Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalizat...Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.展开更多
As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on grayscale images,...As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on grayscale images, with relatively little processing for color images. This paper proposes a quantum color image scaling scheme based on bilinear interpolation, which realizes the 2^(n_(1)) × 2^(n_(2)) quantum color image scaling. Firstly, the improved novel quantum representation of color digital images(INCQI) is employed to represent a 2^(n_(1)) × 2^(n_(2)) quantum color image, and the bilinear interpolation method for calculating pixel values of the interpolated image is presented. Then the quantum color image scaling-up and scaling-down circuits are designed by utilizing a series of quantum modules, and the complexity of the circuits is analyzed.Finally, the experimental simulation results of MATLAB based on the classical computer are given. The ultimate results demonstrate that the complexities of the scaling-up and scaling-down schemes are quadratic and linear, respectively, which are much lower than the cubic function and exponential function of other bilinear interpolation schemes.展开更多
We redesign the parameterized quantum circuit in the quantum deep neural network, construct a three-layer structure as the hidden layer, and then use classical optimization algorithms to train the parameterized quantu...We redesign the parameterized quantum circuit in the quantum deep neural network, construct a three-layer structure as the hidden layer, and then use classical optimization algorithms to train the parameterized quantum circuit, thereby propose a novel hybrid quantum deep neural network(HQDNN) used for image classification. After bilinear interpolation reduces the original image to a suitable size, an improved novel enhanced quantum representation(INEQR) is used to encode it into quantum states as the input of the HQDNN. Multi-layer parameterized quantum circuits are used as the main structure to implement feature extraction and classification. The output results of parameterized quantum circuits are converted into classical data through quantum measurements and then optimized on a classical computer. To verify the performance of the HQDNN, we conduct binary classification and three classification experiments on the MNIST(Modified National Institute of Standards and Technology) data set. In the first binary classification, the accuracy of 0 and 4 exceeds98%. Then we compare the performance of three classification with other algorithms, the results on two datasets show that the classification accuracy is higher than that of quantum deep neural network and general quantum convolutional neural network.展开更多
We show that the quantum-mechanical fundamental representations,say,the coordinate representation,the coherent state representation,the Fan-Klauder entangled state representation can be recast into s-ordering operator...We show that the quantum-mechanical fundamental representations,say,the coordinate representation,the coherent state representation,the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion,which is elegant in form and has many applications in deriving new operator identities.This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.展开更多
We consider the quantum measurements on a finite quantum system in coherence-vector representation. In this representation, all the density operators of an N-level(N≥2) quantum system constitute a convex set M^(N)emb...We consider the quantum measurements on a finite quantum system in coherence-vector representation. In this representation, all the density operators of an N-level(N≥2) quantum system constitute a convex set M^(N)embedded in an(N^2- 1)-dimensional Euclidean space R^((N^2)-1), and we find that an orthogonal measurement is an(N- 1)-dimensional projector operator on R^((N^2)-1). The states unchanged by an orthogonal measurement form an(N- 1)-dimensional simplex, and in the case when N is prime or power of prime, the space of the density operator is a direct sum of(N + 1) such simplices. The mathematical description of quantum measurement is plain in this representation, and this may have further applications in quantum information processing.展开更多
Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual con...Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual conjugates:coordinate representation and momentum representation.This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics,a field that has been developing rapidly.These two new convolution methods have potential value in signal processing.展开更多
基金National Natural Science Foundation of China under Grant No.10775097
文摘Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.
基金the National Natural Science Foundation of China (Grant No. 6217070290)Shanghai Science and Technology Project (Grant Nos. 21JC1402800 and 20040501500)。
文摘As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on grayscale images, with relatively little processing for color images. This paper proposes a quantum color image scaling scheme based on bilinear interpolation, which realizes the 2^(n_(1)) × 2^(n_(2)) quantum color image scaling. Firstly, the improved novel quantum representation of color digital images(INCQI) is employed to represent a 2^(n_(1)) × 2^(n_(2)) quantum color image, and the bilinear interpolation method for calculating pixel values of the interpolated image is presented. Then the quantum color image scaling-up and scaling-down circuits are designed by utilizing a series of quantum modules, and the complexity of the circuits is analyzed.Finally, the experimental simulation results of MATLAB based on the classical computer are given. The ultimate results demonstrate that the complexities of the scaling-up and scaling-down schemes are quadratic and linear, respectively, which are much lower than the cubic function and exponential function of other bilinear interpolation schemes.
基金Project supported by the Natural Science Foundation of Shandong Province,China (Grant No. ZR2021MF049)the Joint Fund of Natural Science Foundation of Shandong Province (Grant Nos. ZR2022LLZ012 and ZR2021LLZ001)。
文摘We redesign the parameterized quantum circuit in the quantum deep neural network, construct a three-layer structure as the hidden layer, and then use classical optimization algorithms to train the parameterized quantum circuit, thereby propose a novel hybrid quantum deep neural network(HQDNN) used for image classification. After bilinear interpolation reduces the original image to a suitable size, an improved novel enhanced quantum representation(INEQR) is used to encode it into quantum states as the input of the HQDNN. Multi-layer parameterized quantum circuits are used as the main structure to implement feature extraction and classification. The output results of parameterized quantum circuits are converted into classical data through quantum measurements and then optimized on a classical computer. To verify the performance of the HQDNN, we conduct binary classification and three classification experiments on the MNIST(Modified National Institute of Standards and Technology) data set. In the first binary classification, the accuracy of 0 and 4 exceeds98%. Then we compare the performance of three classification with other algorithms, the results on two datasets show that the classification accuracy is higher than that of quantum deep neural network and general quantum convolutional neural network.
基金supported by the National Natural Science Foundation of China(Grant Nos.10775097 and 10874174)the Special Funds of the National Natural Science Foundation of China(Grant No.10947017/A05)+1 种基金the Higher School Fund of Outstanding Young Talent(Grant No.2010SQRL132)the Scientific Research Starting Foundation of Chizhou University(Grant No.2010RC036)
文摘We show that the quantum-mechanical fundamental representations,say,the coordinate representation,the coherent state representation,the Fan-Klauder entangled state representation can be recast into s-ordering operator expansion,which is elegant in form and has many applications in deriving new operator identities.This demonstrates that Dirac's symbolic method can be merged into Newton-Leibniz integration theory in a broad way.
基金supported by the National Natural Science Foundation of China(Grant Nos.11405136 and 11547311)the Fundamental Research Funds for the Central Universities of China(Grant No.2682014BR056)
文摘We consider the quantum measurements on a finite quantum system in coherence-vector representation. In this representation, all the density operators of an N-level(N≥2) quantum system constitute a convex set M^(N)embedded in an(N^2- 1)-dimensional Euclidean space R^((N^2)-1), and we find that an orthogonal measurement is an(N- 1)-dimensional projector operator on R^((N^2)-1). The states unchanged by an orthogonal measurement form an(N- 1)-dimensional simplex, and in the case when N is prime or power of prime, the space of the density operator is a direct sum of(N + 1) such simplices. The mathematical description of quantum measurement is plain in this representation, and this may have further applications in quantum information processing.
基金National Natural Science Foundation of China(Grant Number:11304126)College Students' Innovation Training Program(Grant Number:202110299696X)。
文摘Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual conjugates:coordinate representation and momentum representation.This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics,a field that has been developing rapidly.These two new convolution methods have potential value in signal processing.
