ORCID ID

0000-0001-8671-0123

Date Awarded

Summer 2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Physics

Advisor

George Vahala

Committee Member

William Cooke

Committee Member

John Delos

Committee Member

Marc Sher

Committee Member

Robert Rubinstein

Abstract

We present an improved Quantum Lattice Gas (QLG) algorithm as a mesoscopic unitary perturbative representation of the mean field Gross Pitaevskii (GP) equation for Bose–Einstein Condensates (BECs). The method employs an interleaved sequence of unitary collide and stream operators. QLG is applicable to many different scalar potentials in the weak interaction regime and has been used to model the Korteweg–de Vries (KdV), Burgers and GP equations. It can be implemented on both quantum and classical computers and is extremely scalable. We present results for 1D soliton solutions with positive and negative internal interactions, as well as vector solitons with inelastic scattering. In higher dimensions we look at the behavior of vortex ring reconnection. A further improvement is considered with a proper operator splitting technique via a Fourier transformation. This is great for quantum computers since the quantum FFT is exponentially faster than its classical counterpart which involves non-local data on the entire lattice (Quantum FFT is the backbone of the Shor algorithm for quantum factorization). We also present an imaginary time method in which we transform the Schrödinger equation into a diffusion equation for recovering ground state initial conditions of a quantum system suitable for the QLG algorithm.

DOI

http://dx.doi.org/10.21220/s2-2dcm-7v23

Rights

© The Author

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