Quantum computation and optimization have recently garnered considerable attention, with a noticeable focus on their floating-point and arithmetic designs. In classical computing, numerical optimization problems are commonly employed to assess the performance of optimization algorithms before their application to real-world issues. Nevertheless, precision issues impact the performance analysis of these algorithms, and neglecting these predictable exceptions can lead to unforeseen consequences. Therefore, this study systematically organizes potential precision issues related to how the floating-point storage format impacts optimization. These issues cause the optimal solution to deviate from the theoretical value, introducing imprecision or multiple optimal values, which in turn affects the usability of optimization algorithms, the direction of the search, and the assessment of convergence levels. These analyses offer valuable insights into the practical behavior of optimization algorithms when applied to function optimization problems, aiding researchers in accurately assessing and enhancing algorithm performance. Moreover, these findings contribute to the advancement of both classical and quantum computation.
Quantum computation and optimization have recently garnered considerable attention, with a noticeable focus on their floating-point and arithmetic designs. In classical computing, numerical optimization problems are commonly employed to assess the performance of optimization algorithms before their application to real-world issues. Nevertheless, precision issues impact the performance analysis of these algorithms, and neglecting these predictable exceptions can lead to unforeseen consequences. Therefore, this study systematically organizes potential precision issues related to how the floating-point storage format impacts optimization. These issues cause the optimal solution to deviate from the theoretical value, introducing imprecision or multiple optimal values, which in turn affects the usability of optimization algorithms, the direction of the search, and the assessment of convergence levels. These analyses offer valuable insights into the practical behavior of optimization algorithms when applied to function optimization problems, aiding researchers in accurately assessing and enhancing algorithm performance. Moreover, these findings contribute to the advancement of both classical and quantum computation.
The rapid development of Quantum Computing (QC) as a promising computing paradigm has garnered significant attention for its ability to harness quantum mechanical properties for computation. With classical computing facing limitations outlined by Moore’s Law, QC emerges as a potential alternative for tackling complex computational problems. Yet, to unlock its full potential, robust and optimized compilers are pivotal, especially in addressing challenges posed by circuits with numerous qubits. In this systematic literature review, we analyze 18 articles to identify proposed optimizations for quantum compilers, exploring their applications, performance impacts, and emerging trends. Our primary goal is to offer valuable insights into the recent advancements and challenges in QC compiler optimizations. This will be achieved through the clustering of optimization groups, ultimately facilitating further progress in the development of highly optimized quantum algorithms and circuits.
Optimization problems across domains such as logistics, finance, and artificial intelligence often involve complex and NP-hard formulations that are computationally challenging for classical algorithms due to scalability and efficiency limitations. The study aims to systematically investigate the role of Quantum Machine Learning (QML) in addressing complex optimization problems and to analyze its advantages over traditional optimization techniques. A comprehensive survey and comparative analysis of key QML algorithms, including Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), Quantum Neural Networks (QNNs), and Quantum Support Vector Machines (QSVMs), is conducted by examining their working principles, optimization capabilities, and real-world applications. The findings indicate that QML algorithms demonstrate significant potential in exploring large solutions spaces efficiently, achieving faster convergence, and providing improved optimization performance compared to classical approaches, although challenges such as quantum noise, scalability, and hardware limitations remain. The novelty of this study lies in providing a unified and critical comparative framework that integrates multiple QML optimization algorithms, highlights their practical feasibility, and identifies key research gaps hindering their real-world deployment. The implications of this research provide valuable insights for researchers and practitioners in selecting appropriate QML techniques and emphasize the need for advancements in hybrid quantum -classical systems, algorithms design, and quantum hardware to enable practical large-scale optimization.
Quantum algorithms offer promising advancements in solving complex optimization problems that are critical in various fields, including logistics, finance, and machine learning. Classical optimization techniques, while effective, often struggle with large-scale and high-dimensional data sets, leading to inefficiencies and long processing times.Quantum algorithms, leveraging the principles of superposition, entanglement, and quantum parallelism, provide a potential solution by exponentially speeding up certain computational tasks. This paper explores key quantum algorithms for optimization, including Grover's algorithm, the Quantum Approximate Optimization Algorithm (QAOA), and the Quantum Annealing method. We analyze their theoretical foundations, implementation challenges, and practical applications. Special attention is given to the performance comparisons between quantum and classical approaches in solving combinatorial optimization problems, such as the traveling salesman problem and portfolio optimization. We also discuss the limitations of current quantum hardware and the prospects for future improvements that could make quantum optimization algorithms more practical for real-world use.Our findings suggest that, while quantum algorithms are still in their early stages, they hold immense potential for transforming optimization in a variety of domains, offering new pathways toward more efficient problem-solving in both theoretical and applied contexts. we explore how hybrid quantum-classical approaches can enhance optimization results by combining the strengths of both paradigms. Future research directions are highlighted, focusing on improving quantum error correction, scaling quantum systems, and developing more robust quantum algorithms to tackle increasingly complex optimization problems.
Quantum computing has emerged as a promising paradigm for addressing computational challenges in physics that remain intractable for classical methods. This study presents a quantitative benchmarking analysis of prominent quantum algorithms applied to representative physics problem classes, with the objective of evaluating their computational performance relative to state-of-the-art classical algorithms. Using standardized performance metrics—including execution time, algorithmic complexity, resource utilization, accuracy, scalability, and quantum advantage ratios—the study systematically compares quantum and classical approaches across multiple experimental configurations. The results demonstrate that quantum algorithms exhibit measurable performance gains for specific problem types, particularly in terms of runtime efficiency and scaling behavior, while also highlighting practical constraints related to qubit requirements and circuit depth. Visual and tabulated analyses further reveal that quantum advantage is highly problem-dependent and influenced by algorithmic structure and system size. Overall, the findings provide empirical evidence that quantum algorithms can offer substantial computational benefits for selected physics applications, while underscoring the importance of quantitative benchmarking in distinguishing theoretical promise from practical performance. This work contributes to ongoing efforts to objectively assess quantum advantage and informs future research directions in quantum algorithm development and physics-based applications.
Quantum computing, with its potential to revolutionize computation, relies fundamentally on the development of efficient algorithms to leverage its unparalleled processing capabilities. This research delves into the creation, exploration, and refinement of quantum computing algorithms, focusing on their applications in optimization, cryptography, and machine learning. Quantum algorithms such as Shor's and Grover's have demonstrated remarkable advantages in factorization and search problems, while more recent innovations are tackling complex challenges in global optimization and data analysis. By integrating principles of quantum mechanics—such as superposition, entanglement, and interference—these algorithms promise exponential speed-ups over classical counterparts in specific domains. This study critically analyzes existing quantum algorithms, proposes advancements in hybrid quantum-classical frameworks, and explores their implications for practical problem-solving. Through simulations and theoretical evaluations, it aims to bridge the gap between quantum theory and real-world applications, contributing to the evolution of quantum computing as a transformative technology.
A groundbreaking advancement in computing theory, quantum search algorithms leverage quantum mechanics to outperform their classical counterparts in solving search issues. With a focus on their theoretical underpinnings, practical applications, and performance in a variety of computational contexts, this systematic review carefully investigates the evolution, progress, and current state of quantum search algorithms. We present a thorough analysis of significant algorithms, such as Grover’s search algorithm, together with recent developments in quantum optimization and quantum-enhanced search techniques. We also go over the challenges with quantum error correction, scalability, and hardware constraints that prevent the broad application of quantum search techniques.