The Application Of Convolutional Neural Network In Quantum Information

Quantum information and machine learning are both emerging and rapidly developing disciplines.In the past one or two decade,with the development of computer hardware and the progress of quantum theory and experimental technology,it has been found that they can promote each other and develop together.On the one hand,machine learning is used to study quantum information and quantum physics because of its ability to generalize underlying laws from complex data.On the other hand,people are also studying how to bring quantum advantages to machine learning.In this work,we focus on using traditional machine learning to study quantum information concerns.We consider both convolutional layer of artificial neural networks and observable operators in quantum mechanics.We demonstrate that,in discrete level systems,convolutional layers can be used to accurately compute the averages of observable operators,and that the data of the parts of the convolutional layers can keep Hermitian in gradient-descent-based optimization methods.It means the observable operator of the discrete level system is a special convolutional kernel.Then,we design the branching convolutional neural network,which consists of several independent convolutional paths and fully connected layers.The convolutional path consists of several convolutional layers,and its structure can be set according to the research requirements.In principle,the branching convolutional neural network can train observable operators which can extract the required information according to the characteristics of the quantum state,the structure of the convolutional path and the specific learning task.After training,the trained observable operators can be gained from convolutional paths,so only subsequent fully connected layers need to be kept during testing or practice process.To demonstrate the effectiveness of our method,we use branching convolutional neural network to classify whether 2 qubits quantum states are entangled or not.The branching convolutional neural network can achieve higher accuracy based on fewer observable operators(than previous works)when classifying the entanglement of three type of quantum states with special forms.When classifying the entanglements of arbitrary 2 qubits states,we test three different architectures of convolutional paths and compare their performance.Since arbitrary quantum state has no other constraints,the branching convolutional neural network can only achieve high accuracy classification when all the quantum state information can be obtained by convolutional paths.