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2004

Electrical and Computer Engineering

Algorithms

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Quantum Lattice Representation Of Dark Solitons, George Vahala, Linda L. Vahala, Jeffrey Yepez Jan 2004

Quantum Lattice Representation Of Dark Solitons, George Vahala, Linda L. Vahala, Jeffrey Yepez

Electrical & Computer Engineering Faculty Publications

The nonlinear Schrodinger (NLS) equation in a self-defocusing Kerr medium supports dark solitons. Moreover the mean field description of a dilute Bose-Einstein condensate (BEC) is described by the Gross-Pitaevskii equation, which for a highly anisotropic (cigar-shaped) magnetic trap reduces to a one-dimensional (1D) cubic NLS in an external potential. A quantum lattice algorithm is developed for the dark solitons. Simulations are presented for both black (stationary) solitons as well as (moving) dark solitons. Collisions of dark solitons are compared with the exact analytic solutions and coupled dark-bright vector solitons are examined. The quantum algorithm requires 2 qubits per scalar field …