April 15-17

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Author: Linda Vahala
Requested Type: Poster
Submitted: 2019-02-21 18:39:53

Co-authors: G. Vahala, M. Soe, A. Ram and J. Yepez

Contact Info:
Old Dominion University
Hampton Boulevard
Norfolk, Virginia   23529
USA

Abstract Text:
The ubiquitous nonlinear Schrodinger (NLS) equation describes the evolution of quasi-monochromatic waves in weakly nonlinear dispersive media (e.g., the propagation of Langmuir waves in hot plasmas). In 1D, the defocusing NLS is exactly soluble with stable dark solitons (these are the analog of quantum vortices in Bose Einstein condensates). However in 3D there are no such stable structures and the NLS equation is no longer integrable. A number of studies have been performed to find quasi-stable 3D vortex soliton structures by appropriate generalization of the standard NLS. In particular, Efremidis [1] generalized the 3D NLS equation so that the 2D transverse dark soliton could be stabilized by a longitudinal bright soliton. This was achieved by transforming the standard elliptic -operator into hyperbolic form . We present a novel unitary qubit lattice algorithm (QLA) for the solutions to this generalized NLS. This algorithm is not only ideally parallelized on a classical supercomputer (no saturation seen at 750K cores) but is immediately encodable on a quantum computer. Lattice Boltzmann and Cellular Automata are distant cousins of QLA – except in QLA the collision operator must be unitary. The qubit is a generalization of the binary bit. For a scalar field, we require only 2 qubits per lattice site. The collision operator entangles the two qubits locally at each site while the streaming operator spreads this entanglement throughout the lattice. An appropriate interleaved sequence of these non-commuting unitary collide-stream operators can be shown (using Mathematica) to recover the required generalized NLS to 2nd order. Somewhat interestingly the switch from elliptic to hyperbolic operator can be achieved by generalizing the collision operator and not the streaming operator. 3D QLA simulations will be presented showing meta-stable vortex solitons.
[1]. N. K. Efremidis et. al. Phys Rev. Lett. 98, 113901 (2007)

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