Buch ; Online: Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
2023
Abstract: In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure that, under a ...
| Abstract | In variational quantum algorithms (VQAs), the most common objective is to find the minimum energy eigenstate of a given energy Hamiltonian. In this paper, we consider the general problem of finding a sufficient control Hamiltonian structure that, under a given feedback control law, ensures convergence to the minimum energy eigenstate of a given energy function. By including quantum non-demolition (QND) measurements in the loop, convergence to a pure state can be ensured from an arbitrary mixed initial state. Based on existing results on strict control Lyapunov functions, we formulate a semidefinite optimization problem, whose solution defines a non-unique control Hamiltonian, which is sufficient to ensure almost sure convergence to the minimum energy eigenstate under the given feedback law and the action of QND measurements. A numerical example is provided to showcase the proposed methodology. Comment: Accepted for IFAC 2023 - 22nd World Congress of the International Federation of Automatic Control |
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| Schlagwörter | Quantum Physics ; Electrical Engineering and Systems Science - Systems and Control ; Mathematics - Optimization and Control |
| Thema/Rubrik (Code) | 531 |
| Erscheinungsdatum | 2023-04-18 |
| Erscheinungsland | us |
| Dokumenttyp | Buch ; Online |
| Datenquelle | BASE - Bielefeld Academic Search Engine (Lebenswissenschaftliche Auswahl) |
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