Employing Typicality in Optimal Control Theory

TL;DR

This paper introduces a novel approach using quantum typicality to efficiently find control fields for large quantum systems, demonstrated by cooling high-temperature states of the AlF molecule with many internal states.

Contribution

The paper presents a new method employing typicality to assist in quantum control tasks, reducing computational complexity for large Hilbert spaces.

Findings

Successfully simulated ensemble control of large Hilbert spaces

Demonstrated cooling of AlF molecule's high-temperature states

Enabled control of many states simultaneously

Abstract

Controlling the dynamics of quantum systems is a crucial task in quantum science and technology. Obtaining the driving field that transforms the quantum systems to its objective is a typical control task. This task is hard, scaling unfavorably with the size of Hilbert space. To tackle this issue we employ typicality to assist in finding the control field for such systems. To demonstrate the method we choose the control task of cooling the fine structure states of the AlF molecule, from relatively high temperatures which results in large Hilbert space. Using quantum typicality, we demonstrate that we can simulate an ensemble of states, enabling a control task addressing simultaneously many states. We employ this method to find a control field for cooling molecules with large number of internal sates, corresponding to high initial temperatures.