Karabacak, ÖzkanClausen, Henrik GlavindRahman, Salahuddin AbdulKarabacak, OzkanWisniewski, Rafal2024-06-232024-06-23202302405-8963https://doi.org/10.1016/j.ifacol.2023.10.111https://hdl.handle.net/20.500.12469/5707Abdul Rahman, Salahuddin/0009-0002-9686-8586In 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. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)eninfo:eu-repo/semantics/openAccessLyapunov controlquantum non-demolition measurementssemidefinite programmingvariational quantum algorithmsConference Object51715178256WOS:00119670920033310.1016/j.ifacol.2023.10.1112-s2.0-85174482248N/AN/A