Abstract: We study a binary optimal quantum control problem highly corresponding to diverse quantum algorithms. We develop a generic discrete-valued model and several extensions to handle additional side constraints and reduce switches. We propose an algorithmic framework combining modified popular gradient ascent pulse engineering (GRAPE) algorithm, a new alternating direction method of multipliers (ADMM) algorithm, rounding techniques, and a modified trust-region method to obtain high-quality control with less chattering. Furthermore, we develop new approaches to extract controller sequences from fractional discretized control solutions and propose a switching time optimization model with a given controller sequence, which improves the solutions as well as reduces the computation.

Taking the uncertainty of controllers into account, we propose an extended chance-constrained model with a conditional value at risk (CVaR) function. We derive a closed formulation for the non-differentiable and non-convex objective function and solve the model based on our previous modified GRAPE algorithm. We demonstrate that our CVaR model improves the robustness of controls under uncertain circumstances.

Bio: Xinyu Fei is a Ph.D. Candidate at the Department of Industrial and Operations Engineering at the University of Michigan. Her research interest focuses on developing models and efficient algorithms for solving large-scale nonconvex optimization problems in complex networks.