How to solve Quantum Optimal Control Problems using Projection Operator-based Newton Steps

The Quantum PRojection Operator-based Newton method for Trajectory Optimization, a.k.a. Q-PRONTO, is a numerical method for solving quantum optimal control problems. This paper significantly improves prior versions of the quantum projection operator by introducing a regulator that stabilizes the solution estimate at every iteration. This modification is shown to not only improve the convergence rate of the algorithm, but also steer the solver towards better local minima compared to the un-regulated case. Numerical examples showcase Q-PRONTO can be used to solve multi-input quantum optimal control problems featuring time-varying costs and undesirable populations that ought to be avoided during the transient.