Proceedings of SPIE- The International Society for Optical Engineering
Quantum Information and Computation II, April 12-14, 2004
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 at each spatial node. The unitary collision operator quantum mechanically entangles the on-site qubits, and this transitory entanglement is spread throughout the lattice by the streaming operators. These algorithms are suitable for a Type-II quantum computers, with wave function collapse induced by quantum measurements required to determine the coupling potentials.
Original Publication Citation
Vahala, G., Vahala, L., & Yepez, J. (2004). Quantum lattice representation of dark solitons. Paper presented at the Quantum Information and Computation II, April 12-14, 2004, Orlando, FL, United States.
Vahala, George; Vahala, Linda L.; and Yepez, Jeffrey, "Quantum Lattice Representation of Dark Solitons" (2004). Electrical & Computer Engineering Faculty Publications. 50.