Theoretical physics relies on advanced mathematical and physical theories, concepts and tools to study the dynamics of physical systems. Understanding formal mathematical structures is thereby crucial to better our understanding of the laws and principles of Nature.

Mathematical Methods research is performed using analytical tools only (i.e., pen and paper), and computational resources are used only to graphically represent the insights gained. This line of research is particularly interested in obtaining formal expressions that encode physical aspects of interest as generally as possible, not in optimizing or simulating particular tasks or processes.

This avenue of research comprises many studies of the formal structures of mathematical physics, with particular attention to quantum physics, quantum information and quantum field theory in flat or curved spacetime.

Research group: Mathematical Physics
Research topics:

• Cavity quantum field dynamics
• Covariance Matrix Formalism
• Quantum Dynamics and Time Evolution
• Quantum Information
• Symplectic Geomentry and Lie Algebra

External Links:

• Continuous variable quantum information: Gaussian states and beyond review by G. Adesso, S. Ragy, A. R. Lee

Efforts to scale-up quantum computation have reached a point where the principal limiting factor is not the number of qubits, but the entangling gate infidelity. However, the highly detailed system characterization required to understand the underlying error sources is an arduous process and impractical with increasing chip size. Open-loop optimal control techniques allow for the improvement of gates but are limited by the models they are based on. To solve these problems we investigate novel ways to perform optimal control, calibration and characterization or superconducting QPUs and other quantum devices. To that end we employ quantum control theory, optimization theory and machine learning techniques. And we build software which takes these ideas from theory to practice.

Noisy-intermediate scale quantum (NISQ) devices with a growing number of qubits are currently available in different quantum computing platforms. Quantum algorithms that take into account the noisy nature of these devices have been proposed and have shown the potential to compete with the best classical algorithms for some tasks. Understanding how to best use these devices, is crucial in order to find practical applications. In this endeavor, ideas on how to mitigate the effect of noise have also been shown to be fundamental in fully exploiting the power of the NISQ devices. Remarkably, the study of quantum algorithms has also sparked ideas of quantum-inspired classical algorithms that try to mimic the behavior of a quantum algorithm.

Classical thermodynamics has been applied successfully to most areas of science. Classical thermodynamics assumes that the number of constituents of a system is large, and variations of relevant quantities around the mean are small.

Quantum thermodynamics extends concepts of classical thermodynamics, such as temperature and work, to quantum systems with few (potentially one) constituents. This approach has opened the way to a better understanding of nature in the quantum realm, using concepts that have a simple yet powerful interpetation in the classical world.

The basic intuition behind this field is that the thermodynamic limit for quantities of interest cannot be taken when few (quantum) constituents are considered. In this case, fluctuations around the mean become important and novel phenomena can be expected.

Out of equilibrium pheonomena are expected to become more relevant due to the fact that relaxation times become shorter, and even small interactions can have significant effects.

Reserach group: Mathematical Physics
Reserach topics:

• Quantum Thermodynamics
• Cavity-field thermodynamics

External Links:

• Wikipedia page
• Focus on Quantum Thermodynamics article by Janet Anders

Relativistic Quantum Information is a broad apporach to topics at the intersection of Relativity, Quantum Mechanics, Quantum Information and Quantum Field Theory. The idea behind this field is that quantum information protocols occurr in a world that is characterized by both quantum and relativistic features. While quantum mechanics works extremely well in its own domain of validity, and therefore relativistic corrections can be ignred in first approximation, quantum protocols can require regimes and precisions that witness key relativistic properties of the core suystems employed.

Motion is one of the key aspects where relativistic effects can manifest. It is well known that inertial systems witness different phenomena than those that are not inertial, such as uniformly accelerated ones. Therefore, correctly implementing the effects of relativistic motion of core components of quantum infromation protocols can provide corrections to known results. Ideally, new phenomena and tasks that cannot be achieved without considering both quantum mechanical and relativistic aspects are sought.

Gravitation of physical systems and the performance of quantum protocols that exploit them in scnearios where gravity is relevant is the other main aspect that is investigated in Relativistic Quantum Information. Background spacetime curvature is exepcted to affect the propagation of realistic systems, local time flow of a user on Earth or a satellite, or even imply the creation of particles. All of these important features can ultimately degrade or fundamentally alter the performance of protocols, thereby opening the way for quantum sensning of gravitationalparameters, distances and more.

The research in this field covers both foundational and technological aspects, promising to bring about new understanding of the laws of nature while allowing for better characterization of technologies that will operate in regimes of extreme accelerations, or at large distances in a gravtitational potential.

Research group: Mathematical Physics

• Quantum Information protocols in curved spacetime
• Relativistic Quantum Computing
• Relativistic Quantum Metrology

External Links:

• Relativistic Quantum Information article by R. B. Mann and T. C. Ralph

Currently, superconducting qubits are the most widely used candidates for quantum computing systems. These consist of an insulator (typically Aluminum oxide, AlOx) sandwiched between two layers of superconductors (typically Aluminum) , known as the Josephson Junction. These behave as anharmonic oscillators and can be manipulated by using radio frequency pulses. Some of the kinds of superconducting qubits include charge qubits, flux qubits etc. Also these qubits can be fixed frequency or frequency tunable qubits. The main obstacle to scaling these systems of superconducting qubits is to obtain high fidelity quantum gates on these larger systems. We use open-loop optimal control techniques for control, characterization and calibration of different kinds of superconducting qubits to obtain optimal gate fidelities.

There are many challenges scaling up QPUs from the current 20-something qubits and 0.5% entangling-gate error rate. In superconducting QPUs, scale-up will result in a huge number of control lines running from the room-temperature waveform generators into the cryogenic fridge. One possible solution is to use in-fridge single flux quantum waveform generators, which we have explored in. In order to improve gate fidelities on large-scale QPUs, we need fast, efficient and flexible optimal control and calibration methods, which complement analytic design for better gates. And, of course, we must come up with methods of measuring the improved performance, which requires fast & accurate readout.When applicable, we design new superconducting circuits to perform operations faster and more accurately. As QPUs improve, they are capable of running more and more complex algorithms. They way there, however, requires careful understanding of how gate errors affect algorithms, and methods for benchmarking said errors. And it even makes sense to design algorithms which are robust to such noise. All this goes hand-in-hand with a deeper understanding of how complex quantum algorithms map to the lego-like structure of quantum gates and other computational paradigms. Armed with the above insights, we can also design new quantum simulation algorithms. The above breadth of knowledge gained above allows us to provide strategic overviews are the German and European levels.