University of Cambridge > > CQIF Seminar > Quantum Search with Bose-Einstein Condensates and Effective Nonlinearities

Quantum Search with Bose-Einstein Condensates and Effective Nonlinearities

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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 N1/4. This is a significant, but not unreasonable, improvement over the N1/2 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.

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