Integer multiple quantum image scaling based on NEQR and bicubic interpolation

As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.

Quantum color image scaling based on bilinear interpolation

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.

Novel quantum secret image-sharing scheme

In this paper, we propose a novel quantum secret image-sharing scheme which constructs m quantum secret images into m+1 quantum share images. A chaotic image generated by the logistic map is utilized to assist in the construction of quantum share images first. The chaotic image and secret images are expressed as quantum image representation by using the novel enhanced quantum representation. To enhance the confidentiality, quantum secret images are scrambled into disordered images through the Arnold transform. Then the quantum share images are constructed by performing a series of quantum swap operations and quantum controlled-NOT operations. Because all quantum operations are invertible, the original quantum secret images can be reconstructed by performing a series of inverse operations. Theoretical analysis and numerical simulation proved both the security and low computational complexity of the scheme, which has outperformed its classical counterparts. It also provides quantum circuits for sharing and recovery processes.

Quantum watermarking based on threshold segmentation using quantum informational entropy

We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image.The core idea of this scheme is to embed information into object and background of cover image in different ways.First,a threshold method adopting the quantum informational entropy is employed to determine a threshold value.The threshold value can then be further used for segmenting the cover image to a binary image,which is an authentication key for embedding and extraction information.By a careful analysis of the quantum circuits of the scheme,that is,translating into the basic gate sequences which show the low complexity of the scheme.One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image.Furthermore,the analyses of peak signal-to-noise ratio,histogram and capacity of the scheme are also provided.

Towards an efficient variational quantum algorithm for solving linear equations

Variational quantum algorithms are promising methods with the greatest potential to achieve quantum advantage,widely employed in the era of noisy intermediate-scale quantum computing.This study presents an advanced variational hybrid algorithm(EVQLSE)that leverages both quantum and classical computing paradigms to address the solution of linear equation systems.Initially,an innovative loss function is proposed,drawing inspiration from the similarity measure between two quantum states.This function exhibits a substantial improvement in computational complexity when benchmarked against the variational quantum linear solver.Subsequently,a specialized parameterized quantum circuit structure is presented for small-scale linear systems,which exhibits powerful expressive capabilities.Through rigorous numerical analysis,the expressiveness of this circuit structure is quantitatively assessed using a variational quantum regression algorithm,and it obtained the best score compared to the others.Moreover,the expansion in system size is accompanied by an increase in the number of parameters,placing considerable strain on the training process for the algorithm.To address this challenge,an optimization strategy known as quantum parameter sharing is introduced,which proficiently minimizes parameter volume while adhering to exacting precision standards.Finally,EVQLSE is successfully implemented on a quantum computing platform provided by IBM for the resolution of large-scale problems characterized by a dimensionality of 220.

A quantum search algorithm of two-dimensional convex hull

Despite the rapid development of quantum research in recent years,there is very little research in computational geometry.In this paper,to achieve the convex hull of a point set in a quantum system,a quantum convex hull algorithm based on the quantum maximum or minimum searching algorithm(QUSSMA)is proposed.Firstly,the novel enhanced quantum representation of digital images is employed to represent a group of point set,and then the QUSSMA algorithm and vector operation are used to search the convex hull of the point set.In addition,the algorithm is simulated and compared with the classical algorithm.It is concluded that the quantum algorithm accelerates the classical algorithm when the Mpvalue of the convex hull point is under a certain condition.