A Fixed-Phase Quantum Search Algorithm with More Flexible Behavior

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.

Quantum-Inspired Neural Network with Sequence Input

To enhance the approximation and generalization ability of artificial neural network (ANN) by employing the principles of quantum rotation gate and controlled-not gate, a quantum-inspired neuron with sequence input is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-not gate after being rotated by the quantum rotation gates, control the target qubit for reverse. The model output is described by the probability amplitude of state in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the sequence input-based quantum-inspired neurons to the hidden layer and the classical neurons to the output layer, and a learning algorithm is derived by employing the Levenberg-Marquardt algorithm. Simulation results of benchmark problem show that, under a certain condition, the QNNSI is obviously superior to the ANN.

Adaptive Phase Matching in Grover’s Algorithm

When the Grover’s algorithm is applied to search an unordered database, the successful probability usually decreases with the increase of marked items. In order to solve this problem, an adaptive phase matching is proposed. With application of the new phase matching, when the fraction of marked items is greater , the successful probability is equal to 1 with at most two Grover iterations. The validity of the new phase matching is verified by a search example.

Quantum-Inspired Bee Colony Algorithm

To enhance the performance of the artificial bee colony optimization by integrating the quantum computing model into bee colony optimization, we present a quantum-inspired bee colony optimization algorithm. In our method, the bees are encoded with the qubits described on the Bloch sphere. The classical bee colony algorithm is used to compute the rotation axes and rotation angles. The Pauli matrices are used to construct the rotation matrices. The evolutionary search is achieved by rotating the qubit about the rotation axis to the target qubit on the Bloch sphere. By measuring with the Pauli matrices, the Bloch coordinates of qubit can be obtained, and the optimization solutions can be presented through the solution space transformation. The proposed method can simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method is obviously superior to the classical one for some benchmark functions.

Quantum Inspired Differential Evolution Algorithm

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.

Clustering Algorithm of Quantum Self-Organization Network

To enhance the clustering ability of self-organization network, this paper introduces a quantum inspired self-organization clustering algorithm. First, the clustering samples and the weight values in the competitive layer are mapped to the qubits on the Bloch sphere, and then, the winning node is obtained by computing the spherical distance between sample and weight value. Finally, the weight values of the winning nodes and its neighborhood are updated by rotating them to the sample on the Bloch sphere until the convergence. The clustering results of IRIS sample show that the proposed approach is obviously superior to the classical self-organization network and the K-mean clustering algorithm.

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

Electron spins in magnetic materials have preferred orientations collectively and generate the macroscopic magnetization.Its dynamics spans over a wide range of timescales from femtosecond to picosecond,and then to nanosecond.The Landau-Lifshitz-Gilbert(LLG)equation has been widely used in micromagnetics simulations over decades.Recent 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 equation.Therefore,as a generalization,the inertial LLG(iLLG)equation is proposed to model the ultrafast magnetization dynamics.Mathematically,the LLG equation is a nonlinear system of parabolic type with(possible)degeneracy.However,the iLLG equation is a nonlinear system of mixed hyperbolic-parabolic type with degeneracy,and exhibits more complicated structures.It behaves as a hyperbolic system at sub-picosecond timescales,while behaves as a parabolic system at larger timescales spanning from picosecond to nanosecond.Such hybrid behaviors impose additional difficulties on designing efficient numerical methods for the iLLG equation.In this work,we propose a second-order semiimplicit scheme to solve the iLLG equation.The 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 steps.The nonlinear terms are treated semi-implicitly using one-sided interpolation with second-order accuracy.At each time step,the unconditionally unique solvability of the unsymmetric linear system is proved with detailed discussions on the condition number.Numerically,the second-order accuracy of the proposed method in both time and space is verified.At sub-picosecond timescales,the inertial effect of ferromagnetics is observed in micromagnetics simulations,in consistency with the hyperbolic property of the iLLG model;at nanosecond timescales,the results of the iLLG model are in nice agreements with those of the LLG model,in consistency with the parabolic feature of the iLLG model.