Research On Quantum Steering Based On Fully Connected Neural Network

Since the optimal measurement strategy is unknown,it is still very difficult and time-consuming to obtain the guidance of any quantum state effectively.Now we use the fully connected neural network to build a regression model to predict the steerability of two qubits.Firstly,the density matrix is randomly generated by MATLAB according to the characteristics of the density matrix,and the corresponding the steerability of two qubits is calculated as the original data,and the data is preprocessed.Then,a fully connected neural network model is established,which is mainly composed of forward propagation and backward propagation.The purpose of forward propagation is to output the predicted value and loss value,while the purpose of backward propagation is to allocate the loss value to each neuron by gradient descent algorithm,so as to change the corresponding weight and threshold value of each neuron and reduce the loss.In this way,the error can be controlled in a certain range,the error can be reduced as much as possible,and the predicted value can be closer to the real value.Finally,we use the judgment coefficient(R2)and mean absolute error(MAE)as the evaluation indexes of the model to evaluate the prediction effect.It can be concluded that the error between the predicted value of quantum steerability obtained by the fully connected neural network model and the real quantum steerability is small,and the goodness of fit between the predicted value of quantum steerability and the real quantum steerability is good.In addition,in order to improve the prediction ability of the model for quantum steerability,we use cross validation and t-test to analyze the results of quantum steerability and its corresponding predicted values.It is found that the mean error between the predicted values of the model for quantum steerability and the real quantum steerability obeys normal distribution.In order to verify the generalization ability of the model,the physical models of Werner state and noise interference are used to verify.The results show that the average absolute error between the predicted value and the real value of quantum steerability is small,and the goodness of fit of the model prediction is good.The model greatly optimizes the calculation time of quantum guidance.Which reveals the effective application of machine learning method in exploring quantum steerability.