Supervisors info:
Εμμανουήλ Φλωράτος, Ομότιμος Καθηγητής, Τμήμα Φυσικής ,ΕΚΠΑ
Summary:
In this thesis, we made 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. In the first part, we discused the basics of group theory in order to construct an anyon model. For our anyon model, we used the group and calculated the different combinations of fluxons and chargeons for every anyon of this model.
In the second part, we talked about the differencies between anyons and 3D particles and that we (in theory) could construct a quantum computer based on these properties. Quantum gates are very sensitive to decoherence, but gates based on the rotation of anyons can guarantee a much better protection of the information. Furthermore, we studied the operations which can occur between anyons and how they can be simulated with F and R matrices. In the end, we studied the simplest of all anyon models, the Fibonacci anyon model, which allows (in theory) universal quantum computing. We constructed the F and R matrices for the Fibonacci anyons using some conditions known as pentagon and hexagon equations.
Keywords:
Topological Quantum Computing, Anyons, Braid Group, Quantum Double, Fusion Rules
