Research On Noise Reduction Of Quantum Tomography Data Based On Machine Learning

Quantum tomography is one of the key technologies in quantum information processing.It obtains data by repeating measurements and statistical averaging of different observations,and reconstructs matrix representations of states or evolutionary processes based on these data.Since the information obtained from a single quantum measurement is limited,the number of measurements will increase rapidly with the increase in the dimensions of the quantum system and the required measurement accuracy.Therefore,how to improve the efficiency is the core problem in quantum chromatography experiments.To solve the problem of obtaining measurement data requires a lot of repeated measurement problems,this paper proposes a general-purpose quantum tomography data noise reduction model based on machine learning,and uses simulation experiments to study the effect of noise reduction under different noises.The specific results are as follows:(1)Based on the neural network theory of machine learning,general-purpose and deconvolutional autoencoder noise reduction model were designed to analyze the quantum tomography data.Comparing the simulation results of the two models,this paper shows that the proper neural network structure has the ability to learn the structural information of high-dimensional physical quantities,so it can be used to design the noise reduction model of quantum tomography experiments.This learning ability is not limited to a specific quantum system.It is the basis for the universality of the noise reduction model in improving the efficiency of quantum chromatography experiments.(2)For the quantum state tomography problems,a deconvolutional and noise reduction autoencoder model,capable of achieving a certain noise reduction effect under various noise types,complexity,and intensities,was trained.The simulation results show that based on the model,a noise reduction model can be trained from a large enough number of existing experimental data,and when a new quantum state tomography experiment of the same type is performed,with fewer measurement times,data with larger noise will be obtained.The data is then denoised by the noise reduction model to obtain data that would otherwise require more measurements,thus effectively improving the efficiency of the quantum state tomography experiment.(3)For the quantum process tomography problems,a noise reduction model was also designed based on the deconvolutional autoencoder model.The denoising of the quantum state tomography experiment is aimed at the 4-dimensional density matrix,and the noise reduction of the quantum process tomography experiment is aimed at the 16-dimensional process matrix.The length of the input vector of the noise reduction model changes from 16 to 256.With a large increase in the data dimension,the noise reduction model can still effectively reduce noise.This effectively proves that the deconvolutional model has good scalability in the noise reduction of quantum tomography experiments.It is not only can be applied to both types of quantum tomography but also to different quantum system's dimensions.