Solving quantum optimal control problems using projection-operator-based Newton steps

TL;DR

This paper introduces an improved quantum optimal control method, Q-PRONTO, which uses a regulator to enhance convergence and solution quality, demonstrated through numerical examples involving complex quantum control scenarios.

Contribution

The paper presents a novel regulator-enhanced version of the quantum projection operator-based Newton method, improving convergence and solution optimality in quantum control problems.

Findings

Enhanced convergence rate with the regulator

Better local minima compared to unregulated methods

Effective in complex multi-input quantum control scenarios

Abstract

The Quantum Projection Operator-Based NewtonMethod for Trajectory Optimization (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 unregulated case. Numerical examples showcase how 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.