on 30-06-2017
Daniel Reitzner
Instituto Superior Técnico, Lisbon, Room P9, Mathematics Building, Friday, June 30th, 15:00h
Quantum searches are used to localize a specific element within the Hilbert space. Usually such element is a base state, or a small subspace of the Hilbert space. We expand this set by searching for a path in a maze between two specific vertices using quantum walks. A particular type of maze we use is a chain of connected stars. We show, that having M stars, each of them containing N spikes, we can find the whole path in O(M N^1/2) steps. Standard choice of the initial state in a large, albeit phase-modulated superposition leads to the usual Grover search. However, such state is usually hard to prepare and a choice of a ocalized state is preferred. In such case we show, that it is possible to find the path with the same efficiency (up to a multiplicative constant) successively, by starting on the first star and uncovering successive stars by short searches of O(N^1/2) steps.
Quantum Computation and Information Seminar
http://math.tecnico.ulisboa.pt/seminars/qci/index.php.en?action=next
Support: Phys-Info (IT), SQIG (IT) and CAMGSD, with support from FCT and FEDER, namely via the Doctoral Programme in the Physics and Mathematics of Information (DP-PMI), and projects UID/EEA/50008/2013, QuNet, ProQuNet, and NQuN.
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on 21-06-2017
Louis Kauffman
Instituto Superior Técnico, Lisbon, Room P3.10, Mathematics Building, Wednesday, June 21th, 14:15h
We will discuss the mathematics of Majorana Fermions and the structure of representations of the Artin Braid group that are associated with them. We will discuss how one class of representations is related to the Temperley Lieb algebra, and another class of representations is related to a Hamiltonian constructed from the Bell-Basis solution of the Yang-Baxter equation, and the relationship of this Hamiltonian with the Kitaev spin chain. We will discuss how these braiding representations are related to topological quantum computing.
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