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Anyon model based on the symmetry group D4 and Fibonacci anyons

Anyon model based on the symmetry group D4 and Fibonacci anyons

Ostatnia modyfikacja: 
poniedziałek, 10 maja 2021 roku, 15:08

 

Zapraszamy w czwartek 12.05.2021 o godz. 14:00 na seminarium.

Seminarium ONLINE pod tytułem: "Anyon model based on the symmetry group D4 and Fibonacci anyons" poprowadzi  Grigoris Anastasiou

Abstrac: In this presentation, we will make a wide introduction to topological quantum computing. Quantum computers use qubits in order to function and topological quantum computers use anyons, 2D particles, to encode qubits. Anyons can be determined based on the magnetic flux and the charge they are consisted of. In the first part, we will discuss the basics of group theory in order to construct an anyon model. For our anyon model, we used the group D4 and calculated the different combinations of fluxes and charges for every anyon of this model. In the second part, we will talk about the differences between anyons and 3D particles and that we (in principle) could construct a quantum computer based on the properties of anyons. Quantum gates are very sensitive to decoherence, but gates based on the rotation of anyons can guarantee a much better protection of the information. Using the Aharonov-Bohm effect, we will examine how the quantum states acquire a phase which can be used for the coding of the information. On our study, we further examined the operations which can occur between anyons and how they can be simulated with F and R matrices. In the end, we will study the simplest of all anyon models, the Fibonacci anyon model, which allows (in principle) universal quantum computing. To conduct this study, we constructed the F and R matrices for the Fibonacci anyons using some conditions known as pentagon and hexagon equations.