Second-Order Adjoint Method for Quantum Optimal Control

TL;DR

This paper introduces a second-order adjoint method for quantum optimal control that efficiently computes gradients and Hessians, enabling faster and more accurate optimization of control fields for molecular systems.

Contribution

We derive and implement a second-order adjoint method for quantum control, improving optimization efficiency over first-order methods and allowing arbitrary control parameterizations.

Findings

Second-order adjoint method computes Hessians and gradients efficiently.

Pairing with trust region optimizer reduces iterations and wall time.

Method outperforms first-order methods in molecular control problems.

Abstract

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.