Quantum Search with Bose-Einstein Condensates and Effective Nonlinearities

Add to your list(s) Download to your calendar using vCal

• Tom Wong, University of Latvia
• Thursday 05 February 2015, 14:15-15:15
• MR4, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact William Matthews.

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 equation. Bose-Einstein condensates, for example, can be described by the Gross-Pitaevskii Equation under certain conditions, which has a term proportional to the cube of the wavefunction. We show that with such a nonlinearity, 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 reduces the necessary measurement precision, the 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 conclude by considering the implications of such nonlinear dynamics arising as an approximation to the quantum evolution of multiple particles, and we arrive at a quantum information-theoretic argument for the number of particles needed for the Gross-Pitaevskii equation to accurately describe the linear, multi-particle dynamics of a Bose-Einstein condensate.

This talk is part of the CQIF Seminar series.

This talk is included in these lists:

• All CMS events
• CMS Events
• CQIF Seminar
• DAMTP info aggregator
• Hanchen DaDaDash
• Interested Talks
• MR4, Centre for Mathematical Sciences, Wilberforce Road, Cambridge
• bld31

Note that ex-directory lists are not shown.