The Study of the NMR Algorithms

• Main Authors: Chih-Cheng Hsueh, 薛智誠
• Other Authors: Chien-Yuan Chen
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/66777940319560423462

博士 === 義守大學 === 資訊工程學系博士班 === 94 === In this dissertation, we first review two Nuclear Magnetic Resonance (NMR) algorithms, the ensemble search algorithm and the ensemble counting algorithm. The ensemble search algorithm, proposed by Brüschweiler, requires O(logN) oracle queries for searching a signal object in N=2^n unsorted elements. In Gorver''s quantum search algorithm, O(N^(1/2)) is required. Thus, Brüschweiler''s ensemble search algorithm is faster than Grover''s quantum search algorithm. The ensemble counting algorithm, proposed by Kunihiro and Yamashita, outputs the number of assignments satisfying the value of the oracle query function. Based on these two ensemble algorithms, we propose four ensemble algorithms: ensemble factorization algorithm, ensemble search algorithm, ensemble sorting algorithm, and ensemble selection algorithm. Our ensemble factorization algorithm employs Brüschweiler''s ensemble search algorithm to factor the RSA modulus N=pq. It only requires O(logN^(1/2)) oracle queries to discover one factor of N. In our ensemble search algorithm, we use n ancillary qubits to improve Brüschweiler''s algorithm such that O(1) oracle query is required. Furthermore, we modify the ensemble counting algorithm to propose an ensemble sorting algorithm. Our ensemble sorting algorithm requires O(N) oracle queries, while the classical sorting algorithm requires O(NlogN) oracle queries. Lastly, we propose an ensemble selection algorithm based on the ensemble counting algorithm. Our algorithm requires O(log|D|) oracle queries for adequate measure accuracy to find the k-th smallest element, where |D| denotes the size of D.