Introduction We present Quantum Adaptive Search (QAGS), a hybrid quantum-classical algorithm for global optimization of multivariate functions. The method employs an adaptive mechanism that dynamically narrows the search space based on a quantum-estimated probability distribution of the objective function. Methods A quantum state encodes information about solution quality through a complex-amplitude mapping, enabling identification of promising regions and progressive tightening of the search bounds; a classical optimizer then performs local refinement. The analysis shows contraction of the search space toward global optima with controlled computational complexity. Results In simulation on standard benchmarks (Rastrigin, Styblinski-Tang, Rosenbrock), QAGS attains solutions at or near the true minima with very small absolute errors. Against an Adaptive Grid Search on the Sphere function, QAGS achieves comparable accuracy and shows increasing efficiency with dimensionality. Discussion These results indicate that amplitude-encoded region selection combined with classical refinement effectively contracts the search space and can reduce time and space requirements, especially at higher dimensions, while practical hardware implementations of amplitude encoding remain challenging.
Introduction We present Quantum Adaptive Search (QAGS), a hybrid quantum-classical algorithm for global optimization of multivariate functions. The method employs an adaptive mechanism that dynamically narrows the search space based on a quantum-estimated probability distribution of the objective function. Methods A quantum state encodes information about solution quality through a complex-amplitude mapping, enabling identification of promising regions and progressive tightening of the search bounds; a classical optimizer then performs local refinement. The analysis shows contraction of the search space toward global optima with controlled computational complexity. Results In simulation on standard benchmarks (Rastrigin, Styblinski-Tang, Rosenbrock), QAGS attains solutions at or near the true minima with very small absolute errors. Against an Adaptive Grid Search on the Sphere function, QAGS achieves comparable accuracy and shows increasing efficiency with dimensionality. Discussion These results indicate that amplitude-encoded region selection combined with classical refinement effectively contracts the search space and can reduce time and space requirements, especially at higher dimensions, while practical hardware implementations of amplitude encoding remain challenging.
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.
This paper introduces a novel probabilistic graph search algorithm, dubbed "Quantum Adaptive Probability Search" (QAPS), that leverages quantum self-adaptation to enhance exploration within complex search spaces. Traditional probabilistic graph search methods often suffer from inefficiency, particularly in problems with intricate search landscapes. QAPS employs a quantum-inspired self-adaptation mechanism to dynamically restructure the graph, facilitating more efficient exploration and ultimately, the identification of optimal solutions. We demonstrate the algorithm's efficacy through a series of benchmark problems, highlighting its superior performance compared to established methods in terms of both search time and solution quality. The core mechanism centers around the creation of a quantum-informed probability graph, allowing for adaptive node and edge weights, which significantly improves the algorithm's ability to navigate challenging search spaces.
Large-scale optimization (LSO) problems—those with hundreds to thousands of decision variables—are prevalent in engineering design, logistics, telecommunications, and machine learning hyperparameter search. Classical evolutionary algorithms often struggle in this regime due to premature convergence and prohibitive search costs. This manuscript presents a Quantum-Inspired Genetic Algorithm (QIGA) that transfers three ideas from quantum computation into a purely classical algorithm: (i) Q-bit angle encoding that maintains a compact, uncertainty-aware distribution over decision values, (ii) rotation-gate adaptation that updates search probabilities toward promising regions while preserving exploration, and (iii) quantum observation that draws diverse candidate solutions from the encoded amplitudes at each generation. We further couple the core QIGA with (a) an island-model decomposition for ultra-high dimensionality, (b) surrogate-assisted local refinement for exploitation at low cost, and (c) a feasibility-aware penalty for constraints. We evaluate the approach on five canonical continuous benchmarks in 1,000 dimensions (Sphere, Rosenbrock, Rastrigin, Ackley, Griewank) under a fixed computational budget. Across 30 independent runs per function, QIGA achieves lower final objective values and higher success rates than classical GA, PSO, and DE baselines. A non-parametric Wilcoxon signed-rank test indicates statistically significant improvements for QIGA (adjusted p < 0.01) on all functions. We analyze the algorithm’s scaling behavior, the role of angle-space step control, and the contribution of island-level diversity. The results suggest that quantum-inspired probability evolution provides a robust inductive bias for LSO by decoupling representation capacity from point estimates and by enabling distribution-aware search moves. We conclude with practical guidelines for tuning and discuss extensions to constrained and mixed-variable problems.
This paper introduces Quantum-Inspired Optimization via Adaptive Sampling (QIAO), a novel technique for complex system optimization. Traditional optimization methods often struggle with the inherent complexity of real-world problems, frequently requiring exhaustive search or computationally expensive approximations. QIAO leverages quantum-inspired principles to dynamically sample regions of the solution space, focusing on areas exhibiting higher potential for improvement. This adaptive sampling strategy significantly enhances efficiency compared to traditional methods, particularly in scenarios with high dimensionality and complex interactions within the system. We present a detailed explanation of the algorithm's design, its implementation, and preliminary results demonstrating its efficacy in a simulated optimization problem. The focus is on demonstrating the practical advantages of this approach through a quantifiable improvement in performance.
This paper presents an Adaptive Quantum Annealing Optimization Algorithm (AQAO) designed to address the limitations of traditional quantum annealing approaches in tackling complex, non-convex optimization problems. The core of the AQAO lies in its dynamic analysis of the objective function's energy landscape and the subsequent adaptive adjustment of annealing parameters. Unlike conventional quantum annealing, which often employs fixed parameters, the AQAO continuously monitors the quantum annealing process and adjusts parameters such as the annealing rate and jump probability based on real-time changes in the energy landscape. This adaptive mechanism aims to accelerate convergence towards optimal solutions by effectively responding to the evolving complexities of the optimization problem. The algorithm leverages the inherent search capabilities of quantum annealing while mitigating the issues of slow convergence or failure to find global optima frequently encountered with static parameter settings. The theoretical framework and algorithmic design are presented, emphasizing the key improvements and potential advantages of the AQAO compared to existing methods. The focus is on the adaptive control strategy, providing a robust approach to complex optimization challenges.
This research presents a novel stochastic search algorithm, termed Quantum-Inspired Stochastic Search (QISS), designed to address the challenges posed by complex, high-dimensional, and non-convex optimization landscapes. Traditional stochastic search methods often struggle in these scenarios due to premature convergence and difficulty exploring diverse regions of the solution space. QISS draws inspiration from quantum mechanics, specifically the concepts of superposition and measurement, to enhance exploration and exploitation. The algorithm maintains candidate solutions in a probabilistic superposition of multiple states, and employs randomized projection operations analogous to quantum measurement to collapse the superposition, effectively guiding the search towards potentially optimal regions. The core idea is to mimic the probabilistic nature of quantum states, allowing the algorithm to simultaneously consider multiple possibilities before "measuring" and focusing on the most promising one. This approach demonstrates potential for improved performance compared to conventional stochastic search techniques, particularly in situations where the landscape is highly irregular and contains numerous local optima. The algorithm's performance is evaluated through simulations, showcasing its ability to navigate complex landscapes and converge towards solutions with improved accuracy and efficiency.