Control Landscapes for Observable Preparation with Open Quantum Systems

TL;DR

This paper extends the concept of quantum control landscapes to open systems, showing that their topology remains trap-free and controllability is enhanced, which aids in optimizing observable outcomes despite environmental interactions.

Contribution

It demonstrates that open quantum system control landscapes can be analyzed via an auxiliary closed system, revealing their topology and potential for improved controllability.

Findings

Open system landscapes are equivalent to closed composite system landscapes.

No false traps exist in open system control landscapes for observable optimization.

Open dynamics significantly broaden the range of achievable observable values.

Abstract

A quantum control landscape is defined as the observable as a function(al) of the system control variables. Such landscapes were introduced to provide a basis to understand the increasing number of successful experiments controlling quantum dynamics phenomena. This paper extends the concept to encompass the broader context of the environment having an influence. For the case that the open system dynamics are fully controllable, it is shown that the control landscape for open systems can be lifted to the analysis of an equivalent auxiliary landscape of a closed composite system that contains the environmental interactions. This inherent connection can be analyzed to provide relevant information about the topology of the original open system landscape. Application to the optimization of an observable expectation value reveals the same landscape simplicity observed in former studies on closed systems. In particular, no false sub-optimal traps exist in the system control landscape when seeking to optimize an observable, even in the presence of complex environments. Moreover, a quantitative study of the control landscape of a system interacting with a thermal environment shows that the enhanced controllability attainable with open dynamics significantly broadens the range of the achievable observable values over the control landscape.