Browsing by Author "Wisniewski, Rafal"

Now showing 1 - 5 of 5

Citation - WoS: 3
Citation - Scopus: 2
Adaptive Sampling Noise Mitigation Technique for Feedback-Based Quantum Algorithms
(Springer international Publishing Ag, 2024) Rahman, Salahuddin Abdul; Clausen, Henrik Glavind; Karabacak, Ozkan; Wisniewski, Rafal; Mechatronics Engineering; 05. Faculty of Engineering and Natural Sciences; 01. Kadir Has University
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
Feedback-Based Quantum Algorithm for Constrained Optimization Problems
(Springer International Publishing AG, 2025) Rahman, Salahuddin Abdul; Karabacak, Ozkan; Wisniewski, Rafal; Mechatronics Engineering; 05. Faculty of Engineering and Natural Sciences; 01. Kadir Has University
The feedback-based algorithm for quantum optimization (FALQON) has recently been proposed to find ground states of Hamiltonians and solve quadratic unconstrained binary optimization problems. This paper efficiently generalizes FALQON to tackle quadratic constrained binary optimization (QCBO) problems. For this purpose, we introduce a new operator that encodes the problem's solution as its ground state. Using control theory, we design a quantum control system such that the state converges to the ground state of this operator. When applied to the QCBO problem, we show that our proposed algorithm saves computational resources by reducing the depth of the quantum circuit and can perform better than FALQON. The effectiveness of our proposed algorithm is further illustrated through numerical simulations.
Feedback-Based Quantum Strategies for Constrained Combinatorial Optimization Problems
(Elsevier, 2026) Rahman, Salahuddin Abdul; Karabacak, Ozkan; Wisniewski, Rafal; Mechatronics Engineering; 05. Faculty of Engineering and Natural Sciences; 01. Kadir Has University
Feedback-based quantum algorithms have recently emerged as potential methods for approximating the ground states of Hamiltonians. One such algorithm, the feedback-based algorithm for quantum optimization (FALQON), is specifically designed to solve quadratic unconstrained binary optimization problems. Its extension, the feedback-based algorithm for quantum optimization with constraints (FALQON-C), was introduced to handle constrained optimization problems with equality and inequality constraints. In this work, we extend the feedback-based quantum algorithms framework to address a broader class of constraints known as invalid configuration (IC) constraints, which explicitly prohibit specific configurations of decision variables. We first present a transformation technique that converts the constrained optimization problem with invalid configuration constraints into an equivalent unconstrained problem by incorporating a penalizing term into the cost function. Then, leaning upon control theory, we propose an alternative method tailored for feedback-based quantum algorithms that directly tackles IC constraints without requiring slack variables. Our approach introduces a new operator that encodes the optimal feasible solution of the constrained optimization problem as its ground state. Then, a controlled quantum system based on the Lyapunov control technique is designed to ensure convergence to the ground state of this operator. Two approaches are introduced in the design of this operator to address IC constraints: the folded spectrum approach and the deflation approach. These methods eliminate the need for slack variables, significantly reducing the quantum circuit depth and the number of qubits required. We show the effectiveness of our proposed algorithms through numerical simulations.
Citation - WoS: 4
Citation - Scopus: 4
Measurement-Based Control for Minimizing Energy Functions in Quantum Systems
(Elsevier, 2023) Clausen, Henrik Glavind; Rahman, Salahuddin Abdul; Karabacak, Ozkan; Wisniewski, Rafal; Mechatronics Engineering; 05. Faculty of Engineering and Natural Sciences; 01. Kadir Has University
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/)
Citation - WoS: 1
Citation - Scopus: 2
Weighted Feedback-Based Quantum Algorithm for Excited States Calculation
(IEEE Computer Soc, 2024) Rahman, Salahuddin Abdul; Karabacak, Ozkan; Wisniewski, Rafal; Mechatronics Engineering; 05. Faculty of Engineering and Natural Sciences; 01. Kadir Has University
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.