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Computer Engineering and Applications Journal

Improved quantum multi-object search algorithm

Wei-Yun Ma

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Grover’s quantum mechanical search algorithm solves the unsorted database search with quadratic speed-up over the classical algorithms.But Grover’s algorithm will be inefficient when the number of matching is close to 2n/2.This paper presents a quantum algorithm which can get a target item with certainty by a single query when the number of the target items is more than a quarter.

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This article reviews recent progress in quantum database search algorithms. The subject is presented in a self-contained and pedagogical way. The problem of searching a large database (a Hilbert space) for a target item is performed by the famous Grover algorithm which locates the target item with high probability and a quadratic speed-up compared with the corresponding classical algorithm. If the database is partitioned into blocks and one is searching for the block containing the target item instead of the target item itself, then the problem is referred to as partial search. Partial search trades accuracy for speed and the most efficient version is the Grover–Radhakrishnan–Korepin (GRK) algorithm. The target block can be further partitioned into sub-blocks so that GRK's can be performed in a sequence called a hierarchy. We study the Grover search and GRK partial search in detail and prove that a GRK hierarchy is less efficient than a direct GRK partial search. Both the Grover search and the GRK partial search can be generalized to the case with several target items (or target blocks for a GRK). The GRK partial search algorithm can also be represented in terms of group theory.

International Journal of Modern Physics B•Dec 20, 2009•7 citations
Grover’s quantum mechanical search algorithm solves the unsorted database search with quadratic speed-up over the classical algorithms.But Grover’s algorithm will be inefficient when the number of matching is close to 2n/2.This paper presents a quantum algorithm which can get a target item with certainty by a single query when the number of the target items is more than a quarter.
Grover search algorithm is applied to the current number of objectives in quantum unsorted database, the meaning of each goal difference is not taken into account. When the target is more than a quarter of the total items, the probability of the target falls quickly identify and target increases, and when the target is more than half of the total items, the algorithm will fail. To solve these problems, first of all, based on a weighted index improvement is proposed in which each target in accordance with the right given to the importance of the weight coefficient. These different weight coefficients, we give all the target state, which may make the probability of each target equal weights of the quantum superposition. Secondly, an improved phase matching is proposed the phase rotation in both directions is the same, and the inner product of two states by the target amplitude superposition and initial state of the system is determined. When this inner product is 1/2 or more, when using the improved phase matching, the target may be 100% probability and by only one Grover iteration. Finally, the effectiveness of these measures by a simple search instance validation.
The algorithm proposed by Grover solves the unsorted database search problem with computation complexity of O(2～(1/2)n/m),where the size of database is N=2n and there is m target solutions.However,the successful probability of searching decreases rapidly,when the target solutions m is greater than N/4,And the algorithm is disabled when m is equal to N/2.This paper presents an improved Grover's algorithm,which can find the object with the successful probability at least 98.01% with one step when m is greater than N/4.
The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked states. In this paper, we study the relation between the success rate and the number of iterations in a quantum search algorithm of given λ=M/N, where M is the number of marked state and N is the number of items in the dataset. We develop a robust quantum search algorithm based on Grover–Long algorithm with some uncertainty in the number of marked states. The proposed algorithm has the same query complexity ON as the Grover’s algorithm, and shows high tolerance of the uncertainty in the ratio M/N. In particular, for a database with an uncertainty in the ratio M±MN, our algorithm will find the target states with a success rate no less than 96%.
Abstract Consider the unstructured search of an unknown number I of items in a large unsorted database of size N. The multi-object quantum search algorithm consists of two parts. The first part of the algorithm is to generalize Grover's single-object search algorithm to the multi-object case, and the second part is to solve a counting problem to determine l. In this paper we study the multi-object quantum search algorithm (in continuous time), but in a more structured way by taking into account the availability of partial information. The modeling of available partial information is done simply by the combination of several pre­scribed, possibly overlapping, information sets with varying weights to signify the reliability of each set. The associated statistics is estimated and the algorithm efficiency and complexity are analyzed. Our analysis shows that the search described here may not be more efficient than the unstructured (generalized) multi-object Grover search if there is "misplaced confidence". However, if the information sets have a "basic confidence" property in the sense that each information set contains at least one search item, then a quadratic speedup holds on a much smaller data space, which further expedites the quantum search for the first item.
A quantum Grover search algorithm can find a target item in a database faster than any classical algorithm. One can trade accuracy for speed and find a part of the database (a block) containing the target item even faster; this is partial search. A partial search algorithm was recently suggested by Grover and Radhakrishnan. Here we optimize it. Efficiency of the search algorithm is measured by the number of queries to the oracle. The author suggests a new version of the Grover–Radhakrishnan algorithm which uses a minimal number of such queries. The algorithm can run on the same hardware that is used for the usual Grover algorithm.
This article reviews recent progress in quantum database search algorithms. The subject is presented in a self-contained and pedagogical way. The problem of searching a large database (a Hilbert space) for a target item is performed by the famous Grover algorithm which locates the target item with high probability and a quadratic speed-up compared with the corresponding classical algorithm. If the database is partitioned into blocks and one is searching for the block containing the target item instead of the target item itself, then the problem is referred to as partial search. Partial search trades accuracy for speed and the most efficient version is the Grover–Radhakrishnan–Korepin (GRK) algorithm. The target block can be further partitioned into sub-blocks so that GRK's can be performed in a sequence called a hierarchy. We study the Grover search and GRK partial search in detail and prove that a GRK hierarchy is less efficient than a direct GRK partial search. Both the Grover search and the GRK partial search can be generalized to the case with several target items (or target blocks for a GRK). The GRK partial search algorithm can also be represented in terms of group theory.