Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Information

VERIFIER-BASED ALGORITHM FOR UNSORTED DATABASE SEARCH PROBLEM

Xiao Wu, GUI LU LONG

Published Aug 1, 2007• 7 citations
Publisher

Abstract

Unsorted database search problem is an important science and engineering problem. We proposed quantum algorithm to solve the problem by dividing the database binarily and then use a probabilistic verifier algorithm to determine if the item is within one part of the divided database. We analyzed the computational complexity of this algorithm, and found that in general, the number of steps is proportional to that in the standard Grover algorithm. However in some cases, it is less than that of the Grover algorithm.

DOI
10.1142/s0219749907003067

Related papers

An efficient quantum search engine on unsorted database

Heping Hu, Yingyu Zhang, Zhengding Lu

We consider the problem of finding one or more desired items out of an unsorted database. Patel has shown that if the database permits quantum queries, then mere digitization is sufficient for efficient search for one desired item. The algorithm, called factorized quantum search algorithm, presented by him can locate the desired item in an unsorted database using $O(log_{4}N)$ queries to factorized oracles. But the algorithm requires that all the property values must be distinct from each other. In this paper, we discuss how to make a database satisfy the requirements, and present a quantum search engine based on the algorithm. Our goal is achieved by introducing auxiliary files for the property values that are not distinct, and converting every complex query request into a sequence of calls to factorized quantum search algorithm. The query complexity of our algorithm is $O(P*Q*M*log_{4}N)$, where P is the number of the potential simple query requests in the complex query request, Q is the maximum number of calls to the factorized quantum search algorithm of the simple queries, M is the number of the auxiliary files for the property on which our algorithm are searching for desired items. This implies that to manage an unsorted database on an actual quantum computer is possible and efficient.

arXiv:0904.3060•Apr 20, 2009•0 citations

An Improved Quantum Grover Algorithm

Baoyu Zheng

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.

Journal of Nanjing University of Posts and Telecommunications•Jan 1, 2011•0 citations

Improved quantum multi-object search algorithm

Wei-Yun Ma

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.

Computer Engineering and Applications Journal•Jan 1, 2009•0 citations

Data Search Algorithms based on Quantum Walk

Masataka Fujisaki, Hiromi Miyajima, Noritaka Shigei

For searching any item in an unsorted database with N items, a classical computer takes O(N) steps but Grover’s quantum searching algorithm takes only O( √ N) steps. However, it is also known that Grover’s algorithm is effective only in the case where the initial amplitude distribution of dataset is uniform, but is not always effective in the nonuniform case. In this paper, we propose some quantum search algorithms. First, we propose an algorithm in analog time based on quantum walk by solving the schrodinger equation. The proposed algorithm shows best performance in optimum time. Next, we will apply the result to Grover search algorithm. It is shown that the proposed algorithm shows better performance than the conventional one. Further, we propose the improved algorithm by introducing the idea of the phase rotation. The algorithm shows best performance compared with the conventional ones.

Lecture notes in computer science•Jan 1, 2012•2 citations

Two improvements in Grover's algorithm

Kai Kang

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.

Chinese Control and Decision Conference (CCDC)•May 1, 2015•5 citations

Quantum Query Complexity for Searching Multiple Marked States from an Unsorted Database

Shang Bin

An important and usual sort of search problems is to find all marked states from an unsorted database with a large number of states. Grover's original quantum search algorithm is for finding single marked state with uncertainty, and it has been generalized to the case of multiple marked states, as well as been modified to find single marked state with certainty. However, the query complexity for finding all multiple marked states has not been addressed. We use a generalized Long's algorithm with high precision to solve such a problem. We calculate the approximate query complexity, which increases with the number of marked states and with the precision that we demand. In the end we introduce an algorithm for the problem on a ``duality computer'' and show its advantage over other algorithms.

arXiv:quant-ph/0604059•Communications in Theoretical Physics•Aug 1, 2007•3 citations
Unsorted database search problem is an important science and engineering problem. We proposed quantum algorithm to solve the problem by dividing the database binarily and then use a probabilistic verifier algorithm to determine if the item is within one part of the divided database. We analyzed the computational complexity of this algorithm, and found that in general, the number of steps is proportional to that in the standard Grover algorithm. However in some cases, it is less than that of the Grover algorithm.
We consider the problem of finding one or more desired items out of an unsorted database. Patel has shown that if the database permits quantum queries, then mere digitization is sufficient for efficient search for one desired item. The algorithm, called factorized quantum search algorithm, presented by him can locate the desired item in an unsorted database using O(log4N)O(log_{4}N)O(log4​N) queries to factorized oracles. But the algorithm requires that all the property values must be distinct from each other. In this paper, we discuss how to make a database satisfy the requirements, and present a quantum search engine based on the algorithm. Our goal is achieved by introducing auxiliary files for the property values that are not distinct, and converting every complex query request into a sequence of calls to factorized quantum search algorithm. The query complexity of our algorithm is O(P∗Q∗M∗log4N)O(P*Q*M*log_{4}N)O(P∗Q∗M∗log4​N), where P is the number of the potential simple query requests in the complex query request, Q is the maximum number of calls to the factorized quantum search algorithm of the simple queries, M is the number of the auxiliary files for the property on which our algorithm are searching for desired items. This implies that to manage an unsorted database on an actual quantum computer is possible and efficient.
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.
For searching any item in an unsorted database with N items, a classical computer takes O(N) steps but Grover’s quantum searching algorithm takes only O( √ N) steps. However, it is also known that Grover’s algorithm is effective only in the case where the initial amplitude distribution of dataset is uniform, but is not always effective in the nonuniform case. In this paper, we propose some quantum search algorithms. First, we propose an algorithm in analog time based on quantum walk by solving the schrodinger equation. The proposed algorithm shows best performance in optimum time. Next, we will apply the result to Grover search algorithm. It is shown that the proposed algorithm shows better performance than the conventional one. Further, we propose the improved algorithm by introducing the idea of the phase rotation. The algorithm shows best performance compared with the conventional ones.
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.
An important and usual sort of search problems is to find all marked states from an unsorted database with a large number of states. Grover's original quantum search algorithm is for finding single marked state with uncertainty, and it has been generalized to the case of multiple marked states, as well as been modified to find single marked state with certainty. However, the query complexity for finding all multiple marked states has not been addressed. We use a generalized Long's algorithm with high precision to solve such a problem. We calculate the approximate query complexity, which increases with the number of marked states and with the precision that we demand. In the end we introduce an algorithm for the problem on a ``duality computer'' and show its advantage over other algorithms.