Quantum Implementation of Powell’s Conjugate Direction Method
Kehan Chen*, Fei Yan*, Kaoru Hirota**, and Jianping Zhao*
*School of Computer Science and Technology, Changchun University of Science and Technology
No.7089, Weixing Road, Changchun, Jilin 130022, China
**Beijing Institute of Technology
5 South Zhongguancun Street, Haidian District, Beijing 100081, China
A quantum circuit implementation of Powell’s conjugate direction method (“Powell’s method”) is proposed based on quantum basic transformations in this study. Powell’s method intends to find the minimum of a function, including a sequence of parameters, by changing one parameter at a time. The quantum circuits that implement Powell’s method are logically built by combining quantum computing units and basic quantum gates. The main contributions of this study are the quantum realization of a quadratic equation, the proposal of a quantum one-dimensional search algorithm, the quantum implementation of updating the searching direction array (SDA), and the quantum judgment of stopping the Powell’s iteration. A simulation demonstrates the execution of Powell’s method, and future applications, such as data fitting and image registration, are discussed.
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