At the same time as the development of quantum technologies progresses rapidly, new demands concerning the certification of their operation emerge. A question relevant for the application of various quantum technologies consequently is how the user can ensure the correct functioning of the quantum devices [1]. In a number of instances, specifically in quantum simulation and quantum computing, challenges in appropriately benchmarking components or entire protocols constitute a widely acknowledged bottleneck. This talk will suggest several new takes to the problem at hand: We will see how data from SPAM-robust randomized benchmarking [2] can be used to perform process tomography of quantum gates in an experimentally-friendly and provably sample optimal fashion [3], making use of a machinery of compressed sensing and exploiting structure - that is to say, the components of a quantum circuit. We will see how quantum states can be characterizes provably even with imperfect detectors in what could be called semi-device-dependent tomography [4]. The issue becomes more challenging when one aims at certifying the functioning of an entire device. We will look at limitations to black-box verification for sampling problems that show a quantum advantage or "supremacy" [5], will have a fresh look at Hamiltonian learning [6] and will see that in some instances [7], one can ironically certify the correctness of a device even if one cannot efficiently predict its performance. [1] Quantum certification and benchmarking, J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, E. Kashefi, Nature Reviews Physics 2, 382-390 (2020). [2] Randomized benchmarking for individual quantum gates, E. Onorati, A. H. Werner, J. Eisert, Phys. Rev. Lett. 123, 060501 (2019). [3] Recovering quantum gates from few average gate fidelities, I. Roth, R. Kueng, S. Kimmel, Y.-K. Liu, D. Gross, J. Eisert, M. Kliesch, Phys. Rev. Lett. 121, 170502 (2018). [4] Semi-device-dependent blind quantum tomography, I. Roth, J. Wilkens, D. Hangleiter, J. Eisert, arXiv:2006.03069 (2020). [5] Sample complexity of device-independently certified quantum supremacy, D. Hangleiter, M. Kliesch, J. Eisert, C. Gogolin, Phys. Rev. Lett. 122, 210502 (2019). [6] In preparation (2020). [7] J. Haferkamp, D. Hangleiter, A. Bouland, B. Fefferman, J. Eisert, and J. Bermejo-Vega, arXiv:1908.08069, Phys. Rev. Lett. (2020).

He is known for his research in and has made numerous contributions to quantum information science and quantum many-body theory in condensed matter physics. He has made significant contributions on entanglement theory and the study of quantum computational models, as well as quantum optical implementations of protocols in the quantum technologies and the study of complex quantum systems. He is also notable as one of the co-pioneers of quantum game theory with Maciej Lewenstein and PhD advisor Martin Wilkens.