量子图像乘法运算及其仿真实现

    Quantum Image Multiplication and Its Simulation

    • 摘要: 为了解决图像处理领域中经典图像乘法运算复杂度较高的问题,提出了一种量子图像乘法运算的实现方式. 首先对基于NEQR表示模型的图像制备方式进行改进,采用按行制备的方式以降低时间复杂度;然后根据二进制数的乘法步骤,使用Toffoli门和量子全加器结合移位操作设计量子乘法器;之后将制备好的量子图像使用量子乘法器进行相乘,最终实现量子图像的乘法运算. 使用经典计算机与IBM平台提供的可编程量子模拟器进行量子图像乘法运算的仿真,所得的概率直方图表明该算法实现了图像的相乘. 对比实验表明,该文研究的量子图像乘法运算与经典图像乘法运算相比在时间复杂度上有指数级提升.

       

      Abstract: To solve the problem of high complexity of classical image multiplication in the field of image processing, a quantum image multiplication algorithm was proposed in this paper. First, the method of image preparation based on NEQR representation model was improved, and the method of line preparation was adopted to reduce the time complexity. Then, according to the multiplication steps of binary numbers, a quantum multiplier was designed by using Toffoli gate and quantum total adder combined with shift operation. After that, the prepared quantum image was multiplied by quantum multiplier, and the multiplication operation of quantum image was finally achieved. The quantum image multiplication operation was simulated by using the classical computer and the programmable quantum simulator provided by IBM platform. The probability histogram obtained shows that the algorithm achieves image multiplication. Comparative experiments show that the quantum image multiplication operation has an exponential increase in time complexity compared with the classical image multiplication operation.

       

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