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Quantum algorithm and experimental demonstration for the subset sum problem

Science China(Information Sciences) 2022年第8期65卷 261-274页

作者： Qilin ZHENG Pingyu ZHU Shichuan XUE Yang WANG Chao WU Xinyao YU Miaomiao YU Yingwen LIU Mingtang DENG Junjie WU Ping XU Institute for Quantum Information and State Key Laboratory of High Performance Computing College of Computer Science and TechnologyNational University of Defense Technology

To solve the subset sum problem, a well-known nondeterministic polynomial-time complete problem that is widely used in encryption and resource scheduling, we propose a feasible quantum algorithm that utilizes fewer qubits to encode and achieves quadratic speedup. Specifically, this algorithm combines an amplitude amplification algorithm with quantum phase estimation, and requires n + t + 1 qubits and O(2(0.5+o(1))n) operations to obtain the solution, where n is the number of elements, and t is the number of qubits used to store the eigenvalues. To verify the performance of the algorithm, we simulate the algorithm with the online quantum simulator of IBM named ibmq simulator using Qiskit and then run it on two IBM quantum computers called ibmq santiago and ibmq bogota. The experimental results indicate that compared with the brute force algorithm, the proposed algorithm results in quadratic acceleration for the problem of a set S with four elements and two subsets whose sum equals target w. Using the iterator twice, we obtain success probabilities of 0.940 ± 0.004, 0.751 ± 0.040, and 0.665 ± 0.060 on the simulator, ibmq santiago, and ibmq bogota, respectively, and the fidelity between the theoretical and experimental quantum states is calculated to be 0.944 ± 0.002, 0.753 ± 0.017, and 0.657 ± 0.028, respectively. If the error rates of the experimental quantum logic gates can be reduced, the success probabilities of the proposed algorithm on real quantum devices can be further improved.

关键词： quantum algorithm subset sum quadratic speedup encryption algorithm complexity

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Improved algorithm for line detection

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Jisuanji Gongcheng/Computer Engineering 2006年第16期32卷 172-173+187页

作者： Wang, Jianyong Zhou, Xiaoguang Liao, Qizheng School of Automation Beijing University of Posts and Telecommunications Beijing 100876 China

An improved algorithm of line detection is proposed to aim at the drawbacks of Hough transform. It reduces algorithm complexity based on the principle of 'many-to-one'. The idea 'from partial to global' is also adopted. The parameters of line are gotten in sub-areas in order to reduce quantization error. Then it searches other points of the line within whole image according to the parameters. algorithm complexity is also analyzed. Experiments show that the algorithm has better properties of computing efficiency and robustness.

关键词： algorithm complexity Hough transform Line detection Quantization error

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AN EFFICIENT SEPARABILITY CRITERION FOR n-PARTITE ARBITRARILY DIMENSIONAL QUANTUM STATES

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INTERNATIONAL JOURNAL OF QUANTUM INFORMATION 2011年第4期9卷 1101-1112页

作者： Long, Yinxiang Qiu, Daowen Long, Dongyang Guangdong Tech Coll Water Resources & Elect Engn Dept Comp Informat Engn Guangzhou 510635 Guangdong Peoples R China Sun Yat Sen Univ Dept Comp Sci Guangzhou 510006 Guangdong Peoples R China

In this paper, we obtain an efficient separability criterion for bipartite quantum pure state systems, which is based on the two-order minors of the coefficient matrix corresponding to quantum state. Then, we generalize this criterion to multipartite arbitrarily dimensional pure states. Our criterion is directly built upon coefficient matrices, but not density matrices or observables, so it has the advantage of being computed easily. Indeed, to judge separability for an arbitrary n-partite pure state in a d-dimensional Hilbert space, it only needs at most O(d) times operations of multiplication and comparison. Our criterion can be extended to mixed states. Compared with Yu's criteria, our methods are faster, and can be applied to any quantum state.

关键词： Quantum entanglement separability criterion algorithm complexity

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Note on single machine common flow allowance group scheduling with learning effect and resource allocation

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年 186卷

作者： Qian, Jin Northeastern Univ Dept Math Coll Sci Shenyang Peoples R China

Recent papers (Sun et al., 2020;Lv et al., 2021), they studied single machine due date assignment scheduling problems with learning effect and resource allocation. In this note, we show that the published results of Sun et al. (2020) and Lv et al. (2021) are incorrect by two counter-examples. Then the corrected results are provided, and we also explain why they are incorrect.

关键词： Scheduling Due date assignment Learning effect Resource allocation algorithm complexity

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Hierarchical Manta Ray Foraging Optimization with Weighted Fitness-Distance Balance Selection

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2023年第1期16卷 114-114页

作者： Tang, Zhentao Wang, Kaiyu Tao, Sichen Todo, Yuki Wang, Rong-Long Gao, Shangce Jiangsu Agrianim Husb Vocat Coll Taizhou 225300 Peoples R China Univ Toyama Fac Engn Toyama 9308555 Japan Kanazawa Univ Fac Elect Informat & Commun Engn Kanazawa 9201192 Japan Univ Fukui Fac Engn Fukui 9108507 Japan

Manta ray foraging optimization (MRFO) tends to get trapped in local optima as it relies on the direction provided by the previous individual and the best individual as guidance to search for the optimal solution. As enriching population diversity can effectively solve this problem, in this paper, we introduce a hierarchical structure and weighted fitness-distance balance selection to improve the population diversity of the algorithm. The hierarchical structure allows individuals in different groups of the population to search for optimal solutions in different places, expanding the diversity of solutions. In MRFO, greedy selection based solely on fitness can lead to local solutions. We innovatively incorporate a distance metric into the selection strategy to increase selection diversity and find better solutions. A hierarchical manta ray foraging optimization with weighted fitness-distance balance selection (HMRFO) is proposed. Experimental results on IEEE Congress on Evolutionary Computation 2017 (CEC2017) functions show the effectiveness of the proposed method compared to seven competitive algorithms, and the proposed method has little effect on the algorithm complexity of MRFO. The application of HMRFO to optimize real-world problems with large dimensions has also obtained good results, and the computational time is very short, making it a powerful alternative for very high-dimensional problems. Finally, the effectiveness of this method is further verified by analyzing the population diversity of HMRFO.

关键词： Manta ray foraging optimization Local optima Population diversity Hierarchical structure Greedy selection Weighted fitness-distance balance selection algorithm complexity

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An efficient algorithm for line clipping by convex and non-convex polyhedra in E(3)

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COMPUTER GRAPHICS FORUM 1996年第1期15卷 61-68页

作者： Skala, V Department of Informatics and Computer Science University of West Bohemia Americká 42 Box 314 306 14 Plzen Czech Republic Email: skala@kiv.zcu.cz

A new algorithm for clipping lines against convex polyhedron with O(N) complexity is given with modification for non-convex polyhedron. The suggested algorithm is faster for higher number of facets of the given polyhedron than the traditional Cyrus-Beck's algorithm. Some principal results of comparison of all algorithms are shown and give some ideas how the proposed algorithm could be used effectively.

关键词： line clipping convex polyhedron non-convex polyhedron computer graphics algorithm complexity geometric algorithms algorithms analysis

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LOGIC SYNTHESIS AND OPTIMIZATION algorithm OF MULTIPLE-VALUED LOGIC FUNCTIONS

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 1994年第10期E77D卷 1106-1117页

作者： HAIDAR, AM MORISUE, M Saitama Univ Urawa-shi Japan

This paper presents a novel and successful logic synthesis method for optimizing ternary logic functions of any given number of input variables. A new optimization algorithm to synthesize and minimize an arbitrary ternary logic function of n-input variables can always lead this function to optimal or very close to optimal solution, where [n(n + 1)/2]-1 searches are necessary to achieve the optimal solution. Therefore, the complexity number of this algorithm has been greatly reduced from O(3n) into O(n2). The advantages of this synthesis and optimization algorithm are: (1) Very easy logic synthesis method. (2) algorithm complexity is O(n2). (3) Optimal solution can be obtained in very short time. (4) The method can solve the interconnection problems (interconnection delay) of VLSI and ULSI processors, where very fast and parallel operations can be achieved. A transformation method between operational and polynomial domains of ternary logic functions of n-input variables is also discussed. This transformation method is very effective and simple. Design of the circuits of GF(3) operators, addition and multiplication mod-3, have been proposed, where these circuits are composed of Josephson junction devices. The simulation results of these circuits and examples show the following advantages: very good performances, very low power consumption, and ultra high speed switching operation.

关键词： MULTIPLE-VALUED LOGIC OPTIMIZATION REED-MULLER ALGEBRA algorithm complexity JOSEPHSON JUNCTION DEVICES

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algorithm for visualizing substation areas in electric power systems

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EXPERT SYSTEMS WITH APPLICATIONS 2023年 212卷

作者： Kovacev, Nemanja Gavric, Milan Lendak, Imre Univ Novi Sad Fac Tech Sci Trg Dositeja Obradov 6 Novi Sad 21000 Vojvodina Serbia Eotvos Lorand Univ Data Sci & Engn Dept Fac Informat Pazmany Peter Setany 1-A H-1117 Budapest Hungary

Electric power distribution systems can be represented with mathematical graphs in which the hub nodes are substations receiving electric power from the transmission system and delivering it to the consumers via feeders consisting of transformers, junctions, cables and power lines. High-quality diagrams depicting these systems are key elements of efficient monitoring and control. Existing automatic diagram generation solutions are usually limited to drawing single feeders or contain significant simplifications of the underlying distribution system e.g., visualize multiple feeders with their interconnections removed. The goal of this research was to develop an algorithm capable of generating visually-pleasing diagrams of substation areas consisting of a single hub node and a complex network of thousands of interconnected elements. The resulting algorithm was defined as a sequence of transformations which takes a mathematical graph as input and generates a one-line diagram as output. Multiple novel approaches are incorporated to optimize the algorithm thereby allowing it to run efficiently on regular desktop computers. Also, a novel diagram quality evaluation procedure was developed to automatically measure and compare the usability of each generated diagram. The algorithm was tested on 2510 different substation areas of various complexity extracted from the network models of real-life, European distribution systems. The quality of the generated diagrams was measured with the novel evaluation procedure and verified with a human domain experts on a subset of the resulting diagrams. Based on these analyses, it was concluded that the generated diagrams are usable in newly built supervisory and control systems with minimum human intervention.

关键词： One-line diagram Graph visualization Electric power system Substation area algorithm complexity Diagram evaluation procedure

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The Tensor Production of Block Matrix and its Parallel Computing

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JOURNAL OF algorithmS & COMPUTATIONAL TECHNOLOGY 2009年第4期3卷 503-515页

作者： Tan Guolue Shangrao Normal Coll Dept Math & Comp Shangrao 334001 Jiangxi Peoples R China

First, the result was proved that two matrices tensor product can be exchanged in the sense of permutation similar and this explants that the tensor product of block matrixes can be block calculated in the sense of permutation similar. Second, the convenient constructing method for the permutation matrix is given. Third, the parallel computing models of matrix tensor product are proposed. Final, the thought and process of the algorithm are showed by an example.

关键词： Block Matrix Tensor Product Permutation Similar Parallel Computing algorithm complexity

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SIMULTANEOUS PARALLEL REDUCTION ON SIMD MACHINES

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Parallel Processing Letters 1995年第3期5卷 437-449页

作者： BOLESLAW K. SZYMANSKI WILLIAM MANIATTY BALARAM SINHAROY Department of Computer Science Rensselaer Polytechnic Institute Troy NY 12180-3590 USA IBM Systems Technology and Architecture Division Poughkeepsie NY 12602 USA

Proper distribution of operations among parallel processors in a large scientific computation executed on a distributed-memory machine can significantly reduce the total computation time. In this paper, we propose an operation called simultaneous parallel reduction(SPR), that is amenable to such optimization. SPR performs reduction operations in parallel, each operation reducing a one-dimensional consecutive section of a distributed array. Each element of the distributed array is used as an operand to many reductions executed concurrently over the overlapping array's sections. SPR is distinct from a more commonly considered parallel reduction which concurrently evaluates a single reduction. In this paper we consider SPR on Single Instruction Multiple Data (SIMD) machines with different interconnection networks. We focus on SPR over sections whose size is not a power of 2 with the result shifted relative to the arguments. Several algorithms achieving some of the lower bounds on SPR complexity are presented under various assumptions about the properties of the binary operator of the reduction and of the communication cost of the target architectures.

关键词： Parallel reduction simultaneous evaluation data parallelism algorithm complexity scalability

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