In this paper, a novel Hybrid Quantum-Classical Adaptive Rotation and Quantum Walk (HQC-ARQW) algorithm is introduced for optimal design of the Finite Impulse Response (FIR) digital filters. To bridge the gap between the conventional optimisation methods and move into modern times, the proposed framework uses a mixture of quantum-inspired operators with classical genetic algorithms that efficiently handle the complexity of high-dimensional coefficient spaces. The HQC-ARQW algorithm uses adaptive quantum rotation gates with dynamic angle$(\theta \in[0.15 \pi, 0.50 \pi])$for population evolution and quantum walk local search for fine-grained solution refinement. The quantum walk operator empowers adaptive step-size annealing$\left(\alpha_{0}=0.08, T=30\right.{}$steps). Supported on Qiskit's AerSimulator to validate implementations are practically feasible on the near-term quantum hardware. Experimental results on filter orders 9 and 11 show significant performance improvement over the classical GA. The HQC-ARQW provides a 50%-55% reduction in magnitude MSE and more than 2-fold faster convergence to optimum solutions obtained in 25 generations as opposed to 100 generations for the classical approaches. Our results demonstrate the HQCARQW algorithm as a promising solution for computationally demanding optimisation tasks in digital signal processing.
In this paper, a novel Hybrid Quantum-Classical Adaptive Rotation and Quantum Walk (HQC-ARQW) algorithm is introduced for optimal design of the Finite Impulse Response (FIR) digital filters. To bridge the gap between the conventional optimisation methods and move into modern times, the proposed framework uses a mixture of quantum-inspired operators with classical genetic algorithms that efficiently handle the complexity of high-dimensional coefficient spaces. The HQC-ARQW algorithm uses adaptive quantum rotation gates with dynamic angle(θ∈[0.15π,0.50π])for population evolution and quantum walk local search for fine-grained solution refinement. The quantum walk operator empowers adaptive step-size annealing(α0=0.08,T=30steps). Supported on Qiskit's AerSimulator to validate implementations are practically feasible on the near-term quantum hardware. Experimental results on filter orders 9 and 11 show significant performance improvement over the classical GA. The HQC-ARQW provides a 50%-55% reduction in magnitude MSE and more than 2-fold faster convergence to optimum solutions obtained in 25 generations as opposed to 100 generations for the classical approaches. Our results demonstrate the HQCARQW algorithm as a promising solution for computationally demanding optimisation tasks in digital signal processing.
In this paper a new optimization algorithm named Adaptive Hybrid Quantum-Inspired Optimization Algorithm (AHQSOA) is presented for solving the complex optimization problems effectively. Stochastic traditional algorithms typically fail to come to be stuck in local optimum solutions and they need quite few iterations for converging. Our method integrates two quantum-inspired methodology: Quantum Particle Swarm Optimization (QPSO) for searching a large set solutions based on properties of quantum mechanics - superposition, point are located as randomly as possible, and Quantum Evolutionary Algorithms (QEA) for refining potential solutions by mutation and crossover operation. An adaptive tuning component based on the reinforcement learning dynamically adjusts the algorithm’s parameters, thus balancing the exploration in the wide interval and exploitation in the precise interval. Assessed on the commonly used benchmark functions like Sphere, Rosenbrock, Rastrigin, AHQSOA exhibits faster convergence (only 400 iterations in comparison to 1200 in standard methods), global search superiority (94% whereas 75–87% the traditional methods), and low computational simplicity. These results show all of our algorithm are nicer and faster and more efficient and robust makes for it a good candidate as for high dimensional and complex optimization problems.
Quantum computing promises computational advantages for solving complex optimization problems; however, current Noisy Intermediate-Scale Quantum (NISQ) devices suffer from limited qubit counts, short coherence times, and high error rates. Fully fault-tolerant quantum algorithms remain impractical in the near term, necessitating hybrid approaches that integrate classical and quantum computation. This paper proposes a Hybrid Quantum–Classical Machine Learning Framework (HQC-MLF) for large-scale combinatorial and continuous optimization tasks. The framework leverages parameterized quantum circuits (PQCs) embedded within classical optimization loops, enabling efficient search in high-dimensional spaces while mitigating hardware constraints. We introduce adaptive ansatz selection, classical preconditioning, error mitigation strategies, and resource-aware scheduling to enhance scalability. Experimental evaluations on logistics routing, portfolio optimization, and energy load balancing demonstrate improved convergence speed and solution quality compared to purely classical baselines under realistic NISQ simulations. The proposed architecture provides a practical pathway toward near-term quantum advantage in real-world optimization problems
The fastest growing Internet of Things (IoT) application field necessitates efficient signal processing frameworks with high computational portions that have an incomparably low power consumption, especially among embedded devices subject to very limited resources. In this paper, we present a hybrid quantum-inspired signal processing paradigm combining both theoretical aspects of a quantum-inspired computation we have used along our theoretical aspects of classical DSP, e.g., moving between amplitude encoding, quantum superposition, quantum optimization of rotation gates, adaptive FIR/IIR filtering and discrete wavelet transforms, and fixed-point optimisation. Such theoretical combination solves some of the most important signal processing issues that involve lowered computational complexity, enhanced convergence characteristics of adaptive filters, and heightened noise resilience in non-stationary settings. The hardware-algorithm co-design in the framework uses a combination of fixed-point arithmetic, loop unrolling and memory blocking to facilitate successful real-time deployment on an ARM Cortex-M4 microcontroller. Up to 43 percent reduction of energy, 31 percent improvement on execution speed and 25 percent better in the classification rate compared to baseline DSP methods are also shown through experimental validation. Demonstration of the generalizability of the strategy by utilizing it in the area of biomedical signal denoising, environmental sound analysis, and structural vibration monitoring creates a scalable methodology of realizing elegant signal processing theory under resource-limited embedded IoT devices.
Scalable combinatorial optimization under resource-constrained quantum hardware remains a fundamental challenge in the Noisy Intermediate-Scale Quantum (NISQ) era, due to the mismatch between exponentially growing solution spaces and limited quantum computational capacity. In this work, we propose a NISQ-aware hybrid quantum-classical optimization framework that reformulates large-scale combinatorial optimization as a resource-bounded distribution evolution process. Instead of directly optimizing individual solutions, the proposed framework operates on a probabilistic representation of the solution space, enabling efficient exploration under hardware constraints. Specifically, large problem instances are decomposed into qubit-compatible subproblems via clustering-based decomposition, ensuring resource-bounded optimization. Within each subproblem, a quantum genetic algorithm evolves the solution distribution, while periodically embedded amplitude amplification acts as a controlled quantum enhancement mechanism that accelerates convergence without increasing circuit depth. A classical refinement stage ensures global solution consistency. Extensive experiments on benchmark and synthetic datasets demonstrate that the proposed framework consistently outperforms classical and quantum-inspired baselines, with performance gains that become more pronounced as problem scale increases. This scale-dependent behavior indicates that scalability is achieved through structured decomposition rather than increased quantum complexity. Noise simulations further confirm robustness under realistic NISQ conditions, and ablation studies validate that both quantum evolutionary search and amplitude amplification contribute significantly to performance improvements.
This paper presents a novel approach to complex optimization problems utilizing a hybrid Genetic Algorithm (GA) enhanced with quantum computing techniques. Classical GAs often struggle with slow convergence rates in high-dimensional search spaces. This research addresses this limitation by integrating quantum superposition and interference into the core operations of the GA, specifically crossover and mutation. The proposed method, termed Quantum-Enhanced Genetic Algorithm (Q-GA), aims to significantly accelerate the optimization process by exploring the solution space more efficiently. The core idea is to represent potential solutions within a quantum state, allowing for parallel exploration facilitated by superposition. We detail the architecture of the Q-GA, outlining the integration of classical GA components with quantum algorithms. The performance of the Q-GA is theoretically analyzed, focusing on the potential speedup achievable through quantum computation. The results presented demonstrate the promise of this hybrid approach for tackling computationally intensive optimization problems where classical GAs fall short.
Although quantum computers will not necessarily transform ML in general, they hold immense potential for specific uses, such as dealing with high-dimensional data and complex correlations that cannot be effectively modeled using classical systems. It is, however, difficult to design efficient quantum circuits, especially with the existing Noisy Intermediate-Scale Quantum (NISQ) hardware that has constraints including decoherence, a limited number of qubits, and gate fidelity limitations. The authors propose an Adaptive Quantum Circuit Architecture Search (AQCAS) framework whose structure and parameters are optimized dynamically to improve the performance of the task-specific ML. The framework integrates quantum circuit encoding, a hybrid search strategy that is based on reinforcement learning and evolutionary algorithms, and a task-specific adaptivity mechanism. Benchmark datasets were used for experimental evaluations of both simulation using Qiskit Aer and classical optimization using the Python frameworks TensorFlow and PennyLane. Fixed and standard variational quantum circuits were compared with performance measurements like the classification accuracy, circuit depth, convergence speed, and computational efficiency. The results show that the accuracy of AQCAS can be raised to 94.1%, and the circuit depth is lowered at the same time. It converged rapidly and is computationally efficient. Ablation studies show that both hybrid search and adaptivity mechanisms help to enhance generalization and stability under NISQ constraints. The results demonstrate the potential of AQCAS as a practical approach to using adaptive quantum circuits in specialized ML applications, and lay the groundwork for future development of scaling to larger devices, implementing noise-aware optimization, and integrating with hybrid quantum-classical ML pipelines.