[PAST EVENT] Armen Oganesov : Physics Dissertation Defense
Armen Oganesov , Final Oral Examination for the Ph.D., Title: "Modeling the Gross-Pitaevskii Equation Using the Quantum Lattice Gas Method ."
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 Schr?dinger equation into a diffusion equation for recovering ground state initial conditions of a quantum system suitable for the QLG algorithm.
Bio: Armen Oganesov immigrated to the United States with his family in 1995 at the age of 10. He grew up in New York City and received an undergraduate degree in arts and sciences from Hunter College in 2010. In 2011 he began his physics PhD program at Wiliam and Mary. He began working with George Vahala in the summer of 2012 and is finally on the verge of completing his doctorate.