Unitary Qubit Lattice Algorithm for Three-Dimensional Vortex Solitons in Hyperbolic Self-Defocusing Media

A qubit unitary lattice algorithm is developed for the 3D generalized Gross-Pitaevskii equation in which dark optical vortices are stabilized by a transverse bright soliton. It is shown how to generalize the unitary collision operator in order to switch the elliptic operator into a hyperbolic one. These unitary algorithms can be run on a quantum computer.