2025/05/01 by Bhat, Harish S.
#Chemical Physics (physics.chem-ph) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Optimization and Control (math.OC) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2505.00529
We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a given initial state to a desired target state. For small to moderately sized systems, we demonstrate a vectorized GPU implementation of a second-order adjoint method that computes both Hessians and gradients with wall times only marginally more than those required to compute gradients via commonly used first-order adjoint methods. Pairing our second-order adjoint method with a trust region optimizer (a type of Newton method), we show that it outperforms a first-order method, requiring significantly fewer iterations and wall time to find optimal controls for four molecular systems. Our derivation of the second-order adjoint method allows for arbitrary parameterizations of the controls.