Optimal Pulse Design in Quantum Control: An Ensemble Control Perspective

Designing and implementing time-varying electromagnetic pulses to manipulate the time-evolution of a large quantum ensemble is a long-standing problem in quantum control and an indispensable step that enables many cutting-edge quantum technologies. In practice, such pulse designs are made significantly more challenging because the values of parameters that characterize the dynamics of the quantum ensemble may show variation, so that the system Hamiltonian is not uniform over the ensemble. For example, nuclear magnetic resonance applications often suffer from imperfections such as inhomogeneity in the static magnetic field and in the applied radio-frequency field, variation in the dissipation rates of spins as well as dispersion in their Larmor frequency due to chemical shifts. A good pulse design strategy must be robust to these effects, and such variations need to be considered in the modeling and pulse design stages in order for theoretical predictions to match experimental outcomes.

In this talk, ensemble control-theoretic approaches for optimal pulse design in quantum control will be introduced. A new method that integrates Lie algebras with polynomial approximation for analyzing controllability of spin ensemble systems will be presented. In addition, robust computational methods for optimal pulse synthesis will also be presented, which include a unified computational method based on multidimensional pseudospectral approximations and an optimization-free iterative algorithm based on the singular value decomposition. Commonly used pulses in various fields of quantum control developed by these computational methods will be illustrated, and, moreover, experimental realizations of these optimal pulses will be shown to demonstrate the robustness and applicability of these newly developed methods.