Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control

Optimal control theory is a powerful mathematical tool, which has known rapid development since the 1950s, mainly for engineering applications. More recently, it become widely used method to improve process performance in quantum technologies by means of highly efficient dynamics. This tutorial aims at providing an introduction key concepts optimal that accessible physicists and engineers working or related fields. The different results are introduced intuitively, before being rigorously stated. describes modern aspects theory, with particular focus on Pontryagin maximum principle, main tool determining open-loop laws without experimental feedback. steps solve problem discussed, moving more advanced topics such as existence solutions definition types extremals, namely normal, abnormal, singular. covers various issues their formulation suitable control. connection between principle gradient-based optimization algorithms high-dimensional systems described. solution low-dimensional presented detail, illustrating how tools applied practical way.2 MoreReceived 10 December 2020Revised 21 May 2021DOI:https://doi.org/10.1103/PRXQuantum.2.030203Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasCoherent controlOptimization problemsQuantum controlQuantum Information