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DBSCAN is a famous density-based clustering algorithm that can discover clusters with arbitrary shapes without the minimal requirements of domain knowledge to determine the input parameters. However, DBSCAN is not suitable for databases with different local-density clusters and is also a very time-consuming clustering algorithm. In this paper, we present a quantum mutual MinPts-nearest neighbor graph (MMNG)-based DBSCAN algorithm. The proposed algorithm performs better on databases with different local-density clusters. Furthermore, the proposed algorithm has a dramatic increase in speed compared to its classic counterpart.

A controlled quantum secure direct communication protocol based on four-qubit cluster states and quantum search algorithm is put forward, in which four users, a sender, a receiver and two controllers, are involved in achieving the secure transmission of secret message. The four-qubit cluster state can ensure the feasibility and security of the protocol because of its large persistency of entanglement. Meanwhile, the idea of quantum search algorithm is used to accomplish the task of encoding and decoding secret message. The proposed protocol can successfully avoid the information leakage problem and resist some common attacks including the outsider attacks and the internal attacks, and its qubit efficiency is up to 20%. Furthermore, compared with the previous quantum secure direct communication protocols, it can effectively resist the attacks from the dishonest receiver.

A quantum search algorithm with phase shift of π/18 is proposed to find a multiplicative inverse of an equation in an unsorted database. The unitary operator $$Q{\text{ }}$$ ( $$Q{\text{ = }}I_{t} U^{{ - 1}} I_{0} U$$ ) is operated repeatedly on the initial state with $$\left\lfloor {9\sqrt {{N \mathord{\left/ {\vphantom {N M}} \right. \kern-\nulldelimiterspace} M}} } \right\rfloor$$ times to find a marked item successfully. At least 99.81% of the probability of success could be achieved by this proposed quantum search algorithm with time complexity $$O\left( {\sqrt {{N \mathord{\left/ {\vphantom {N M}} \right. \kern-\nulldelimiterspace} M}} } \right)$$ . Compared with four typical algorithms, the proposed search algorithm has better performance to find out a match in terms of success probability with the same time complexity $$O\left( {\sqrt {{N \mathord{\left/ {\vphantom {N M}} \right. \kern-\nulldelimiterspace} M}} } \right)$$ .

The main objective of this paper is to present granular computing algorithms of finding association rules with different levels of granularity from relational databases or information tables. Firstly, based on the partition model of granular computing, a framework for knowledge discovery in relational databases was introduced. Secondly, referring to granular computing, the algorithms for generating frequent k -itemsets were proposed. Finally, the proposed algorithms were illustrated with a real example and tested on two data sets under different supports. Experiment results show that the algorithms are effective and feasible. Moreover, the meanings of mining association rules based on granular computing are clearly understandable.

Ontology capture is a key topic in constructing an ontology, and it is a procedure of knowledge acquisition. In this paper, by applying the principle of granular computing, some concepts about information granules, including domain feature information granule, domain object information granule, were defined, the context of the domain ontology may be granulated. A domain granule and a domain granule lattice were presented. An algorithm of generating the domain granule lattice was proposed, and was illustrated by a real example. With the domain granule lattice, ontology capture can be fulfilled. Therefore, granular computing should be of great help in representing and constructing an ontology.