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

arXiv:1012.5629

Two-Dimensional Quantum Search Algorithm

Arti Chamoli, Samina Masood

Published Dec 27, 2010• 3 citations
arXivHTMLPDF

Abstract

Quantum mechanical search induces polynomial speed up in an unsorted database search process. In case of classical linear search the computational time increases with the dimensionality of the query. However, quantum parallelism, inherent to quantum systems, does not let multi-dimensional query processing affect the computational time of the quantum search algorithm. In this letter, a two-dimensional search process has been proposed. It has been shown that a two-dimensional search process can be accomplished without increasing the computational time due to implicit quantum parallelism

DOI
10.48550/arxiv.1012.5629

Related papers

Quantum database search can do without sorting

Apoorva D. Patel

Sorting is a fundamental computational process that facilitates subsequent searching of a database. It can be thought of as factorization of the search process. The location of a desired item in a sorted database can be found by classical queries that inspect one letter of the label at a time. For an unsorted database, no such classical quick search algorithm is available. If the database permits quantum queries, however, then mere digitization is sufficient for efficient search. Sorting becomes redundant with the quantum superposition of states. A quantum algorithm is written down that locates the desired item in an unsorted database a factor of two faster than the best classical algorithm can in a sorted database. This algorithm has close resemblance to the assembly process in DNA replication.

arXiv:quant-ph/0012149•Physical Review A•Aug 15, 2001•16 citations

Efficient simulation of quantum-based searching

Tamás Varga, László Bacsárdi

The efficient search in unsorted database is extremely important for our everydays' applications. This type of search is useful in communication networks as well, since routing can be considered as a search in the database of the routing table. From the viewpoint of quantum computing, the not quantum-based solutions are named as classical. The search could be very time-consuming and computationally task if we need to solve it using classical algorithms, particularly for large data sets. This process can be accelerated and be more efficient by the application of quantum search algorithms. To investigate the quantum search, we have developed a Java-based system to simulate different quantum algorithms which are based on elementary quantum gates. In our model, we took into account the computation errors of the elementary quantum gates. We analyzed how these errors affect the efficiency of quantum search.

International Conference on Software, Telecommunications and Computer Networks (SoftCOM)•Sep 1, 2014•2 citations

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

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

Hardware Efficient Quantum Search Algorithm

Ji Liu, Huiyang Zhou

Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's search algorithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grover's search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grover's search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.

arXiv:2103.14196•Mar 26, 2021•6 citations

Quantum Search in Hilbert Space

Michail A. Zak

A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.

•Jan 1, 2003•0 citations
Quantum mechanical search induces polynomial speed up in an unsorted database search process. In case of classical linear search the computational time increases with the dimensionality of the query. However, quantum parallelism, inherent to quantum systems, does not let multi-dimensional query processing affect the computational time of the quantum search algorithm. In this letter, a two-dimensional search process has been proposed. It has been shown that a two-dimensional search process can be accomplished without increasing the computational time due to implicit quantum parallelism
Sorting is a fundamental computational process that facilitates subsequent searching of a database. It can be thought of as factorization of the search process. The location of a desired item in a sorted database can be found by classical queries that inspect one letter of the label at a time. For an unsorted database, no such classical quick search algorithm is available. If the database permits quantum queries, however, then mere digitization is sufficient for efficient search. Sorting becomes redundant with the quantum superposition of states. A quantum algorithm is written down that locates the desired item in an unsorted database a factor of two faster than the best classical algorithm can in a sorted database. This algorithm has close resemblance to the assembly process in DNA replication.
The efficient search in unsorted database is extremely important for our everydays' applications. This type of search is useful in communication networks as well, since routing can be considered as a search in the database of the routing table. From the viewpoint of quantum computing, the not quantum-based solutions are named as classical. The search could be very time-consuming and computationally task if we need to solve it using classical algorithms, particularly for large data sets. This process can be accelerated and be more efficient by the application of quantum search algorithms. To investigate the quantum search, we have developed a Java-based system to simulate different quantum algorithms which are based on elementary quantum gates. In our model, we took into account the computation errors of the elementary quantum gates. We analyzed how these errors affect the efficiency of quantum search.
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.
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's search algorithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grover's search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grover's search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.
A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.