Analysing the Optimal Design Methods for Two-Qubit Quantum Gates

Student: Aleksukhin Vasily

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 two-qubit quantum state through the evolution of Bloch vectors of its reduced states in the three-dimensional Euclidean space and the time variation of the elements of its correlation matrix. Based on this approach and the choice of a quality functional, which is important for applications, we develop a new model for the optimal design of an arbitrary two-qubit gate. For the CNOT gate, the detailed numerical study of the developed model and the three-dimensional visualization of the obtained results are performed via the Python program written in this paper. The present paper contains 44 pages, 34 figures, 1 table, the program code in Python and 7 bibliography references

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