Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the al...Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.展开更多
It is widely believed that Shor＇s factoring algorithm provides a driving force to boost the quantum computing research.However, a serious obstacle to its binary implementation is the large number of quantum gates. No...It is widely believed that Shor＇s factoring algorithm provides a driving force to boost the quantum computing research.However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor＇s algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory（OCT） is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor＇s algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919.展开更多
The computational accuracy and efficiency of modeling the stress spectrum derived from bridge monitoring data significantly influence the fatigue life assessment of steel bridges.Therefore,determining the optimal stre...The computational accuracy and efficiency of modeling the stress spectrum derived from bridge monitoring data significantly influence the fatigue life assessment of steel bridges.Therefore,determining the optimal stress spectrum model is crucial for further fatigue reliability analysis.This study investigates the performance of the REBMIX algorithm in modeling both univariate(stress range)and multivariate(stress range and mean stress)distributions of the rain-flowmatrix for a steel arch bridge,usingAkaike’s Information Criterion(AIC)as a performance metric.Four types of finitemixture distributions—Normal,Lognormal,Weibull,and Gamma—are employed tomodel the stress range.Additionally,mixed distributions,including Normal-Normal,Lognormal-Normal,Weibull-Normal,and Gamma-Normal,are utilized to model the joint distribution of stress range and mean stress.The REBMIX algorithm estimates the number of components,component weights,and component parameters for each candidate finite mixture distribution.The results demonstrate that the REBMIX algorithm-based mixture parameter estimation approach effectively identifies the optimal distribution based on AIC values.Furthermore,the algorithm exhibits superior computational efficiency compared to traditional methods,making it highly suitable for practical applications.展开更多
This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to del...This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to delve into and refine the application of the Dijkstra’s algorithm in this context,a method conventionally esteemed for its efficiency in static networks.Thus,this paper has carried out a comparative theoretical analysis with the Bellman-Ford algorithm,considering adaptation to the dynamic network conditions that are typical for MANETs.This paper has shown through detailed algorithmic analysis that Dijkstra’s algorithm,when adapted for dynamic updates,yields a very workable solution to the problem of real-time routing in MANETs.The results indicate that with these changes,Dijkstra’s algorithm performs much better computationally and 30%better in routing optimization than Bellman-Ford when working with configurations of sparse networks.The theoretical framework adapted,with the adaptation of the Dijkstra’s algorithm for dynamically changing network topologies,is novel in this work and quite different from any traditional application.The adaptation should offer more efficient routing and less computational overhead,most apt in the limited resource environment of MANETs.Thus,from these findings,one may derive a conclusion that the proposed version of Dijkstra’s algorithm is the best and most feasible choice of the routing protocol for MANETs given all pertinent key performance and resource consumption indicators and further that the proposed method offers a marked improvement over traditional methods.This paper,therefore,operationalizes the theoretical model into practical scenarios and also further research with empirical simulations to understand more about its operational effectiveness.展开更多
The objective of this paper concerns at first the motivation and the method of Shor’s algorithm including remarks on quantum computing introducing an algorithmic description of the method.The corner stone of the Shor...The objective of this paper concerns at first the motivation and the method of Shor’s algorithm including remarks on quantum computing introducing an algorithmic description of the method.The corner stone of the Shor’s algorithm is the modular exponentiation that is themost computational component(in time and space).A linear depth unit based on phase estimation is introduced and a description of a generic version of a modular multiplier based on phases is introduced to build block of a gates to efficient modular exponentiation circuit.Our proposal includes numerical experiments achieved on both the IBM simulator using the Qiskit library and on quantum physical optimizers provided by IBM.The shor’s algorithm based on phase estimation succeeds in factoring integer numbers with more than 35 digits using circuits with about 100 qubits.展开更多
Smooth constraint is important in linear inversion, but it is difficult to apply directly to model parameters in genetic algorithms. If the model parameters are smoothed in iteration, the diversity of models will be g...Smooth constraint is important in linear inversion, but it is difficult to apply directly to model parameters in genetic algorithms. If the model parameters are smoothed in iteration, the diversity of models will be greatly suppressed and all the models in population will tend to equal in a few iterations, so the optimal solution meeting requirement can not be obtained. In this paper, an indirect smooth constraint technique is introduced to genetic inversion. In this method, the new models produced in iteration are smoothed, then used as theoretical models in calculation of misfit function, but in process of iteration only the original models are used in order to keep the diversity of models. The technique is effective in inversion of surface wave and receiver function. Using this technique, we invert the phase velocity of Raleigh wave in the Tibetan Plateau, revealing the horizontal variation of S wave velocity structure near the center of the Tibetan Plateau. The results show that the S wave velocity in the north is relatively lower than that in the south. For most paths there is a lower velocity zone with 12-25 km thick at the depth of 15-40 km. The lower velocity zone in upper mantle is located below the depth of 100 km, and the thickness is usually 40-80 km, but for a few paths reach to 100 km thick. Among the area of Ando, Maqi and Ushu stations, there is an obvious lower velocity zone with the lowest velocity of 4.2-4.3 km/s at the depth of 90-230 km. Based on the S wave velocity structures of different paths and former data, we infer that the subduction of the Indian Plate is delimited nearby the Yarlung Zangbo suture zone.展开更多
Many classical encoding algorithms of vector quantization （VQ） of image compression that can obtain global optimal solution have computational complexity O（N）. A pure quantum VQ encoding algorithm with probability...Many classical encoding algorithms of vector quantization （VQ） of image compression that can obtain global optimal solution have computational complexity O（N）. A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45√N times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than √N for most images, and it is more efficient than the pure quantum algorithm.展开更多
Computational fluid dynamics（CFD） can give a lot of potentially very useful information for hydraulic optimization design of pumps, however, it cannot directly state what kind of modification should be made to impro...Computational fluid dynamics（CFD） can give a lot of potentially very useful information for hydraulic optimization design of pumps, however, it cannot directly state what kind of modification should be made to improve such hydrodynamic performance. In this paper, a more convenient and effective approach is proposed by combined using of CFD, multi-objective genetic algorithm（MOGA） and artificial neural networks（ANN） for a double-channel pump＇s impeller, with maximum head and efficiency set as optimization objectives, four key geometrical parameters including inlet diameter, outlet diameter, exit width and midline wrap angle chosen as optimization parameters. Firstly, a multi-fidelity fitness assignment system in which fitness of impellers serving as training and comparison samples for ANN is evaluated by CFD, meanwhile fitness of impellers generated by MOGA is evaluated by ANN, is established and dramatically reduces the computational expense. Then, a modified MOGA optimization process, in which selection is performed independently in two sub-populations according to two optimization objectives, crossover and mutation is performed afterword in the merged population, is developed to ensure the global optimal solution to be found. Finally, Pareto optimal frontier is found after 500 steps of iterations, and two optimal design schemes are chosen according to the design requirements. The preliminary and optimal design schemes are compared, and the comparing results show that hydraulic performances of both pumps 1 and 2 are improved, with the head and efficiency of pump 1 increased by 5.7% and 5.2%, respectively in the design working conditions, meanwhile shaft power decreased in all working conditions, the head and efficiency of pump 2 increased by 11.7% and 5.9%, respectively while shaft power increased by 5.5%. Inner flow field analyses also show that the backflow phenomenon significantly diminishes at the entrance of the optimal impellers 1 and 2, both the area of vortex and intensity of vortex decreases in the whole flow channel. This paper provides a promising tool to solve the hydraulic optimization problem of pumps＇ impellers.展开更多
The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development,including specification generation,program refinement,and formal verification.However,the existi...The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development,including specification generation,program refinement,and formal verification.However,the existing model has two flaws:incompleteness of program refinement and inadequate automation of formal verification.This paper proposes an automatic algorithm programming model based on the improved Morgan’s refinement calculus.It extends the Morgan’s refinement calculus rules and designs the C++generation system for realizing the complete process of refinement.Meanwhile,the automation tools VCG(Verification Condition Generator)and Isabelle are used to improve the automation of formal verification.An example of a stock’s maximum income demonstrates the effectiveness of the proposed model.Furthermore,the proposed model has some relevance for automatic software generation.展开更多
The method of determining the structures and parameters of radial basis function neural networks(RBFNNs) using improved genetic algorithms is proposed. Akaike′s information criterion (AIC) with generalization error t...The method of determining the structures and parameters of radial basis function neural networks(RBFNNs) using improved genetic algorithms is proposed. Akaike′s information criterion (AIC) with generalization error term is used as the best criterion of optimizing the structures and parameters of networks. It is shown from the simulation results that the method not only improves the approximation and generalization capability of RBFNNs ,but also obtain the optimal or suboptimal structures of networks.展开更多
In this study,a novel hybrid Water Cycle Moth-Flame Optimization(WCMFO)algorithm is proposed for multilevel thresholding brain image segmentation in Magnetic Resonance(MR)image slices.WCMFO constitutes a hybrid betwee...In this study,a novel hybrid Water Cycle Moth-Flame Optimization(WCMFO)algorithm is proposed for multilevel thresholding brain image segmentation in Magnetic Resonance(MR)image slices.WCMFO constitutes a hybrid between the two techniques,comprising the water cycle and moth-flame optimization algorithms.The optimal thresholds are obtained by maximizing the between class variance(Otsu’s function)of the image.To test the performance of threshold searching process,the proposed algorithm has been evaluated on standard benchmark of ten axial T2-weighted brain MR images for image segmentation.The experimental outcomes infer that it produces better optimal threshold values at a greater and quicker convergence rate.In contrast to other state-of-the-art methods,namely Adaptive Wind Driven Optimization(AWDO),Adaptive Bacterial Foraging(ABF)and Particle Swarm Optimization(PSO),the proposed algorithm has been found to be better at producing the best objective function,Peak Signal-to-Noise Ratio(PSNR),Standard Deviation(STD)and lower computational time values.Further,it was observed thatthe segmented image gives greater detail when the threshold level increases.Moreover,the statistical test result confirms that the best and mean values are almost zero and the average difference between best and mean value 1.86 is obtained through the 30 executions of the proposed algorithm.Thus,these images will lead to better segments of gray,white and cerebrospinal fluid that enable better clinical choices and diagnoses using a proposed algorithm.展开更多
The discrete Fourier transform （DFT） is the base of modern signal processing. 1-dimensional fast Fourier transform （1D FFT） and 2D FFT have time complexity O（N log N） and O（N^2 log N） respectively. Since 1965,...The discrete Fourier transform （DFT） is the base of modern signal processing. 1-dimensional fast Fourier transform （1D FFT） and 2D FFT have time complexity O（N log N） and O（N^2 log N） respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover＇s iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT （1D QDFT） and two-dimensional quantum DFT （2D QDFT） are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, 1D and 2D QDFT have time complexity O（v/N） and O（N） respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.展开更多
文摘Shor proposed a polynomial time algorithm for computing the order of one element in a multiplicative group using a quantum computer. Based on Miller’s randomization, he then gave a factorization algorithm. But the algorithm has two shortcomings, the order must be even and the output might be a trivial factor. Actually, these drawbacks can be overcome if the number is an RSA modulus. Applying the special structure of the RSA modulus, an algorithm is presented to overcome the two shortcomings. The new algorithm improves Shor’s algorithm for factoring RSA modulus. The cost of the factorization algorithm almost depends on the calculation of the order of 2 in the multiplication group.
基金supported by the National Natural Science Foundation of China(Grant No.61205108)the High Performance Computing(HPC)Foundation of National University of Defense Technology,China
文摘It is widely believed that Shor＇s factoring algorithm provides a driving force to boost the quantum computing research.However, a serious obstacle to its binary implementation is the large number of quantum gates. Non-binary quantum computing is an efficient way to reduce the required number of elemental gates. Here, we propose optimization schemes for Shor＇s algorithm implementation and take a ternary version for factorizing 21 as an example. The optimized factorization is achieved by a two-qutrit quantum circuit, which consists of only two single qutrit gates and one ternary controlled-NOT gate. This two-qutrit quantum circuit is then encoded into the nine lower vibrational states of an ion trapped in a weakly anharmonic potential. Optimal control theory（OCT） is employed to derive the manipulation electric field for transferring the encoded states. The ternary Shor＇s algorithm can be implemented in one single step. Numerical simulation results show that the accuracy of the state transformations is about 0.9919.
基金jointly supported by the Fundamental Research Funds for the Central Universities(Grant No.xzy012023075)the Zhejiang Engineering Research Center of Intelligent Urban Infrastructure(Grant No.IUI2023-YB-12).
文摘The computational accuracy and efficiency of modeling the stress spectrum derived from bridge monitoring data significantly influence the fatigue life assessment of steel bridges.Therefore,determining the optimal stress spectrum model is crucial for further fatigue reliability analysis.This study investigates the performance of the REBMIX algorithm in modeling both univariate(stress range)and multivariate(stress range and mean stress)distributions of the rain-flowmatrix for a steel arch bridge,usingAkaike’s Information Criterion(AIC)as a performance metric.Four types of finitemixture distributions—Normal,Lognormal,Weibull,and Gamma—are employed tomodel the stress range.Additionally,mixed distributions,including Normal-Normal,Lognormal-Normal,Weibull-Normal,and Gamma-Normal,are utilized to model the joint distribution of stress range and mean stress.The REBMIX algorithm estimates the number of components,component weights,and component parameters for each candidate finite mixture distribution.The results demonstrate that the REBMIX algorithm-based mixture parameter estimation approach effectively identifies the optimal distribution based on AIC values.Furthermore,the algorithm exhibits superior computational efficiency compared to traditional methods,making it highly suitable for practical applications.
基金supported by Northern Border University,Arar,Kingdom of Saudi Arabia,through the Project Number“NBU-FFR-2024-2248-03”.
文摘This study is trying to address the critical need for efficient routing in Mobile Ad Hoc Networks(MANETs)from dynamic topologies that pose great challenges because of the mobility of nodes.Themain objective was to delve into and refine the application of the Dijkstra’s algorithm in this context,a method conventionally esteemed for its efficiency in static networks.Thus,this paper has carried out a comparative theoretical analysis with the Bellman-Ford algorithm,considering adaptation to the dynamic network conditions that are typical for MANETs.This paper has shown through detailed algorithmic analysis that Dijkstra’s algorithm,when adapted for dynamic updates,yields a very workable solution to the problem of real-time routing in MANETs.The results indicate that with these changes,Dijkstra’s algorithm performs much better computationally and 30%better in routing optimization than Bellman-Ford when working with configurations of sparse networks.The theoretical framework adapted,with the adaptation of the Dijkstra’s algorithm for dynamically changing network topologies,is novel in this work and quite different from any traditional application.The adaptation should offer more efficient routing and less computational overhead,most apt in the limited resource environment of MANETs.Thus,from these findings,one may derive a conclusion that the proposed version of Dijkstra’s algorithm is the best and most feasible choice of the routing protocol for MANETs given all pertinent key performance and resource consumption indicators and further that the proposed method offers a marked improvement over traditional methods.This paper,therefore,operationalizes the theoretical model into practical scenarios and also further research with empirical simulations to understand more about its operational effectiveness.
文摘The objective of this paper concerns at first the motivation and the method of Shor’s algorithm including remarks on quantum computing introducing an algorithmic description of the method.The corner stone of the Shor’s algorithm is the modular exponentiation that is themost computational component(in time and space).A linear depth unit based on phase estimation is introduced and a description of a generic version of a modular multiplier based on phases is introduced to build block of a gates to efficient modular exponentiation circuit.Our proposal includes numerical experiments achieved on both the IBM simulator using the Qiskit library and on quantum physical optimizers provided by IBM.The shor’s algorithm based on phase estimation succeeds in factoring integer numbers with more than 35 digits using circuits with about 100 qubits.
基金State Natural Science Foundation (49874021).Contribution No. 01FE2002, Institute of Geophysics, China Seismological Bureau.
文摘Smooth constraint is important in linear inversion, but it is difficult to apply directly to model parameters in genetic algorithms. If the model parameters are smoothed in iteration, the diversity of models will be greatly suppressed and all the models in population will tend to equal in a few iterations, so the optimal solution meeting requirement can not be obtained. In this paper, an indirect smooth constraint technique is introduced to genetic inversion. In this method, the new models produced in iteration are smoothed, then used as theoretical models in calculation of misfit function, but in process of iteration only the original models are used in order to keep the diversity of models. The technique is effective in inversion of surface wave and receiver function. Using this technique, we invert the phase velocity of Raleigh wave in the Tibetan Plateau, revealing the horizontal variation of S wave velocity structure near the center of the Tibetan Plateau. The results show that the S wave velocity in the north is relatively lower than that in the south. For most paths there is a lower velocity zone with 12-25 km thick at the depth of 15-40 km. The lower velocity zone in upper mantle is located below the depth of 100 km, and the thickness is usually 40-80 km, but for a few paths reach to 100 km thick. Among the area of Ando, Maqi and Ushu stations, there is an obvious lower velocity zone with the lowest velocity of 4.2-4.3 km/s at the depth of 90-230 km. Based on the S wave velocity structures of different paths and former data, we infer that the subduction of the Indian Plate is delimited nearby the Yarlung Zangbo suture zone.
文摘Many classical encoding algorithms of vector quantization （VQ） of image compression that can obtain global optimal solution have computational complexity O（N）. A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45√N times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than √N for most images, and it is more efficient than the pure quantum algorithm.
基金Supported by National Natural Science Foundation of China(Grant No.51109094)Priority Academic Program Development of Jiangsu Higher Education Institutions of China
文摘Computational fluid dynamics（CFD） can give a lot of potentially very useful information for hydraulic optimization design of pumps, however, it cannot directly state what kind of modification should be made to improve such hydrodynamic performance. In this paper, a more convenient and effective approach is proposed by combined using of CFD, multi-objective genetic algorithm（MOGA） and artificial neural networks（ANN） for a double-channel pump＇s impeller, with maximum head and efficiency set as optimization objectives, four key geometrical parameters including inlet diameter, outlet diameter, exit width and midline wrap angle chosen as optimization parameters. Firstly, a multi-fidelity fitness assignment system in which fitness of impellers serving as training and comparison samples for ANN is evaluated by CFD, meanwhile fitness of impellers generated by MOGA is evaluated by ANN, is established and dramatically reduces the computational expense. Then, a modified MOGA optimization process, in which selection is performed independently in two sub-populations according to two optimization objectives, crossover and mutation is performed afterword in the merged population, is developed to ensure the global optimal solution to be found. Finally, Pareto optimal frontier is found after 500 steps of iterations, and two optimal design schemes are chosen according to the design requirements. The preliminary and optimal design schemes are compared, and the comparing results show that hydraulic performances of both pumps 1 and 2 are improved, with the head and efficiency of pump 1 increased by 5.7% and 5.2%, respectively in the design working conditions, meanwhile shaft power decreased in all working conditions, the head and efficiency of pump 2 increased by 11.7% and 5.9%, respectively while shaft power increased by 5.5%. Inner flow field analyses also show that the backflow phenomenon significantly diminishes at the entrance of the optimal impellers 1 and 2, both the area of vortex and intensity of vortex decreases in the whole flow channel. This paper provides a promising tool to solve the hydraulic optimization problem of pumps＇ impellers.
基金Supported by the National Natural Science Foundation of China(61862033,61902162)Key Project of Science and Technology Research of Department of Education of Jiangxi Province(GJJ210307)Postgraduate Innovation Fund Project of Education Department of Jiangxi Province(YC2021-S306)。
文摘The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development,including specification generation,program refinement,and formal verification.However,the existing model has two flaws:incompleteness of program refinement and inadequate automation of formal verification.This paper proposes an automatic algorithm programming model based on the improved Morgan’s refinement calculus.It extends the Morgan’s refinement calculus rules and designs the C++generation system for realizing the complete process of refinement.Meanwhile,the automation tools VCG(Verification Condition Generator)and Isabelle are used to improve the automation of formal verification.An example of a stock’s maximum income demonstrates the effectiveness of the proposed model.Furthermore,the proposed model has some relevance for automatic software generation.
文摘The method of determining the structures and parameters of radial basis function neural networks(RBFNNs) using improved genetic algorithms is proposed. Akaike′s information criterion (AIC) with generalization error term is used as the best criterion of optimizing the structures and parameters of networks. It is shown from the simulation results that the method not only improves the approximation and generalization capability of RBFNNs ,but also obtain the optimal or suboptimal structures of networks.
文摘In this study,a novel hybrid Water Cycle Moth-Flame Optimization(WCMFO)algorithm is proposed for multilevel thresholding brain image segmentation in Magnetic Resonance(MR)image slices.WCMFO constitutes a hybrid between the two techniques,comprising the water cycle and moth-flame optimization algorithms.The optimal thresholds are obtained by maximizing the between class variance(Otsu’s function)of the image.To test the performance of threshold searching process,the proposed algorithm has been evaluated on standard benchmark of ten axial T2-weighted brain MR images for image segmentation.The experimental outcomes infer that it produces better optimal threshold values at a greater and quicker convergence rate.In contrast to other state-of-the-art methods,namely Adaptive Wind Driven Optimization(AWDO),Adaptive Bacterial Foraging(ABF)and Particle Swarm Optimization(PSO),the proposed algorithm has been found to be better at producing the best objective function,Peak Signal-to-Noise Ratio(PSNR),Standard Deviation(STD)and lower computational time values.Further,it was observed thatthe segmented image gives greater detail when the threshold level increases.Moreover,the statistical test result confirms that the best and mean values are almost zero and the average difference between best and mean value 1.86 is obtained through the 30 executions of the proposed algorithm.Thus,these images will lead to better segments of gray,white and cerebrospinal fluid that enable better clinical choices and diagnoses using a proposed algorithm.
基金supported by Sichuan Normal University,China (Grant No 06lk002)
文摘The discrete Fourier transform （DFT） is the base of modern signal processing. 1-dimensional fast Fourier transform （1D FFT） and 2D FFT have time complexity O（N log N） and O（N^2 log N） respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover＇s iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT （1D QDFT） and two-dimensional quantum DFT （2D QDFT） are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, 1D and 2D QDFT have time complexity O（v/N） and O（N） respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.
