Professor of Mathematics
Quantum mechanics governs materials at tiny atomic scales that are recently becoming accessible to direct manipulation. This is currently leading to a new world of high-impact applications, notably in Quantum Materials (e.g., spintronics), Quantum Information (e.g., in key sharing), Quantum Computation (e.g., for optimization or cryptography), and Quantum Machine Learning (artificial intelligence). However, the striking Quantum Advantage of Quantum Systems comes at the cost of their instability against tiny perturbations through noise and decoherence.
Topology is a general principle for stabilization of quantum systems either in the form of topological quantum fields (as in anyonic quantum gates and in topological phases of matter) or in the form of topologically encoded entanglement (through tensor networks for quantum error-correcting codes). It is these topological stabilization mechanisms that make a practically useful Quantum Computer a realistic possibility. Topology has already proven its power in High Energy Physics and Particle Physics. The tools used there are finding applications to Quantum Materials and Computation through the Holographic Principle. At the same time, Topology is reshaping the applied sciences in the form of Topological Data Analysis (for large and fuzzy data) and Topological Materials (as used for quantum computation).
The utilization of all of: (1) Quantum Systems, protected by (2) Topology, and understood via (3) Holography requires an unusually large scope of interdisciplinary expertise across all of the most cutting-edge developments in Mathematics, Fundamental and Applied Physics, and Computer/Data/Information science and engineering.
The Center for Quantum and Topological Systems serves as a nucleation point for cross-disciplinary expertise in theory and application of Quantum Topological Systems in general, with an emphasis towards the unifying goal of robust Quantum Computation in particular — combining all questions from theoretical foundations (quantum error-correction) over hardware (topological quantum materials and novel quantum chips), architecture (parameterized quantum circuits) and software (quantum programming languages and hardware-aware software optimizations) to applications (quantum machine learning and quantum cryptography).
|Urs Schreiber||Research Scientist in Mathematics|