Chattering Phenomenon in Quantum Optimal Control

TL;DR

This paper investigates the occurrence of chattering phenomena in quantum optimal control problems, highlighting their significance for improving numerical optimization methods and understanding quantum control dynamics.

Contribution

It is the first to identify and analyze chattering in quantum control, applying Pontryagin's maximum principle and numerical algorithms to characterize and address this phenomenon.

Findings

Chattering occurs in a quantum optimal control setting.

Detection of chattering affects the efficiency of numerical algorithms.

A method to characterize and globalize local optimal solutions is presented.

Abstract

We present a quantum optimal control problem which exhibits a chattering phenomenon. This is the first instance of such a process in quantum control. Using the Pontryagin Maximum Principle and a general procedure due to V. F. Borisov and M. I. Zelikin, we characterize the local optimal synthesis, which is then globalized by a suitable numerical algorithm. We illustrate the importance of detecting chattering phenomena because of their impact on the efficiency of numerical optimization procedures.