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arXiv:quant-ph/0509066 · New Journal of Physics

Hybrid cluster state proposal for a quantum game

Mauro Paternostro, Mark Tame, M. S. Kim

Published Oct 24, 2005• 15 citations
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Abstract

We propose an experimental implementation of a quantum game algorithm in a hybrid scheme combining the quantum circuit approach and the cluster state model. An economical cluster configuration is suggested to embody a quantum version of the Prisoners' Dilemma. Our proposal is shown to be within the experimental state of the art and can be realized with existing technology.The effects of relevant experimental imperfections are also carefully examined.

DOI
10.1088/1367-2630/7/1/226

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We propose an experimental implementation of a quantum game algorithm in a hybrid scheme combining the quantum circuit approach and the cluster state model. An economical cluster configuration is suggested to embody a quantum version of the Prisoners' Dilemma. Our proposal is shown to be within the experimental state of the art and can be realized with existing technology.The effects of relevant experimental imperfections are also carefully examined.
We report the first demonstration of a quantum game on an all-optical one-way quantum computer. Following a recent theoretical proposal we implement a quantum version of Prisoner's Dilemma, where the quantum circuit is realized by a four-qubit box-cluster configuration and the player's local strategies by measurements performed on the physical qubits of the cluster. This demonstration underlines the strength and versatility of the one-way model and we expect that this will trigger further interest in designing quantum protocols and algorithms to be tested in state-of-the-art cluster resources.
Theory of games is an important discipline of applied mathematics, which has found numerous applications in psychology, ecology, and social science. While a well-established framework has been established for classical game theory, extending, and generalizing it towards the quantum domain still has some open questions. In this project, we focus on the prisoner’s dilemma-a standard example of a game analyzed in game theory-in a quantum world. Here, we start with the quantum version of prisoner’s dilemma, explain the quantum circuit implementation for describing the behavior of quantum prisoners, and investigate how quantum entanglement can change their strategies. By using the IBM quantum computer, we experimentally study the quantum prisoner dilemma, and we conclude that the best quantum strategies will break the prisoner’s dilemma.
Decision-making by the two negotiating parties is simulated by a prisoner's dilemma game.The game is formulated in a quantum manner, where players strategies are unitary transformations of qubits built over the basis of opposite decision options.Quantum strategies are correlated through the mechanism of quantum entanglement and the result of the game is obtained by the collapse of the resulting transformed state.The range of strategies allowed for quantum players is richer than in case of a classical game and therefore the result of the game can be better optimized.On the other hand, the quantum game is save against eavesdropping and the players can be assured that this type of quantum arbitration is fair.We show that quantum prisoner's dilemma has more favorable Nash equilibria than its classical analog and they are close to the Pareto optimal solutions.Some economical examples of utilizing quantum game Nash equilibria are proposed.