Browsing by Author "Abdul Rahman, Salahuddin"

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Citation - WoS: 3
Citation - Scopus: 3
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; Abdul Rahman, Salahuddin
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: 3
Feedback-Based Quantum Algorithm for Constrained Optimization Problems
(Springer International Publishing AG, 2025) Rahman, Salahuddin Abdul; Karabacak, Ozkan; Wisniewski, Rafal; Abdul Rahman, Salahuddin
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; Abdul Rahman, Salahuddin
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.