Verification and Characterization of Quantum Technology

• Applicant: Professor Dr. Martin Kliesch
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 441423094

Quantum sciences are currently enjoying a large amount of attention including heavy research investments by governments as well as commercial companies. A central promise is that classical computations will be outperformed by using quantum resources. This has potential applications in numerous fields such as in quantum chemistry, optimization, and artificial intelligence. An important milestone for achieving such ambitious aims is the demonstration of quantum supremacy: this means to solve some problem by using quantum capabilities that cannot practically be solved otherwise. It is to be expected that quantum supremacy will be announced in the near future. However, what would it actually tell us? A convincing demonstration of quantum supremacy would show that quantum computers have reached a level where they might actually become useful. But, if a quantum device cannot practically be simulated how can one make sure that its outcome is correct? In particular, how can a skeptic be convinced of quantum supremacy? Many of the proposed quantum supremacy demonstrations –specifically quantum sampling experiments– have the caveat that there is no convincing practical test of whether or not they have been correctly solved. Two tasks are utterly important for the development of trusted quantum devices: (i) the verification of their functioning as a whole and (ii) the precise characterization of their single components; the latter being crucial for their development itself. There is a range of methods targeted at these two and also intermediate tasks. This includes quantum state verification, quantum process validation (such as randomized benchmarking), certain classical simulation techniques and quantum tomography. However, experimentally practical methods that also feature precise theoretical performance guarantees are still rare. Now is the right time to close this gap. On the one hand, there are new powerful mathematical techniques and results. They range from vector and operator concentration inequalities, over tensor reconstruction, non-convex optimization, and new developments in machine learning to new precisely controlled sampling methods in quantum information theory. On the other hand, the precisely controlled quantum systems have become so large that new efficient data processing techniques are required. The proposed Emmy-Noether group will open the investigation of worst-case errors in the verification of quantum dynamics, provide practical quantum process tomography schemes with theoretical guarantees, provide the first systematic investigation of the role of temporal noise correlations in quantum processes, and investigate the role of noise for the complexity of classical simulations of complex quantum systems. This project aims at the development of methods that are practical and mathematically rigorous at the same time, as desirable in the regime of high complexity.

• DFG Programme: Independent Junior Research Groups