Unitary qubit lattice algorithm for three-dimensional vortex solitons in hyperbolic self-defocusing media

Abstract

To obtain stable vortex structures in three-dimensional (3D) nonlinear optics, Efremidis et al. (2007) have introduced a generalized Nonlinear Schrodinger equation (NLS) in which the transverse quantum vortex components are stabilized by a longitudinal bright soliton: i.e., the elliptic operator ∇2 is replaced by its hyperbolic counterpart ∇⊥2−∂2/∂z2. A new 3D mesoscopic qubit unitary lattice algorithm is developed for this generalized NLS. One introduces 2 qubits for each lattice site and entangles them with a local unitary collision operator. This entanglement is then spread throughout the lattice by nearest neighbor streaming. These interwined operators lead to an extremely well parallelized code on classical supcomputers while their unitary structure will permit encoding onto a quantum computer. Somewhat unexpectedly, the hyperbolic operator can be realized from variations in the collision operator, without introducing variations in the streaming operator. The initial line vortices are generated by Pade asymptotics. The energy constraint is conserved to 10 digit accuracy.