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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation
B. O. Volkovab, A. N. Pechenab a Steklov Mathematical Institute of Russian Academy of Sciences, Department of Mathematical Methods for Quantum Technologies, Moscow, Russia
b University of Science and Technology MISIS, Moscow, Russia
Аннотация:
In this work, we study the detailed structure of quantum control landscape for the problem of single-qubit phase shift gate generation on the fast time scale. In previous works, the absence of traps for this problem was proven on various time scales. A special critical point which was known to exist in quantum control landscapes was shown to be either a saddle or a global extremum, depending on the parameters of the control system. However, in the case of a saddle the numbers of negative and positive eigenvalues of the Hessian at this point and their magnitudes have not been studied. At the same time, these numbers and magnitudes determine the relative ease or difficulty for practical optimization in a vicinity of the critical point. In this work, we compute the numbers of negative and positive eigenvalues of the Hessian at this saddle point and, moreover, give estimates on magnitude of these eigenvalues. We also significantly simplify our previous proof of the theorem about this saddle point of the Hessian [Theorem 3 in B. O. Volkov, O. V. Morzhin, A. N. Pechen, J. Phys. A: Math. Theor. 54, 215303 (2021)].
Bibliography: 42 titles.
Ключевые слова:
quantum control, qubit, coherent control, phase shift gate.
Поступило в редакцию: 28.04.2022 Исправленный вариант: 21.09.2022
Образец цитирования:
B. O. Volkov, A. N. Pechen, “On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation”, Изв. РАН. Сер. матем., 87:5 (2023), 57–70; Izv. Math., 87:5 (2023), 906–919
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/im9364https://doi.org/10.4213/im9364 https://www.mathnet.ru/rus/im/v87/i5/p57
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