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.
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