Browsing by Author "Karabacak, Ozkan"

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Citation Count: 0
Adaptive Sampling Noise Mitigation Technique for Feedback-Based Quantum Algorithms
(Springer international Publishing Ag, 2024) Karabacak, Özkan; Clausen, Henrik Glavind; Karabacak, Ozkan; Wisniewski, Rafal
Inspired by Lyapunov control techniques for quantum systems, feedback-based quantum algorithms have recently been proposed as alternatives to variational quantum algorithms for solving quadratic unconstrained binary optimization problems. These algorithms update the circuit parameters layer-wise through feedback from measuring the qubits in the previous layer to estimate expectations of certain observables. Therefore, the number of samples directly affects the algorithm's performance and may even cause divergence. In this work, we propose an adaptive technique to mitigate the sampling noise by adopting a switching control law in the design of the feedback-based algorithm. The proposed technique can lead to better performance and convergence properties. We show the robustness of our technique against sampling noise through an application for the maximum clique problem.
Citation Count: 0
Certification of almost global phase synchronization of all-to-all coupled phase oscillators
(Pergamon-Elsevier Science Ltd, 2023) Karabacak, Özkan; Kudeyt, Mahmut; Koksal-Ersoz, Elif; Ilhan, Ferruh; Karabacak, Ozkan
Coupled oscillators may exhibit almost global phase synchronization, namely their phases tend to asymp-totically overlap for almost all initial conditions. We consider certification of this property using Rantzer's dual Lyapunov approach with sum of squares (SOS) programming. To this aim, we use a stereographic transformation from a hypertorus to an Euclidean space. For the case of all-to-all coupling, this transformation converts the problem of certifying stability into the problem of certifying divergence of almost all solutions to infinity. We show that the latter can be solved using a polynomial Lyapunov density, which can be constructed via SOS programming. This leads to the certification of almost global phase synchronization of all-to-all coupled phase oscillators. We apply our method to an example of coupled phase oscillators and to an example of coupled van der Pol oscillators, and show that it can support the existing tools of local stability analysis by ensuring almost global phase synchronization.
Citation Count: 0
Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
(Elsevier, 2023) Karabacak, Özkan; Rahman, Salahuddin Abdul; Karabacak, Ozkan; Wisniewski, Rafal
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. 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/)