FET: Small: An Integrated Framework for the Optimal Control of Open Quantum Systems --- Theory, Quantum Algorithms, and Applications

Numerous emerging applications in the fields of computer science, material science, chemical engineering, and quantum biology rely extensively on harnessing the quantum properties exhibited by underlying physical systems. These properties can be fine-tuned and optimized through control variables, typically achieved by manipulating external fields. However, due to the substantial dimensionality of quantum systems and their continuous interactions with the environment, determining the optimal control variables through direct computer simulations has posed a significant and unresolved challenge.

The primary objective of this project is to establish a comprehensive mathematical framework that effectively characterizes the dynamics of quantum systems in the presence of environmental noise. By developing this mathematical description, the investigators aim to pave the way for the construction of efficient quantum algorithms capable of obtaining the optimal control parameters for such systems.

In addition to conducting rigorous theoretical analyses to ensure model accuracy and evaluate the complexity of algorithms, this project places a significant emphasis on the development of efficient quantum algorithms specifically tailored for simulating open quantum systems in non-Markovian regimes. In such regimes, the interactions between the quantum system and its environment occur on comparable time scales, resulting in intricate dynamics that necessitate novel mathematical descriptions.

By focusing on this aspect, the investigators aim to address the challenges posed by realistic scenarios where the influence of the environment on the quantum system cannot be treated as a simple Markovian process. Furthermore, a crucial aspect of this project centers around the design and implementation of quantum algorithms capable of accurately estimating the gradient of objective functions.

This is achieved by carefully calibrating the statistics of the measurement noise, which plays a pivotal role in the complexity of the optimization procedure. The project involves active undergraduate student mentoring to pursue careers in science and research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.