Title: Efficient parallel implementation of Bose Hubbard model: Exact numerical groundstates and dynamics of gaseous Bose-Einstein Condensates for investigating Schrödinger cat states

Speaker: Mary Ann Leung, Von Neumann Fellowship Interview Candidate, University of Washington

Date/Time: Wednesday, January 17, 2007, 9:00am – 10:00am

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: As an illustration of the consequence of applying quantum theory to large objects, Erwin Schrödinger proposed a thought experiment involving a cat simultaneously alive and dead. While a cat that is both dead and alive seems a preposterous idea, superposition states have been created in the laboratory and have important utility in the field of quantum information processing. In this talk, I describe my work investigating the creation of Schrödinger cat states with the gaseous atomic Bose-Einstein condensate. I present a parallel implementation of the Bose Hubbard model, using imaginary time propagation to find the lowest quantum eigenstate and real time propagation for simulation of quantum dynamics. Scaling issues, performance of sparse matrix-vector multiplication, and a parallel algorithm for determining nonzero matrix elements are described. Implementation of imaginary time propagation yields an O(N) linear convergence on a single processor and slightly better than ideal performance on up to 160 processors. The determination of the nonzero matrix elements is intractable using sequential non-optimized techniques for large problem sizes. Thus, I discuss a parallel algorithm that takes advantage of the intrinsic structural characteristics of the Fock-space matrix representation of the Bose Hubbard Hamilitonian and utilizes a parallel implementation of a Fock state look up table to make this task solvable within reasonable timeframes. The parallel algorithm demonstrates near ideal scaling on thousand of processors. I include results for a matrix 22.6 million square, with 202 million nonzero elements, utilizing 2048 processors.