P14: Systems Theory of Quantum Algorithms: Fundamentals and Applications to Noisy Quantum Computers

Members: Dr. Julian Berberich (University of Stuttgart), Mirko Legnini (University of Stuttgart)

Quantum computers promise substantial computational speedups for selected problems that are intractable for classical computers, with potential applications in simulation, cryptography, optimization, and beyond. Although rapid progress in quantum hardware has led to the emergence of intermediate-scale quantum devices, realizing practical quantum advantage remains a major challenge. A central obstacle is the presence of noise caused, for example, by imperfect isolation of quantum systems from their environment. 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.

The goal of this project is to develop methodological foundations for robustness-aware quantum algorithm design and thereby contribute to the development of reliable quantum software for noisy quantum hardware. Specifically, building on tools from systems and control theory, the project will develop methods for analyzing algorithmic robustness and performance degradation in the presence of noise. As an intermediate step, we will develop methods for estimating accurate noise models in collaboration with Prof. Mariami Gachechiladze (TU Darmstadt). Based on our analysis, new approaches for robustness-aware compilation and algorithm design will be developed, enabling quantum algorithms to be mapped to hardware in a way that improves their intrinsic tolerance to noise. The theoretical developments will be validated through implementations on existing quantum hardware platforms, including Rydberg-atom systems (Prof. Tilman Pfau, U Stuttgart) and commercially available superconducting qubit devices.

Moreover, a particular focus lies on hybrid quantum-classical algorithms, such as variational quantum algorithms and dynamic circuits, which are tailored for near-term hardware. These algorithms can be naturally interpreted as feedback interconnections of quantum and classical subsystems and therefore provide an ideal setting for applying control-theoretic analysis methods. The project will exploit this perspective to study systems-theoretic properties (e.g., convergence and robustness) of hybrid algorithms in order to improve their reliability on imperfect hardware. 

Overall, the project contributes methodological building blocks for robust quantum algorithms, compilation strategies, and performance analysis, thereby supporting the development of a reliable quantum software stack for near-term quantum computing platforms.