A Fast Quantum Search Algorithm and its Application

• Main Authors: Chien-hsing Yeh, 葉建興
• Other Authors: none
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/93712296814320678370

碩士 === 國立臺灣科技大學 === 電子工程系 === 95 === Quantum computation and quantum information science, which combine the exploration of quantum mechanics and new physical principals, have been a promise for solving complicated problems that are not tractable by conventional computers. In this thesis, we consider quantum search algorithms to search the minimum in an unordered database of N items. Traditionally, the running time required to locate the minimum is O(N) steps. To alleviate the computational load, various quantum search algorithm of complexity O(N^{1/2}) have been addressed. This thesis presents two fast Grove-based quantum search algorithms to more efficiently find the minimum. The first one uses the quantum counting to estimate the number of marked states to determine the number of iterations required, whereas the second one, to reduce the complexity called for, adaptively adjusts the number of iterations based on whether we can find a lower minimum or not in the present iteration. Comparison with other related quantum search algorithm is also thoroughly made. To justify the validity of the new algorithm, we apply it to antenna selection and block-based motion estimation problems. As shown by provided simulations, the new algorithm offers lower computational complexity compared with previous works in various scenarios.