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SUMMARY:Quantum Search with Bose-Einstein Condensates and Effective Nonlin
 earities - Tom Wong\, University of Latvia
DTSTART:20150205T141500Z
DTEND:20150205T151500Z
UID:TALK57640@talks.cam.ac.uk
CONTACT:William Matthews
DESCRIPTION:Although quantum mechanics is linear\, there are nevertheless 
 quantum systems with multiple interacting particles in which the effective
  evolution of a single particle is governed by a nonlinear Schrodinger equ
 ation. Bose-Einstein condensates\, for example\, can be described by the G
 ross-Pitaevskii Equation under certain conditions\, which has a term propo
 rtional to the cube of the wavefunction. We show that with such a nonlinea
 rity\, the unstructured search problem can be solved in constant time. Our
  algorithm\, however\, requires increasingly precise time measurement with
  increasing problem size\, N\, but since solving the problem more slowly r
 educes the necessary measurement precision\, the resource requirements can
  be jointly optimized to scale as N<sup>1/4</sup>. This is a significant\,
  but not unreasonable\, improvement over the N<sup>1/2</sup> scaling of Gr
 over's algorithm. We conclude by considering the implications of such nonl
 inear dynamics arising as an approximation to the quantum evolution of mul
 tiple particles\, and we arrive at a quantum information-theoretic argumen
 t for the number of particles needed for the Gross-Pitaevskii equation to 
 accurately describe the linear\, multi-particle dynamics of a Bose-Einstei
 n condensate.
LOCATION:MR4\,  Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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