# Extraspecial two-Groups, generalized Yang-Baxter equations and braiding quantum gates

@article{Rowell2007ExtraspecialTG,
title={Extraspecial two-Groups, generalized Yang-Baxter equations and braiding quantum gates},
author={Eric C. Rowell and Yong Zhang and Yong-Shi Wu and Mo-Lin Ge},
journal={Quantum Inf. Comput.},
year={2007},
volume={10},
pages={685-702}
}
• Published 12 June 2007
• Mathematics
• Quantum Inf. Comput.
In this paper we describe connections among extraspecial 2-groups, unitary representations of the braid group and multi-qubit braiding quantum gates. We first construct new representations of extraspecial 2-groups. Extending the latter by the symmetric group, we construct new unitary braid representations, which are solutions to generalized Yang-Baxter equations and use them to realize new braiding quantum gates. These gates generate the GHZ (Greenberger-Horne-Zeilinger) states, for an…
• Mathematics
Quantum
• 2020
A solution-generating technique is introduced to solve the $(d,m,l)$-generalized Yang-Baxter equation, for $m/2\leq l \leq m$, which allows to systematically construct families of unitary and non-unitary braiding operators that generate the full braid group.
• Physics
Quantum Information and Computation
• 2020
Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at
• Mathematics
• 2014
We investigate the generalized braid relation for an arbitrary multipartite d-level system and its application to quantum entanglement. By means of finite-dimensional representations of quantum plane
• Mathematics
• 2012
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary
• Mathematics
Communications in Mathematical Physics
• 2011
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary
• Mathematics
• 2020
For a generic n-qubit system, local invariants under the action of SL(2,C)⊗n characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to
• Mathematics
• 2012
Inspired by quantum information theory, we look for representations of the braid groups B_n on V^(⊗(n+m−2)) for some fixed vector space V such that each braid generator σ_i, i = 1, ..., n−1, acts on
• Physics
Quantum Inf. Comput.
• 2020
Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally
It is shown that the separability of varPsi \rangle = B|0⟩⊗N is closely related to the diagrammatic version of the braid operator $$\mathcal {B}$$B.
• Physics
• 2018
The Yang-Baxter equation has become a significant theoretical tool in a variety of areas of physics. It is desirable to investigate the quantum simulation of the Yang-Baxter equation itself,

## References

SHOWING 1-10 OF 51 REFERENCES

• 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 matrix) of the Yang–Baxter equation is a universal
• Physics, Mathematics
Quantum Inf. Process.
• 2005
The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, the unitary solutions
• Mathematics
Quantum Inf. Process.
• 2007
The Bell matrix is defined to yield all the Greenberger–Horne–Zeilinger (GHZ) states from the product basis, proved to form a unitary braid representation and presented as a new type of solution of the quantum Yang–Baxter equation.
• Mathematics
• 2008
The Bell matrix has become an interesting interdisciplinary topic involving quantum information theory and the Yang–Baxter equation. It is an antisymmetric unitary solution of the braided Yang–Baxter
• Mathematics
• 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.
• H. Dye
• Physics
Quantum Inf. Process.
• 2003
All unitary solutions to the Yang–Baxter equation in dimension four are determined, which will assist in clarifying the relationship between quantumEntanglement and topological entanglement.
• Mathematics
• 1991
We present an explicit prescription for trigonometric Yang-Baxterization. Given a braid group representation (BGR) in appropriate form, our prescription generates explicit solutions to the quantum
• Physics
• 2004
It is fundamental to view unitary braiding operators describing topological entanglements as universal quantum gates for quantum computation. This paper derives a unitary solution of the quantum
It is proved that one of two mixed states can be transformed into the other by single-qubit operations if and only if these states have equal values of all 18 invariants, which provides a complete description of nonlocal properties.
• Physics
• 2008
Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of