Quantum Game Learning And Its Experimental Research On Photonic Quantum Chips

Game theory is an essential branch of applied mathematics that uses mathematical models to analyze decision-making processes rather than conscious choices in complex situations.It plays a vital role in economics,psychology,politics,ecology,biology,and other fields.Quantum game theory is a cross-research direction of game theory and quantum information,which has attracted significant attention of the academic field in recent years.On the one hand,a large number of researchers believe that the laws of quantum mechanics dominate the behavior of game players at the microscopic level,such as molecules and atoms,and the research of quantum game theory may help to solve the mystery of human decision-making behavior.On the other hand,theoretical research has proved that in the quantum game model,game players can use quantum resources such as quantum entanglement to obtain the upper limit of payoff that exceeds the classical game,such as ”getting the prisoner out of the predicament.”Machine learning studies how to make machines obtain the ability to approach or even surpass humans through computing.The researchers find that machine learning can discover better game strategies of games.In 2016,Alpha Go defeated the best human Go player for the first time,marking significant progress in machine learning.Go is a classic game,and Alphago uses the classic machine learning algorithms.So a natural problem is what will happen if game theory and machine learning ”meet in a quantum context.”Therefore,this paper proposes the concept and classification of quantum game learning.According to whether the game model and learning algorithms are classical or quantum,we divide quantum game learning into four categories: 1)Classical game model and classical learning algorithm(CGCL).Alpha Go belongs to this type.2)Classical game model and quantum learning(CGQL).The Quantum learning algorithm has a more robust performance than the classical learning algorithm and can be used to solve classical game problems that are more complex than Go.3)Quantum game model and classical learning(QGCL).Can classical learning algorithms help quantum players win in quantum games? 4)Quantum game model and quantum learning algorithm(QGQL).The type is the most complicated situation.This paper focuses on studying QGCL-type quantum game learning and finds that the classical learning algorithm can also help the quantum player win as they help classical players.And we design a photonic quantum chip structure for the QGCL-type quantum game learning and confirm its availability experimentally.The specific contributions of the paper include:1)We propose the concept and classification of quantum game learning,which includes classical game model and classical learning algorithm(CGCL),classical game model and quantum learning(CGQL),quantum game model and classical learning(QGCL),and quantum game model and quantum learning algorithm(QGQL).In the quantum game model and classical learning algorithm category,a quantum game learning model for a Bayesian game is designed.We realize and compare a set of learning algorithms for the Bayesian quantum game model.Theoretical analysis and numerical simulation results show that these learning algorithms can help players obtain the best payoff of the model.The BFGS algorithm using the Armijo criterion is significantly better than other algorithms in terms of convergence speed and accuracy of solution results.2)We design and implement a photonic quantum chip structure for a two-person quantum game model and realize the quantum game learning model of a Bayesian game experimentally,which is the first physical experiment based on the photonic quantum chip platform in the field of the quantum game.The chip structure realizes the game process of a two-player quantum game by dynamically generating and regulating quantum entangled states and configuring players’ strategic parameters on the optical network.The experiment shows the payoff change process of the Bayesian game from classical strategy to quantum strategy and verifies the advantages of the quantum game.At the same time,we realize the quantum game learning algorithm of the Bayesian quantum game experimentally and prove the effectiveness of quantum game learning.3)We propose a set of dynamic calibration software techniques and conduct experiments on a photonic quantum chip to verify the effectiveness of the pro-posed calibration techniques.Inspired by quantum game learning,we transform the calibration problem into a two-player game model between the chip and thermal noise.The error of on-chip calculation results caused by thermal noise is dynamically corrected through the chip output feedback.The calibration speed and accuracy of various dynamic calibration technologies are compared through experimental results.The experimental results show that the proposed calibration techniques can effectively eliminate the interference of thermal noise in a short time and improve the manipulation precision of on-chip quantum states.