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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 5: Quantum information
MP 5.3: Talk
Wednesday, March 23, 2022, 11:50–12:10, MP-H5
Markovian Quantum Systems with Full and Fast Hamiltonian Control — •Emanuel Malvetti1,2, Frederik vom Ende1,2, Thomas Schulte-Herbrüggen1,2, and Gunther Dirr3 — 1Dept. Chem., TU-München (TUM) — 2Munich Centre for Quantum Science and Technology (MCQST) and Munich Quantum Valley (MQV) — 3Institute of Mathematics, Universität Würzburg
Markovian quantum systems with full and fast Hamiltonian control can be reduced to an equivalent control system on the eigenvalues of the density matrix describing the state. First we consider the case of a single qubit, presenting explicit solutions of the optimal control problem for a large family of Lindblad operators. For the cases where analytic solutions seem out of reach, we can still efficiently compute numerical solutions. Second we consider quantum systems of arbitrary finite dimension. While analytic solutions to optimal control problems do not exist in the general case, the reduced control system on the eigenvalues is still a powerful tool. As an example, we derive necessary and sufficient conditions for a Markovian quantum system to be coolable.