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

Clustering Algorithm Based on Quantum Game and Grid

Huang De-ca

Published Jan 1, 2014• 1 citation
OpenAlex

Abstract

Quantum game is an analogy of classical game.Using the quantum entanglement,game players interact with each other implicitly,and the game will result in a different way.Quantum game was applied to clustering.A clustering algorithm based on quantum game and grid was proposed where data points are regarded as players.By embeding distance function into payoff matrix,similar data points can get more payoff,and clusters will be formed in that way.In addition,a rule about merging grid was designed to simplify the game.Simulations show the clustering quality of this algorithm is superior to K-means etc.At last,several parameters in this algorithm were discussed and some recommendations about parameters selection were provided.

Related papers

A novel clustering algorithm based on quantum games

Qiang Li, Yan He, Jing-ping Jiang

Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each player's expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

arXiv:0812.0743•Journal of Physics A Mathematical and Theoretical•Oct 8, 2009•14 citations

A Novel Clustering Algorithm Based on Quantum Games

Qiang Li, Yan Li He, Jiang Jing-ping

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and develop clustering algorithms based on it, in which data points in a dataset are considered as players who can make decisions and play quantum strategies in quantum games. After playing quantum games, each player’s expected payoff is calculated and then he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them for maximizing his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

•Jan 1, 2008•18 citations

Quantum Hierarchical Clustering Algorithm Based on the Nearest Cluster Centroids Distance

Fengbo Kong, Hong Lai, Hailing Xiong

It is getting harder to deal with the large data sets by the classical hierarchical clustering algorithm, so we propose an efficient quantum hierarchical clustering algorithm, in which the quantum bit (qubit) is used to represent the data point in the space.For quantum entanglement, the distance between two data points is calculated through adding an auxiliary particle to construct the entangled state.Then a projective measurement is performed on the auxiliary particle alone.The distance between two points is acquired by the projective measurement.We use the distance of the cluster centroids as a measure of similarity between clusters.Also, based on the principle of the minimum cluster centroids distance, the nearest two clusters are merged.We aim at improving time and space complexity and effect of the clustering of the hierarchical clustering algorithm.

International Journal of Machine Learning and Computing•Oct 1, 2017•2 citations

Study of quantum games

Ahmad Razavi

Game theory is the study of strategic competition used in many branches of science. In general, a game is a match between two or more players and each wants to maximize his or her score. In a game, the player’s score depends on their strategies. The goal is to find the optimized decision, with regard to the payoff, in conformity with the rules of the game. This thesis considers the games with two players who know both their own and their rival’s payoff. However, they do not know the strategy chosen by the opponent.\nIn a classical game, the options of players are referred to as cooperation and defect. Quantum game theory is a generalization of classical game theory. In quantum games a linear combination of two options specify the strategy based on qubit. The quantum domain is characterized by entanglement. The quantum entanglement coefficient (y) varies from 0 to . The game is in the classical regime when y is smaller than a threshold. Quantum entanglement is intrinsically non-local.\nIn an iterated game tournament, 63 different strategies contest with four known strategies. Depending on the result, they are divided to a number of groups. The competition specifies which group of strategies can obtain a higher score.\nOther types of games are discussed in the thesis. They are known as incomplete information games. In these games one player has two payoff matrixes, and the rival does not know which of them is used. We discuss the advantage of using quantum strategy over the classical game, particular in avoiding the dilemma in classical games.

•Jan 1, 2015•0 citations

Quantum Game Simulator, Using the Circuit Model of Quantum

Panagiotis Vlachos, Ioannis G. Karafyllidis

We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2times2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well known quantum games, the Battle of Sexes and the Chicken game.

Panhellenic Conference on Informatics•Jan 1, 2009•1 citation

Quantum games

Mei Lyn Jaclyn Thang

Quantum games have demonstrated to propose a new point of view for the solution of the classical problems and dilemmas in game theory. It has been shown in many literatures that quantum games are more efficient than classical games and provide a greater and more efficient solution. As interest in multi-player quantum games grow, methods are proposed to analyze and obtain efficient solutions for these problems. In quantum games with cooperation, analysis so far have taken into consideration all possible scenarios for the multiple players playing different strategies and in the calculation of payoff, setting the payoff of scenarios not possible to be zero. Chapter 5 presents the analysis of multiple players (three players and four players) using this method of analysis. In Chapter 6, a modification of the analysis was done. In Chapter 5, it should be noted that the probabilities of participating scenarios do not sum to unity which is technically not ideal. Hence Chapter 6 addresses this by performing re-normalizing the probabilities of the participating scenarios so that the probabilities sum to unity. The analysis was done for three and four player games and a comparison was made between the un-normalized method and the re-normalized method. It was found that re-normalization provides a more accurate representation of the classical game and hence can be a better solution for the quantum game.

•Jan 1, 2010•0 citations
Quantum game is an analogy of classical game.Using the quantum entanglement,game players interact with each other implicitly,and the game will result in a different way.Quantum game was applied to clustering.A clustering algorithm based on quantum game and grid was proposed where data points are regarded as players.By embeding distance function into payoff matrix,similar data points can get more payoff,and clusters will be formed in that way.In addition,a rule about merging grid was designed to simplify the game.Simulations show the clustering quality of this algorithm is superior to K-means etc.At last,several parameters in this algorithm were discussed and some recommendations about parameters selection were provided.
Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each player's expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and develop clustering algorithms based on it, in which data points in a dataset are considered as players who can make decisions and play quantum strategies in quantum games. After playing quantum games, each player’s expected payoff is calculated and then he uses an link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them for maximizing his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.
It is getting harder to deal with the large data sets by the classical hierarchical clustering algorithm, so we propose an efficient quantum hierarchical clustering algorithm, in which the quantum bit (qubit) is used to represent the data point in the space.For quantum entanglement, the distance between two data points is calculated through adding an auxiliary particle to construct the entangled state.Then a projective measurement is performed on the auxiliary particle alone.The distance between two points is acquired by the projective measurement.We use the distance of the cluster centroids as a measure of similarity between clusters.Also, based on the principle of the minimum cluster centroids distance, the nearest two clusters are merged.We aim at improving time and space complexity and effect of the clustering of the hierarchical clustering algorithm.
Game theory is the study of strategic competition used in many branches of science. In general, a game is a match between two or more players and each wants to maximize his or her score. In a game, the player’s score depends on their strategies. The goal is to find the optimized decision, with regard to the payoff, in conformity with the rules of the game. This thesis considers the games with two players who know both their own and their rival’s payoff. However, they do not know the strategy chosen by the opponent.\nIn a classical game, the options of players are referred to as cooperation and defect. Quantum game theory is a generalization of classical game theory. In quantum games a linear combination of two options specify the strategy based on qubit. The quantum domain is characterized by entanglement. The quantum entanglement coefficient (y) varies from 0 to . The game is in the classical regime when y is smaller than a threshold. Quantum entanglement is intrinsically non-local.\nIn an iterated game tournament, 63 different strategies contest with four known strategies. Depending on the result, they are divided to a number of groups. The competition specifies which group of strategies can obtain a higher score.\nOther types of games are discussed in the thesis. They are known as incomplete information games. In these games one player has two payoff matrixes, and the rival does not know which of them is used. We discuss the advantage of using quantum strategy over the classical game, particular in avoiding the dilemma in classical games.
We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2times2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well known quantum games, the Battle of Sexes and the Chicken game.
Quantum games have demonstrated to propose a new point of view for the solution of the classical problems and dilemmas in game theory. It has been shown in many literatures that quantum games are more efficient than classical games and provide a greater and more efficient solution. As interest in multi-player quantum games grow, methods are proposed to analyze and obtain efficient solutions for these problems. In quantum games with cooperation, analysis so far have taken into consideration all possible scenarios for the multiple players playing different strategies and in the calculation of payoff, setting the payoff of scenarios not possible to be zero. Chapter 5 presents the analysis of multiple players (three players and four players) using this method of analysis. In Chapter 6, a modification of the analysis was done. In Chapter 5, it should be noted that the probabilities of participating scenarios do not sum to unity which is technically not ideal. Hence Chapter 6 addresses this by performing re-normalizing the probabilities of the participating scenarios so that the probabilities sum to unity. The analysis was done for three and four player games and a comparison was made between the un-normalized method and the re-normalized method. It was found that re-normalization provides a more accurate representation of the classical game and hence can be a better solution for the quantum game.