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A Second-Order Semi-Implicit Method for the Inertial Landau-lifshitz-Gilbert Equation

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Numerical Mathematics(Theory,Methods and Applications) 2023年第1期16卷 182-203页

作者： panchi li Lei Yang Jin Lan Rui Du Jingrun Chen School of Mathematical Sciences Soochow UniversitySuzhou 215006China School of Computer Science and Engineering Macao University of Science and TechnologyMacao SARChina Center for Joint Quantum Studies and Department of Physics School of ScienceTianjin University92 Weijin RoadTianjin 300072China Mathematical Center for Interdisciplinary Research Soochow UniversitySuzhou 215006China Suzhou Institute for Advanced Research University of Science and Technology of ChinaSuzhouJiangsu 215123China School of Mathematical Sciences University of Science and Technology of ChinaHefeiAnhui 230026China

Electron spins in magnetic materials have preferred orientations collectively and generate the macroscopic *** dynamics spans over a wide range of timescales from femtosecond to picosecond,and then to *** Landau-lifshitz-Gilbert(LLG)equation has been widely used in micromagnetics simulations over *** theoretical and experimental advances have shown that the inertia of magnetization emerges at sub-picosecond timescales and contributes significantly to the ultrafast magnetization dynamics,which cannot be captured intrinsically by the LLG ***,as a generalization,the inertial LLG(iLLG)equation is proposed to model the ultrafast magnetization ***,the LLG equation is a nonlinear system of parabolic type with(possible)***,the iLLG equation is a nonlinear system of mixed hyperbolic-parabolic type with degeneracy,and exhibits more complicated *** behaves as a hyperbolic system at sub-picosecond timescales,while behaves as a parabolic system at larger timescales spanning from picosecond to *** hybrid behaviors impose additional difficulties on designing efficient numerical methods for the iLLG *** this work,we propose a second-order semiimplicit scheme to solve the iLLG *** second-order temporal derivative of magnetization is approximated by the standard centered difference scheme,and the first-order temporal derivative is approximated by the midpoint scheme involving three time *** nonlinear terms are treated semi-implicitly using one-sided interpolation with second-order *** each time step,the unconditionally unique solvability of the unsymmetric linear system is proved with detailed discussions on the condition ***,the second-order accuracy of the proposed method in both time and space is *** sub-picosecond timescales,the inertial effect of ferromagnetics is observed in micromagnetics simulations,in consistency wi

关键词： Inertial Landau-lifshitz-Gilbert equation semi-implicit scheme second-order accuracy micromagnetics simulations

Learning algorithm and application of quantum BP neural networks based on universal quantum gates

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Journal of Systems Engineering and Electronics 2008年第1期19卷 167-174页

作者： li panchi li Shiyong Dept. of Control Science and Engineering Harbin Inst. of Technology Harbin 150001 P. R. China Dept. of Computer Science and Engineering Daqing Petroleum Inst. Daqing 163318 P. R. China

A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which （1） is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects： convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.

关键词： quantum computing universal quantum gate quantum neuron quantum neural networks

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Grover quantum searching algorithm based on weighted targets

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Journal of Systems Engineering and Electronics 2008年第2期19卷 363-369页

The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.

关键词： Grover algorithm targets weighting quantum searching quantum computing.

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Model and Algorithm of Sequence-Based Quantum-Inspired Neural Networks

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Chinese Journal of Electronics 2018年第1期27卷 9-18页

作者： li panchi ZHAO Ya School of Computer and Information Technology Northeast Petroleum University

To enhance the approximation ability of traditional Artificial neural network(ANN), by introducing the quantum rotation gates and the multi-qubits controlled-NOT gates to ANN, we proposed a Sequence input-based quantum-inspired neural network(SIQNN).In our model, the hidden nodes are composed of some multi-qubits controlled-NOT gates, the inputs are described by the multi-dimensional discrete qubits sequences,the output nodes are the traditional neurons. The model parameters include the rotation angles of quantum rotation gates in hide layer and the weights in output *** learning algorithms were derived by employing the Levenberg-Marquardt algorithm. Simulation results of predicting the runoff of the Hongjiadu Reservoir show that,the SIQNN is obviously superior to the ANN.

关键词： Quantum computation Quantum rotation gate Multi-qubits controlled-NOT gate Quantum inspired neuron Quantum-inspired neural network

Design and Implementation of Color Image Encryption Based on Qubit Rotation About Axis

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Chinese Journal of Electronics 2018年第4期27卷 799-807页

作者： liU Xiande XIAO Hong li panchi ZHAO Ya School of Computer and Information Technology Northeast Petroleum University

Currently, almost all color image encryption/decryption algorithms are designed based on a classical computer, in which the key space is relatively small,and the huge gains from quantum parallelism are not obtained. To address this problem, we propose a novel color image encryption/decryption method based on random rotation of qubit and Quantum Fourier transform(QFT).First, the color image is represented in a quantum superposition state |Image>, in which the color information of each pixel is described by only one qubit |c>. Then, the |c> are randomly rotated on the Bloch sphere about three coordinate axis, and the QFT is performed on the |Image>.Once again, the |c> is randomly rotated on the Bloch sphere and then the inverse QFT is performed on the |Image>,which the encryption process is implemented. The keys are the rotation angles of two above-mentioned *** decryption is the inverse process of the *** method may run on a quantum computer in the future. The simulation results on the classic computer show that our approaches have better security.

关键词： Color image representing Color image encrypting Qubit rotating Quantum Fourier transform Quantum image processing

Behavior of quantum search algorithm with small phase rotations

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High Technology Letters 2011年第1期17卷 91-96页

作者：李欣 Cheng Chuntian li panchi Xu Shaohua School of Electronics and Information Engineering Dalian University of Technology Dalian 116024 P.R. China Institute of Hydropower System and Hydroinformatics I）alian University of Technology Dalian 116024 P.R. China School of Computer ＆ Information Technology Northeast Petroleum University Daqing 163318 P.R. China

When the Grover's original algorithm is applied to search an unordered database, the success probability decreases rapidly with the increase of marked items. Aiming at this problem, a general quantum search algorithm with small phase rotations is proposed. Several quantum search algorithms can be derived from this algorithm according to different phase rotations. When the size of phase rotations are fixed at 0.01π, the success probability of at least 99.99% can be obtained in O(√N/M) iterations. Copyright © by High Technology Letters Press.

关键词：量子搜索算法相位旋转量子行为数据库

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灵活的固定相位量子搜索算法

北京工业大学学报 2023年第6期49卷 630-638页

作者：肖红刘新彤李盼池东北石油大学计算机与信息技术学院黑龙江大庆163318

为解决Grover算法的普适性不够理想的问题,提出一种灵活的量子搜索算法.首先,通过设计包含任意数目基态的量子均衡叠加态,实现任意大小无序数据库的构建;其次,通过求解算法的迭代方程,导出旋转相位与成功概率及搜索步数之间的定量关系,... 详细信息

为解决Grover算法的普适性不够理想的问题,提出一种灵活的量子搜索算法.首先,通过设计包含任意数目基态的量子均衡叠加态,实现任意大小无序数据库的构建;其次,通过求解算法的迭代方程,导出旋转相位与成功概率及搜索步数之间的定量关系,其中旋转相位可取(0,π]内的任意值;再次,通过迭代步数与成功概率的统计分析,确定当标记态数未知时旋转相位的最佳取值,并设计搜索方案;最后,考察不同旋转相位及不同标记态数下,成功概率及迭代步数的数值结果.理论分析表明该算法可以实现经典算法的二次加速.

关键词：量子计算量子算法量子搜索相位匹配量子叠加态量子线路设计

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A Fixed-Phase Quantum Search Algorithm with More Flexible Behavior

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Journal of Quantum Information Science 2012年第2期2卷 28-34页

作者： Xin li panchi li School of Computer & Information Technology Northeast Petroleum University Daqing China

When the Grover’s algorithm is applied to search an unordered database, the probability of success usually decreases with the increase of marked items. To address this phenomenon, a fixed-phase quantum search algorithm with more flexible behavior is proposed. In proposed algorithm, the phase shifts can be fixed at the different values to meet the needs of different practical problems. If research requires a relatively rapid speed, the value of the phase shifts should be appropriately increased, if search requires a higher success probability, the value of the phase shifts should be appropriately decreased. When the phase shifts are fixed at , the success probability of at least 99.38% can be obtained in iterations.

关键词： Quantum Computing Quantum Searching Grover Algorithm Fixed Phase Shifting

Quantum Inspired Differential Evolution Algorithm

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Open Journal of Optimization 2015年第2期4卷 31-39页

作者： Binxu li panchi li School of Computer and Information Technology Northeast Petroleum University Daqing China

To enhance the optimization performance of differential evolution algorithm, by studying the implementation mechanism of differential evolution algorithm, a new idea of incorporating differential strategy and rotation of qubits in the Bloch sphere is proposed in this paper. In the proposed approach, the individuals are encoded by qubits described on Bloch sphere, and the rotation angles of qubits in current individual are obtained by differential strategy. The axis of rotation is designed by using vector product theory, and the rotation matrixes are constructed by using Pauli matrixes. Taking the corresponding qubits in current best individual as targets, the qubits in current individual are rotated to the target qubits about the rotation axis on the Bloch sphere. The Hadamard gates are used to mutate individuals. The simulation results of optimizing the minimum value of functions indicate that, for an iterative step, the average time of the proposed approach is 13 times as long as that of the classical differential evolution algorithm. When the same limited steps are applied in two approaches, the average optimization result of the proposed approach is 0.3 times as great as that of the classical differential evolution algorithm;when the same running time is applied in two approaches, the average optimization result of the proposed approach is 0.4 times as great as that of the classical differential evolution algorithm. These results suggest that the proposed approach is inefficient in computational ability;however, it is obviously efficient in optimization ability, and the overall optimization performance is better than that of the classical differential evolution algorithm.

关键词： Quantum Computation Qubits Encoding Bloch Spherical Search Quantum Differential Evolution