Numerical methods for optimal control of open quantum systems

September 26, 2016 to September 28, 2016
Location : Free University Berlin, Institute of Mathematics, Arnimallee 6 ("Pi-Building"), 14195 Berlin, Germany


  • Carsten Hartmann (BTU Cottbus-Senftenberg, Germany)
  • Burkhard Schmidt (Free University Berlin, Germany)
  • Reinhold Schneider (Technical University Berlin, Germany)
  • Peter Saalfrank (University of Potsdam, Germany)



Zuse Institute Berlin


Optimal control of open quantum systems has recently become a popular interdisciplinary research topic beyond the physical- chemical community, but there is a lack of robust numerical methods and algorithms that limits the applicability of the models when going to larger scales. On the other hand, numerical methods for bilinear control systems have recently been analysed and developed by applied mathematicians—largely unnoticed by the physical-chemical community. Both fields have reached a certain degree of maturity, and we believe that it is about time to let them join forces. The workshop is supposed to serve this purpose: Berlin and Potsdam groups who are active in quantum control and open quantum dynamics, e.g., at U Potsdam, FU Berlin or the Fritz-Haber Institute, next door to groups at FU Berlin, TU Berlin or the Zuse Institute Berlin who are doing state-of-the-art research in optimal control, model reduction and numerical linear algebra (including software development). Hence Berlin would be a good place to bring together some of the key players in the field, which could also be used to kick-start some of the activities in the recently accepted EU/CECAM-EINFRA bid, in which quantum control plays a prominent role.

A central theme of the workshop therefore will be numerical methods for model reduction and reduced basis methods for open quantum molecular systems, with a special focus on optimal control and filtering. A side theme will be different models of open quantum systems (beyond the Lindblad semigroup) and current software developments in the field.


[1] A. Borzi, J. Salomon, and S. Volkwein. J. Comput. Appl. Math. 216:170–197, 2008.
[2] P. Benner and T. Breiten. SIAM J. Matrix Anal. Appl., 33:859–885, 2012.
[3] H.-P. Breuer, W. Huber, and F. Petruccione. Comput. Phys. Commun. 104:46–58, 1997.
[4] B.A. Chase. Parameter Estimation, Model Reduction and Quantum Filtering. PhD thesis, University of New Mexico. Dept. of Physics & Astronomy, 2009.
[5] G. Ciaramella, J. Salomon, and A. Borzi. Intl. J. Control 88(4):682–702, 2015.
[6] J. Gough, J. Math. Phys. 51:123518-1--123518-25, 2010.
[7] C. Hartmann, A. Zueva, and B. Schäfer-Bung. J. Control Optim. 52:2356–2378, 2013.
[8] Ch. Lubich. From quantum to classical molecular dynamics: reduced models and numerical analysis. European Math. Soc., 2008.
[9] Y. Ohtsuki, W. Zhu, and H. Rabitz.Monotonically convergent algorithm for quantum optimal control with dissipation. J. Chem. Phys. 110:9825, 1999.
[10] B. Schäfer-Bung, C. Hartmann, B. Schmidt, and Ch. Schütte. J. Chem. Phys., 135:014112, 2011.
[11] M. Schröder, J.-L. Carreon-Macedo, and A. Brown. Phys. Chem. Chem. Phys. 10:850–856, 2008.
[12] J.C. Tremblay. J. Chem. Phys. 134:174111, 2011.
[13] L. Zhang and J. Lam. Automatica 38:205–216, 2002.