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SUMMARY:Iterated dynamical maps on a quantum computer - Professor Gerard J
  Milburn\, The University of Queensland
DTSTART:20080116T160000Z
DTEND:20080116T170000Z
UID:TALK10017@talks.cam.ac.uk
CONTACT:Berry Groisman
DESCRIPTION:I will discuss an alternative to simulating Hamiltonian flows 
 with a quantum computer. A Hamiltonian system is a continuous time dynamic
 al system represented as a flow of points in phase space.  An alternative 
 dynamical system\, first introduced by Poincare\, is defined in terms of a
 n area preserving map. The dynamics is not continuous but discrete and suc
 cessive dynamical states are labelled by integers rather than a continuous
  time variable.  Discrete unitary maps are naturally adapted to the quantu
 m computing paradigm. Grover's algorithm\, for example\, is an iterated un
 itary map. In this talk I will discuss examples of nonlinear dynamical map
 s which are well adapted to simple ion trap quantum computers\, including 
 a transverse field Ising map\, a non linear rotor map and a  Jahn-Teller m
 ap.  I will show how a good understanding of the quantum phase transitions
  and entanglement exhibited in these models can be gained by first describ
 ing the classical bifurcation structure of fixed points. \n
LOCATION:Centre for Mathematical Sciences\, Wilberforce Road\, Lecture roo
 m MR5
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