Optimal control and visualization of quantum dynamics in NMR and quantum information processing
Prof. Steffen Glaser (Technische Universität München)

Analytical and numerical tools of optimal control theory (1) have found widespread applications in NMR and EPR spectroscopy, imaging, and in quantum information processing (2). In the last decade, these tools not only provided pulse sequences of unprecedented performance and capabilities, but also new analytical and geometrical insight and a deeper understanding of pulse optimization problems. The definition of the figure of merit for a pulse sequence is crucial for the optimization for a desired range of applications.

In addition to standard figures of merit for excitation, inversion and refocusing pulses, more general figures of merits have made it possible to significantly extend the range of applications. This will be illustrated for recent examples from the field of NMR and the control of trapped cold atoms (3). Furthermore, based on the DROPS (4) and BEADS (5) representations, novel intuitive visualization approaches have been developed to see the dynamics of multi-qubit systems in quantum information processing and beyond.

(1) N. Khaneja, R. Brockett, S. J. Glaser, Phys. Rev. A 63, 032308/1-13 (2001); N. Khaneja, S. J. Glaser, R. Brockett, Phys. Rev. A 65, 032301 (2002); N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, S. J. Glaser, J. Magn. Reson. 172, 296-305 (2005).
(2) S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny, F. K. Wilhelm, Eur. Phys. J. D 69, 279/1-24 (2015); C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. J. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbrüggen, D. Sugny, F. K. Wilhelm, Eur. Phys. J. Quantum Technology 9, 19/1-60 (2022).
(3) Z. Zhang, L. Van Damme, M. Rossignolo, L. Festa, M. Melchner, R. Eberhard, D. Tsevas, K. Mours, E. Reches, J. Zeiher, S. Blatt, I. Bloch, S. J. Glaser, A. Alberti, arXiv:2410.02452 [quant-ph] (2024); L. Van Damme, Z. Zhang, A. Devra, S. J. Glaser, A. Alberti, arXiv:2410.02452 [quant-ph] (2024).
(4) A. Garon, R. Zeier, S. J. Glaser, Phys. Rev. A 91, 042122 (2015); D. Leiner, R. Zeier, S. J. Glaser, J. Phys. A: Math. Theor. 53, 495301 (2020).
(5) D. Huber, S. J. Glaser, arXiv:2410.01446 [quant-ph] (2024).