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arXiv:2610.26725

Quantum Optimal Control Primer

Ignacio R. Sola

quant-phSubmitted Oct 19, 2026• Announced Oct 20, 2026• 0 citations
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Abstract

This is a set of detailed notes that are part of a Ph.D. Course on Quantum Control delivered at the Department of Chemistry of Seoul National University in 2014. Part of this course was also taught in the Department of Chemistry of the Friedrich Schiller University Jena. It focuses on quantum optimal control and quantum optimal control algorithms based on the gradient and extended gradient methods.

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This is a set of detailed notes that are part of a Ph.D. Course on Quantum Control delivered at the Department of Chemistry of Seoul National University in 2014. Part of this course was also taught in the Department of Chemistry of the Friedrich Schiller University Jena. It focuses on quantum optimal control and quantum optimal control algorithms based on the gradient and extended gradient methods.
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References [1] A. Peruzzo, M. Lobino, J. C. F. Matthews et al., Science 329, 1500 (2010). [2] A. S. Solntsev, A. A. Sukhorukov, D. N. Neshev, Y. S. Kivshar, Phys. Rev. Lett. 108, 023601 (2012). [3] M. Grafe, A. S. Solntsev, R. Keil, A. A. Sukhorukov, M. Heinrich, A. Tunnermann, S. Nolte, A. Szameit, Yu. S. Kivshar, Scientific Reports 2, 562 (2012). A. S. Solntsev1,+, F. Setzpfandt2, A. S. Clark3, C. W. Wu1, M. J. Collins3, C. Xiong3, F. Eilenberger2, A. Schreiber4, F. Katzschmann4, R. Schiek5, W. Sohler4, A. Mitchell6, C. Silberhorn4, B. J. Eggleton3, T. Pertsch2, A. A. Sukhorukov1, D. N. Neshev1, and Yu. S. Kivshar1 1Nonlinear Physics Centre and Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), Australian National University, Australia; 2Institute of Applied Physics, Friedrich-Schiller-University Jena, Germany; 3CUDOS, University of Sydney, Australia; 4Universitat Paderborn, Germany; 5University of Applied Sciences Regensburg, Germany; 6CUDOS, RMIT University, Australia +Phone: +61-2-6125-3423 Email: sun124@physics.anu.edu.au
These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of many-body quantum systems. In particular, I explain successful applications and inherent limitations due to the exponential complexity of the many-body problem. In the second part of the course, I show how using highly controllable quantum system such as ultracold atoms will provide a way to overcome the limitations of classical simulation methods. I discuss several theoretical and experimental achievements and outline the road for future developments.