Unit:
Κατεύθυνση Πυρηνική Φυσική και Φυσική Στοιχειωδών Σωματιδίων (ΒΑΣΙΚΗ ΦΥΣΙΚΗ)Library of the School of Science
Author:
Kolotouros Ioannis
Supervisors info:
Φλωράτος Εμμανουήλ, Ομότιμος Καθηγητής, Τμήμα Φυσικής, ΕΚΠΑ
Original Title:
Τοπολογική Κβαντική Υπολογιστική
Translated title:
Topological Quantum Computation
Summary:
In chapter 1 we begin with a brief introduction on how anyons and their topological
properties can be used for fault tolerant quantum computation. In chapter
2 we examine the symmetries of the hexagonal lattice, place spin 1/2 particles
in each site, let them interact with a Kitaev’s honeycomb lattice Hamiltonian
and find that in a special case it allows the existence of abelian anyons. In chapter
3 we add a small perturbation that breaks the time reversal symmetry of
the model creating an energy gap. This gap is sufficient for nonabelian anyons
whose fusion states can be used for creating the encoding computational states.
Moreover, in chapter 4 we work on a continuous gauge theory broken down to
the finite group S3, find the anyons of the model, construct the quantum double
D(S3) and derive the fusion rules. Finally in chapter 5 and 6 we prove how
to construct the fundamental gates with a nonabelian superconductor and with
Fibonacci anyons repsectively and how measurements can be done to achieve
universal quantum computation.
Main subject category:
Science
Keywords:
Topological Quantum Computation, Kitaev’s Model, Quantum Double, Fibonacci anyons