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Jisuanji gongcheng yu sheji

Quantum algorithm for finding optimal loading

Li Sun

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

With the growth of Grover's quantum search algorithms,it is applied to practical uses gradually.By introducing of the fun-damental principles of quantum parallelism and quantum algorithms and studying the improved Grover searching algorithm,a quantum mechanical algorithm is given to solve optimal loading problem,and is proved its time complexity to O().As to the optimal loading problem,two methods are given to resolve the problem respectively,that is,greed algorithm in the classic computers and quantum al-gorithm.The time complexity of this two algorithms is gained.In the conclusion,quantum algorithms solve many search problems more efficiently than classic algorithms.

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With the growth of Grover's quantum search algorithms,it is applied to practical uses gradually.By introducing of the fun-damental principles of quantum parallelism and quantum algorithms and studying the improved Grover searching algorithm,a quantum mechanical algorithm is given to solve optimal loading problem,and is proved its time complexity to O().As to the optimal loading problem,two methods are given to resolve the problem respectively,that is,greed algorithm in the classic computers and quantum al-gorithm.The time complexity of this two algorithms is gained.In the conclusion,quantum algorithms solve many search problems more efficiently than classic algorithms.
This paper illustrated the optimality of Grover quantum search algorithm, and simulated the number of iterations and the specific implementation steps of quantum search algorithm with QCL in Linux operating systems, then validated the time complexity of Grover's quantum searching algorithm is O(√(N)) while the algorithm's time complexity on classical computers is O(N). The Grover quantum search algorithm were shown to improve the performance significantly in the random database search problem. This conclusion was drawn from the simulation in the Linux operating systems adopted to quantum computation language. The present study highlighted the importance of high efficiency of the Grover quantum search algorithm to achieve the best possible performance in such cases. The existence of such efficiency is an outstanding advantage of quantum search algorithm over the conventional approach.
The scientists have given various kinds of quantum mechanical algorithms for different kinds of problems in recent years. Because of massive quantum parallelism, quantum computer can solve many problems more efficiently. 0/1 knapsack problem is a typical NPC problem. Its computing complexity is O(2 n ) steps. This paper gives a quantum mechanical algorithm to solve 0/1 knapsack problem, which is based on Grover algorithm and quantum exponential searching algorithm. The algorithm doesn't involve any classical method to improve search efficiency and the solution can be obtained in O(c2 n2 ) steps with a probability of at least 1-12 c.
Grover′s quantum search algorithm utilizes the parallel properties of quantum mechanics,which has been studied and applied extensively because of its great search efficiency.The principle and performance of Grover′s quantum searching algorithm is researched,especially the quantum algorithm for finding the minimum of a database is deeply researched.Because the search number of the algorithm is high,an improved quantum algorithm which named double threshold for finding a maximum in a database is proposed.The conclusion that the search number of this algorithm is less than the original one through the simulation.The algorithm is applied in multi-user detection,experiment results show that the bit error rate performance of the algorithm is close to the optimal multi-user detection algorithm,and the complexity is less than the optimal one.
The study examines the use of Grover's quantum algorithm to optimize global search problems, demonstrating its quadratic speedup over classical methods for improved efficiency. The research tackles practical challenges, including quantum noise, scalability, and resource constraints, by proposing innovative solutions. The techniques developed integrate quantum search principles into large-scale optimization tasks across diverse fields. This work lays a foundational framework for applying quantum algorithms to solve complex scientific and industrial problems.
The article examines methods for applying quantum computing to solve optimization problems, which are critical in various fields such as logistics, finance, resource management, energy, and others. The potential of quantum algorithms, such as Grover's algorithm and Variational Quantum Algorithms (VQA), is explored for enhancing computational efficiency compared to classical methods. Quantum computing enables significant acceleration of optimal solution search processes and reduces the complexity of problems through parallel computing and quantum superposition.
Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.