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CATEGORIES:CQIF Seminar
SUMMARY:Quantum Search with Bose-Einstein Condensates and
Effective Nonlinearities - Tom Wong\, University o
f Latvia
DTSTART;TZID=Europe/London:20150205T141500
DTEND;TZID=Europe/London:20150205T151500
UID:TALK57640AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/57640
DESCRIPTION:Although quantum mechanics is linear\, there are n
evertheless quantum systems with multiple interact
ing particles in which the effective evolution of
a single particle is governed by a nonlinear Schro
dinger equation. Bose-Einstein condensates\, for e
xample\, can be described by the Gross-Pitaevskii
Equation under certain conditions\, which has a te
rm proportional to the cube of the wavefunction. W
e show that with such a nonlinearity\, the unstruc
tured search problem can be solved in constant tim
e. Our algorithm\, however\, requires increasingly
precise time measurement with increasing problem
size\, N\, but since solving the problem more slow
ly reduces the necessary measurement precision\, t
he resource requirements can be jointly optimized
to scale as N^{1/4}. This is a significant
\, but not unreasonable\, improvement over the N~~1/2 scaling of Grover's algorithm. We con
clude by considering the implications of such nonl
inear dynamics arising as an approximation to the
quantum evolution of multiple particles\, and we a
rrive at a quantum information-theoretic argument
for the number of particles needed for the Gross-P
itaevskii equation to accurately describe the line
ar\, multi-particle dynamics of a Bose-Einstein co
ndensate.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfo
rce Road\, Cambridge
CONTACT:William Matthews
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