Estimation of quantum systems
The estimation of quantum system components plays a central role in the implementation and verification of quantum computers. For example, quantum state tomography aims at reconstructing an unknown quantum state from measurements, whereas quantum process tomography tries to identify unknown quantum operations from input-output samples. In our research, we develop robust estimation methods which can reliably estimate quantum objects in the presence of noise. To this end, we employ tools from robust optimization to rigorously understand and suppress the effects of noise.
Control of quantum systems
Realizing quantum systems such as quantum sensors of quantum computers requires controlling microscopic quantities in real-time. This has motivated the development of specialized tools for quantum control to address the unique challenges arising from quantum physical phenomena. We are developing methods for controlling quantum systems based on robust and predictive control, targeting especially robustness against noise. We focus on generic control methods that are applicable across different hardware platforms. The dynamics occurring in quantum control problems can be described via the Schrödinger equation. The bilinearity of these dynamics as well as uncertainties commonly encountered in quantum systems pose key challenges for efficiently and accurately solving control problems.
Moreover, we tackle robust quantum control problems using model predictive control (MPC). While MPC is one of the most powerful and successful modern control techniques, no systematic framework exists for its application to quantum systems. Our research aims at developing a framework for model predictive quantum control which is mathematically rigorous and can solve challenging quantum hardware problems, especially in the presence of noise. Further, we develop data-driven quantum control methods in order to manipulate unknown quantum systems based directly on measurements. We investigate indirect approaches combining model estimation and model-based robust quantum control as well as direct approaches achieving a controller design without prior system identification.
While our research is methodological, we are also investigating applications in concrete quantum systems such as quantum computers or quantum sensors together with our partners.
Representative publications
Tutorial and perspective article
- J. Berberich, R. L. Kosut, T. Schulte-Herbrüggen - "Bringing quantum systems under control: A tutorial invitation to quantum computing and its relation to bilinear control systems" - IEEE Conference on Decision and Control (CDC) 2024. Link
Control of quantum systems
- Y. Lee, J. Berberich, I. R. Petersen, D. Dong - "Data-driven control of a single-qubit system based on unitary evolution reconstruction" - IFAC Journal of Systems and Control, 2026. Link
- E. Guizani, J. Berberich - "Model predictive quantum control: A modular approach for efficient and robust quantum optimal control" - arXiv:2509.05167. Link
Collaborations
D. Dong (UT Sydney, AU)
R. L. Kosut (SC Solutions, Quantum Elements, Inc., and Princeton University, US)
I. R. Petersen (Australian National University, AU)
T. Schulte-Herbrüggen (TU Munich, DE)
Planned:
C. Braxmaier (University of Ulm, DE)