Choi and Korepin [Quantum Information Processing 6(2007)243] presented a quantum partial search algorithm of a database with several target items which can find a target block quickly when each target block contains the same number of target items. Actually, the number of target items in each target block is arbitrary. Aiming at this case, we give a condition to guarantee performance of the partial search algorithm to be performed and the number of queries to oracle of the algorithm to be minimized. In addition, by further numerical computing we come to the conclusion that the more uniform the distribution of target items, the smaller the number of queries.
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle function, which abstracts the process of matching a search item (returning 1 for a match and 0 otherwise), where searching for 1 target item in a search space of size N scales as O(N) oracle queries. In this article, we explore the idea of associating a separate oracle with each bit of the matching condition, obtaining multiple partial oracle functions which can be tested independently. Exploring this idea leads to a multi-stage hybrid search algorithm, whose performance can fall within a wide range, anywhere between O(N) (same as Grover) or O(log(N)). The algorithm is validated against the simplest kind of search scenario, where the incoming index bits are scrambled using a permutation operation.
By quantum Grover search algorithm,people can find a target item in a database faster than any classical algorithm.In this search algorithm the initial state is the equally weighted superposition of all basis states,which is operated by the unitary operator repeatedly.Consequently,non-target states transfer their amplitude to the target state,so we can find the target item with larger probability.However,sometimes we just want to know partial information,so we only need to find the subdatabase(a block) containing the target item,which is partial search.A partial search algorithm was suggested by Grover and Radhakrishnan,which is denoted as Grover-Radhakrishnan Algorithm of Partial Search(GRK),in which they considered the database contains one target item.In our paper,we study the database which contains several target items,and they are randomly distributed in two target blocks.Our algorithm is based on GRK.We minimize the number of queries to the oracle for blocks of large size,and compare this case with the one that each target block contains the same number of target items.