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Computer Physics Communications

Quantum game simulator, using the circuit model of quantum computation

Panagiotis Vlachos, Ioannis G. Karafyllidis

Published May 15, 2009• 7 citations
Publisher
DOI
10.1016/j.cpc.2009.05.007

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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.
Game theory problems are widely applied in many research areas such as computer science and finance, with the key issue being how to quickly make decisions. Here, we present a novel quantum algorithm for game theory problems based on a continuous quantum walk. Our algorithm exhibits quantum advantage compared to classical game algorithms. Furthermore, we exploit the analogy between the wave function of the Schrödinger equation and the voltage in Kirchhoff's law to effectively translate the design of quantum game trees into classical circuit networks. We have theoretically simulated the quantum game trees and experimentally validated the quantum functionality speedup on classical circuit networks. Due to the robust scalability and stability inherent in classical circuit networks, quantum game trees implemented within this framework hold promise for addressing more intricate application scenarios.