Optimal Control of Finite-Dimensional Quantum Systems

Student: Leonenko Aleksei

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2021

In the present paper, we construct a system of linear ordinary differential equations, describing the unitary evolution of a one-qubit quantum system under an arbitrary nonstationary influence via the evolution of a unit vector in a fourdimensional Euclidean space. Based on this approach and the choice of a quality functional, which is important for applications, we develop a new universal model for the optimal design of an arbitrary one-qubit gate. We perform the detailed numerical study of the developed optimal design model for the case of the quantum gate NOT and present the qualitative analysis of the obtained numerical results. The present paper contains 30 pages, 15 figures and 10 bibliography references.

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