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SUMMARY:Propagator Generation of Quantum Systems
DTSTART:20130429T141500
DTEND:20130429T151500
DTSTAMP:20260510T013121Z
UID:0dd5b41f0e40e2a51c5d8a759a893e905553c9e4d5eb7598e9f37b00
CATEGORIES:Conferences - Seminars
DESCRIPTION:Paulo Sergio Pereira da Silva\nThis work treats the problem of
  generating any desired goal\npropagator for a driftless quantum system th
 at evolves on the special\nunitary group SU(n) (or U(n)) . The physical re
 levance of such control\nproblem is the realization of arbitrary quantum g
 ates in quantum\ncomputers. Assuming only the controllability of the syste
 m\, the presentation\nconstructs explicit control laws that assure global 
 asymptotic\nconvergence of the  propagator of the system towards the goal
 \npropagator.  The controls laws rely on a reference trajectory that\ncro
 sses the desired goal propagator in a time-periodic fashion and\nsuch that
  its corresponding linearised system generates the Lie\nalgebra su(n) (or 
 u(n)). Their existence is ensured by the Return\nMethod of  Coron. The st
 ability of the tracking of the reference\ntrajectory is  assured by a con
 venient Application of a version LaSalle's\nInvariance Theorem [1]. The ef
 ficience of the control law can be improved\nwhen one combines this contro
 l law with a random selection of some\ncontrol parameters. In this case\, 
 the closed loop stability can be shown\nas an application of Kushner's The
 orem (a stochastic version of Lassale's\nInvariance Theorem) [2].\n[1]  H
 . Bessa Silveira\, P. S. Pereira da Silva\, an P. Rouchon.\nExplicit Contr
 ol Laws for the Periodic Motion Planning of Controllable\nDriftless System
 s on SU(n). IEEE Conference on Decision and Control\nCDC'2012. p. 3640-364
 5.\n[2] H. Bessa Silveira\, P. S. Pereira da Silva\, an P. Rouchon.\nA Sto
 chastic Lyapunov Feedback Technique for  Propagator Generation of\nQuantu
 m Systems on U(n). Submitted to ECC'2013.\nAuthors: Hector Bessa Silveira\
 , Paulo Sergio Pereira da Silva and Pierre Rouchon.
LOCATION:ME C2 405
STATUS:CONFIRMED
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