Global optimization plays an essential role in physics and chemistry, from circuit quantum electrodynamics quantum computing to ultracold collisions. The cost of testing all possible grid points on a search space grows exponentially as the dimensionality increases and is nicknamed the “curse of dimensionality.” I will introduce the Iterative Power Algorithm (IPA), a physical approach related to imaginary time propagation that we developed to address this problem. The method uses the low-rank quantics tensor train (QTT) representation to avoid the cost associated with standard grid-based methods. The method successfully identifies global minima of highly multidimensional potential energy surfaces, which is essential to molecular geometry optimization, and determines prime factors of large integers, a central goal in the field of quantum algorithms.

I also will discuss complex absorbing potentials, which are frequently used to simulate open quantum systems from chemical reactions to low-energy physics. For the past thirty years, both quantum scattering and dynamics calculations have been plagued by the fact the technique often generates unphysical reflection of low-energy components of wave packets. With the advent of ultracold physics and chemistry, a solution is in even greater demand. I will introduce a physical, semiclassical solution we developed based on classical trajectories and demonstrate the method reduces anomalous reflection by several orders of magnitude relative to the standard approach.

References:

M. B. Soley, P. Bergold, V. S. Batista, Iterative Power Algorithm for Global Optimization with Quantics Tensor Trains, Journal of Chemical Theory and Computation, (2021) in press. https://pubs.acs.org/doi/10.1021/acs.jctc.1c00292

M. B Soley, K. N. Avanaki, E. J. Heller, Reducing anomalous reflection from complex absorbing potentials: A semiclassical approach. Physical Review A, 103 (2021) L041301. https://doi.org/10.1103/PhysRevA.103.L041301