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Modern Electronics Technique

Improved Quantum Algorithm for Finding the Minimum of Database

Zhou Lin

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
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 classical optimal solution of CDMA multi-user detection is consistent with the optimization of a quadratic function, and to find the optimum is a NP hard problem. Reducing the complexity of optimum based on quantum parallel computation is a new trend of multi-user detection techniques. In this paper, we propose a scheme based on Grover's searching algorithm to find the optimum. We give the relationship of bit error rate against signal-to-noise and correlation coefficient by numerical simulation, and simply evaluate the computational complexity of our proposed scheme. The results show that our solution has almost the same performance to the classical optimal one, however, with low complexity
Finding a maximum or minimum is a fundamental building block in many mathematical models. Compared with classical algorithms, Durr, Hoyer's quantum algorithm (DHA) achieves quadratic speed. However, its key step, the quantum exponential searching algorithm (QESA), which is based on Grover algorithm, is not a sure-success algorithm. Meanwhile, quantum circuits encounter the gate decomposition problem due to variation of the scale of data. In this paper, we propose an optimized quantum algorithm for searching maximum and minimum, based on DHA and the optimal quantum exact search algorithm. Furthermore, we provide the corresponding quantum circuits, together with three equivalent simplifications. In circumstances when we can exactly estimate the ratio of the number of solutions M and the searched space N, our method can improve the successful probability close to 100%. Furthermore, compared with DHA, our algorithm shows an advantage in complexity with large databases and in the gate complexity of constructing oracles. Experiments have been executed on an IBM superconducting processor with two qubits, and a practical problem of finding the minimum from Titanic passengers' age was numerically simulated. Both showed that our optimized maximum or minimum performs more efficiently compared with DHA. Our algorithm can serve as an important subroutine in various quantum algorithms which involves searching maximum or minimum.
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.
At present, the scale of quantum computers in the real sense is still small, and quantum simulation has become one of the important ways of quantum theory research, grover quantum search algorithm is suitable for the search problem of disordered database. Firstly, according to the implementation principle of Grover algorithm and Boolean logic relationship, the design idea of multi-objective Oracle is analyzed, based on IBMQ quantum cloud platform, the quantum circuit of Grover algorithm with multi-objective items is simulated. Based on the characteristics of Grover algorithm and the simulation process of quantum gate, the action of multiple identical quantum gates is combined to reduce the update times of probability amplitude and improve the simulation efficiency. The libquantum quantum simulator is used for experiments and the target item is successfully searched, which proves the feasibility of the optimization method and provides reference for the simulation and optimization of other quantum algorithms.