Browsing by Author "Wisniewski, Rafal"

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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 - WoS: 2
Citation - Scopus: 2
Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
(Elsevier, 2023) Clausen, Henrik Glavind; 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/)
Weighted Feedback-Based Quantum Algorithm for Excited States Calculation
(IEEE Computer Soc, 2024) Rahman, Salahuddin Abdul; Karabacak, Ozkan; Wisniewski, Rafal
Drawing inspiration from the Lyapunov control technique for quantum systems, feedback-based quantum algorithms have been proposed for calculating the ground states of Hamiltonians. In this work, we consider extending these algorithms to tackle calculating excited states. Inspired by the weighted subspace-search variational quantum eigensolver algorithm, we propose a novel weighted feedback-based quantum algorithm for excited state calculation. We show that depending on how we design the weights and the feedback law, we can prepare the pth excited state or lowest energy states up to the pth excited state. Through an application in quantum chemistry, we show the effectiveness of the proposed algorithm, evaluating its efficacy via numerical simulations.