Improving Bayesian Optimization for Quantum Material Control (2023)

by Malhar Manohar Thombare

Abstract: Using light one can desirably change the properties of materials. An electromagnetic (EM) field signal can excite a material or chemical system into a higher eigenstate and, as a result, change its properties. We develop an algorithm to find the right EM signal for a chemical system simulated in NIC-CAGE (Novel Implementation of Constrained Calculations for Automated Generation of Excitations). NIC-CAGE simulates the influence of an EM field on a quantum system and provides the probability of desired transition as well as the gradient of the probability as a function of the EM field. The simulation is calculated in a system with one degree-of-freedom which still preserves most of the dynamics of a real high degree-of-freedom systems. A single query on the simulator takes about a second to calculate the probability and more time to find the gradient at the evaluation point. Given the parameters of the quantum system, and the source and target eigenstates, the software provides a theoretical frequency for a sinosoidal EM signal. The optimal frequency may lie in a big region around it. Bayesian Optimization (BO) is suitable to this problem because it minimizes the number of costly evaluations and avoids the need for costlier gradient calculation. However, typical BO methods expect uniform smoothness over all the search space in the evaluation function to be optimized. For our problem, this is not true for the frequency parameter which leads to slower performance. We found that frequencies with high evaluation probability are present in very small regions and the rest of the space has a uniformly low probability. We propose three methods to minimize the search over these low-probability regions. The first method crops the part of the search space based on the last best point and searches in it. The second method extends the previous method by dynamically adjusting the size of cropped search space and searches over it. The third method warps the search region such that the variance of probability is high and more uniform over the search space. We demonstrate the improved performance of our methods on a suite of quantum control problems.

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Malhar Manohar Thombare (2023). Improving Bayesian Optimization for Quantum Material Control. Masters thesis, University of California at Riverside.

Bibtex citation

@mastersthesis{Tho23,
   author = "Malhar Manohar Thombare",
   title = "Improving {B}ayesian Optimization for Quantum Material Control",
   school = "University of California at Riverside",
   schoolabbr = "UC Riverside",
   year = 2023,
   month = Mar,
}

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