Systems Theory of Quantum Algorithms: Fundamentals and Applications to Noisy Quantum Computers

• Applicant: Dr.-Ing. Julian Berberich
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 579821331

Quantum computers promise to accelerate computing by efficiently solving selected problems which are intractable for classical computers. They hold high potential for major technological advancements in diverse fields including cryptography, simulation, and optimization. Although recent years have seen tremendous progress in quantum computing, realizing computational advantages in practice remains a widely open problem. The presence of noise, e.g., resulting from insufficient isolation from the environment, is a key obstacle. Most existing techniques for addressing noise separate the error handling from the algorithm analysis and design, e.g., via subsequent error correction or mitigation steps, leaving unused significant potential for robustness improvements on the algorithmic side. It is the goal of this project to address this gap by studying systems-theoretic properties of quantum algorithms, improving their theoretical understanding as well as their practical reliability on noisy quantum computers. A key focus lies on the development of methods for analyzing robustness of quantum algorithms against hardware errors. Subsequently, these insights will be exploited to design and compile quantum algorithms which are inherently more robust and, therefore, may be implemented on noisy quantum computers in a more reliable fashion. The practicality of the theoretical results will be shown in applications to quantum computers based on Rydberg atoms and superconducting qubits. Further, the project will investigate algorithms with feedback structures such as variational quantum algorithms and dynamic circuits. These algorithms can be mathematically represented as feedback loops of quantum and classical components and, hence, they are ideally suited for analysis via control-theoretic methods. In the present project, this new angle will be exploited to study systems-theoretic properties such as convergence, stability, and robustness, and to improve these properties in the design. Addressing the described problems under the umbrella of systems and control theory poses new mathematical challenges which require the development of tailored analysis and design tools. Hence, this project aims to contribute not only to quantum computing but also to systems and control theory by developing new methods which are motivated by problems arising in quantum algorithms, but which may be of independent interest for further application domains.

• DFG Programme: Emmy Noether Independent Research Groups