Toric codes in topological quantum computation

Postgraduate Thesis uoadl:2938085 12 Read counter

Κατεύθυνση Πυρηνική Φυσική και Φυσική Στοιχειωδών Σωματιδίων
Library of the School of Science
Deposit date:
Karaiskos Georgios
Supervisors info:
Εμμανουήλ Φλωράτος, Ομότιμος Καθηγητής, Τμήμα Φυσικής, Εθνικό Καποδιστριακό Πανεπιστήμιο Αθηνών (κύριος επιβλέπων)
Αλέξανδρος Καρανίκας, Αφυπηρετήσας Καθηγητής, Τμήμα Φυσικής, Εθνικό Καποδιστριακό Πανεπιστήμιο Αθηνών
Φώτιος Διάκονος, Αναπληρωτής Καθηγητής, Τμήμα Φυσικής, Εθνικό Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Toric codes in topological quantum computation
Translated title:
Toric codes in topological quantum computation
For decades now, the realization of an operational quantum computer has captured the scientific community’s interest. Such a device will be able to exploit the core concepts of quantum mechanics (superposition, entanglement) in order to solve specific problems, that would take an impractical amount of time for any conventional computer. The big obstacle we need to overcome for an idea like that to work is the sensitivity of quantum systems to what we call quantum noise. We begin our thesis by presenting the key ideas upon which the error correcting codes theory is structured. That is the theory responsible to deal with the fragile stability of quantum systems. The idea is to use a large number of physical quantum degrees of freedom (e.g. qubits) and restrict their possible states to a specific subspace of the original Hilbert space, hence, encoding a smaller number of logical quantum degrees of freedom.
We continue by analyzing the most famous such code -the toric code- in a manner that gives birth to the concept of error correction at the physical level. What we, succinctly, do is introducing a Hamiltonian that involves only local interactions. The ground state of this Hamiltonian coincides with the subspace we talked about earlier. The degeneracy of that space, as well as its inaccessibility from local operations, makes it a prime candidate for safe quantum information storage. We then study the information process capabilities of this model.
Next comes a generalization of the toric code (called generalized Kitaev model) in which we use higher dimensional degrees of freedom to build our system. We analyze the new processes that emerge and see how these can aid our cause.
Finally we comment on the adequacy of our models to be used as topological quantum memories and briefly review the recent literature oriented towards the realization of a more optimal model for the tasks of quantum information storage and process.
Main subject category:
toric code, topological quantum computation, Abelian Kitaev models, topological quantum memories, quantum computers
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