Two fundamental problems exist in the use of quantum computation to process an image or signal. The first one is how to represent giant data, such as image data, using quantum state without losing information. The second one is how to load a colossal volume of data into the quantum registers of a quantum CPU from classical electronic memory. Researches on these two questions are rarely reported. Here an entangled state is used to represent an image (or vector) for which two entangled registers are used to store a vector component and its classical address. Using the representation, n
 1 + n
 2 + 8 qubits are used to store the whole information of the gray image that has a $2^{n_1 } \times 2^{n_2 } $
 size at a superposition of states, a feat is not possible with a classic computer. The way of designing a unitary operation to load data, such as a vector (or image), into the quantum registers of a quantum CPU from electronic memory is defined herein as a quantum loading scheme (QLS). In this paper, the QLS with time complexity O(log2
 N) is presented where N denotes the number of vector components, a solution that would break through the efficiency bottleneck of loading data. QLS would enable a quantum CPU to be compatible with electronic memory and make possible quantum image compression and quantum signal processing that has classical input and output.

A theoretical framework for quantum image representation and data loading scheme

Quantum image recognition is a technology by using quantum algorithm to process the image information. It can obtain better effect than classical algorithm. In this paper, four different quantum algorithms are used in the three stages of palmprint recognition. First, quantum adaptive median filtering algorithm is presented in palmprint filtering processing. Quantum filtering algorithm can get a better filtering result than classical algorithm through the comparison. Next, quantum Fourier transform (QFT) is used to extract pattern features by only one operation due to quantum parallelism. The proposed algorithm exhibits an exponential speed-up compared with discrete Fourier transform in the feature extraction. Finally, quantum set operations and Grover algorithm are used in palmprint matching. According to the experimental results, quantum algorithm only needs to apply square of N operations to find out the target palmprint, but the traditional method needs N times of calculation. At the same time, the matching accuracy of quantum algorithm is almost 100%.

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Research on Palmprint Identification Method Based on Quantum Algorithms

Traditional iris recognition method has low speed and searching rate in large-scale unstructured database. Three different quantum algorithms are proposed in iris recognition. Quantum filtering algorithm can get a better filtering result than classical algorithm in iris filtering process. Quantum Fourier transforms exhibits an exponential speed-up compared with discrete Fourier transform in feature extraction. Improved Grover algorithm can reduce the matching time in the step of iris matching. The experiment results show that matching numbers and matching time reduce greatly.

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Research on Iris Recognition Method Based on Quantum Algorithms

When introduce the wavelet theory to filter the hologram and the reconstructed image in the digital holography, the noise of the reconstructed image is greatly reduced In the off-axis digital holography, the zero-order wave is decreased dramatically when after a wavelet filter, at the same time, the speckle noise is also reduced, and it turns out that the resolution of the reconstruction image is improved greatly The system launches the research thoroughly on the three-dimensional body digital holographic technology, from the theory to the application, from the simulation to the experiment, and has elaborated and analyzed each characteristic of three-dimensional body digital holographic technology It proposes many kinds of improved effective method of three-dimensional body digital holographic restructuring information, and finally has effectively explored the three-dimensional body digital holographic technology application through the experiment

The Analysis and Research on Digital Holography Signal Based on Wavelet Theory

The rapid development of big data puts forward higher requirements on computational efficiency and storage capacity. But the traditional mining algorithms based on classical computing were unable to satisfy the demand of data analysis and computing. Because of quantum systems unique ability of hyper parallel computation and hyper acceleration, the large-scale computing and data storage can be solve well. Although the development of quantum computer has not yet achieved a qualitative leap, quantum computing in big data application has achieved lots of theoretical achievements. In this paper, we make quantum data mining as a starting point. Since we have no sufficient space to store candidate sets of association rules and have low computation ability in the processing of association rules, we propose a novel quantum method of data storage and retrieval for association rules mining based on Boolean matrix, we propose the algorithm called Q-Eclat can accelerate the computation of candidate sets support. According to our analysis based on open data source, the proposed method outperforms the classical Eclat algorithm in terms of storage capacity and computing ability

Association Rules Mining with Quantum Computing and Quantum Storage

The discrete Fourier transform (DFT) is the base of modern signal processing 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N2 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 (ID 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, ID and 2D QDFT have time complexity O(√N) and O (N) respectively QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible

Hu Ben-Qiong

Papers

A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing