Trapping behavior in some quantum control landscapes

Control of quantum systems is important for modern quantum technologies. A typical quantum control problem can be formulated as a problem of maximizing an objective functional that depends on the quantum state of the system. Traps are controls that complicate the work of local search algorithms, which are used to find optimal control. We discuss such traps that arise in problems of controlling closed quantum systems. In particular, we discuss the phenomenon of a stronger trapping behavior in Λ-type quantum systems with symmetry. This work was partially supported by grant RSF No. 22-11-00330-P in Steklov Mathematical Institute and “Priority 2030” Program (MISIS Strategic Project Quantum Internet).