model, a unitary braid group representation that is universal for quantum computation. This paper is dedicated to Professor C. N. Yang, on his 85th… Expand

Quantizing knots, groups and graphs

- Mathematics, Engineering
- Defense + Commercial Sensing
- 2011

This paper formulates a generalization of our work on quantum knots to explain how to make quantum versions of algebraic and combinatorial structures. We include a description of work of the first… Expand

Search for Majorana Fermions in Superconductors

- Physics
- 2011

Majorana fermions (particles that are their own antiparticle) may or may not exist in nature as elementary building blocks, but in condensed matter they can be constructed out of electron and hole… Expand

Knot Logic and Topological Quantum Computing with Majorana Fermions

- Mathematics, Physics
- 2013

This paper is an introduction to relationships between quantum topology and quantum computing. We take a foundational approach, showing how knots are related not just to braiding and quantum… Expand

Anyons in an exactly solved model and beyond

- Physics
- 2006

A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may… Expand