Quantum control landscapes for quantum systems and impulse controls

In this talk, we discuss the appearance of traps of 3rd and 7th orders for three-level Lambda-type quantum systems. We numerically show that 7th order trap much more significantly affects (decreases) efficiency of optimization using GRAPE [1]. For open quantum systems, we provide an analysis of generation of a universal set of gates (H, T, C-NOT) that shows that generation of the Clifford gates H and C-NOT is likely to be free of traps while for a non-Clifford T gate trapping like behaviour has been revealed [2,3]. An important subject is the appearance of impulse quantum controls. For this, recently the problem of time-optimal control for state transfer of an open qubit was analytically solved and it was discovered that optimal controls are impulses in the beginning and the end, with a smooth function in between [4]. Moreover, an almost optimal controls were constructed which consist of four impulses only.
[1] B. Volkov, A. Myachkova, A. Pechen, Phenomenon of a stronger trapping behaviour in \Lambda-type quantum systems with symmetry, arXiv:2404.06937. [2] V. Petruhanov, A. Pechen, Quantum gate generation in two-level open quantum systems by coherent and incoherent photons found with gradient search, Photonics 10, 220 (2023). [3] A. Pechen, V. Petruhanov, O. Morzhin, B. Volkov, Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving, Eur. Phys. J. Plus, 139, 411 (2024). [4] L. Lokutsievskiy, A. Pechen, M. Zelikin, Time-optimal state transfer for an open qubit,, J. Phys. A: Math. Theor. 57, 275302 (2024).