Theoretical Study On Quantum Control In Open System

Precise manipulation of quantum systems is one of the fundamental prerequisites for quantum information processing.In the last decade,quantum control has become a hotspot in quantum science.Many advances,including obtaining high-fidelity quantum gates,performing quantum state transfer,and preparing quantum target states,have been made in theoretical and experimental regimes.In recent years,the rapid development of machine learning techniques has demonstrated their potential and advantage for solving and optimizing complex nonlinear problems and therefore several interdisciplines are further emergent.In particular,the training and strategies optimizing process in a machine learning scheme are similar to the process of designing control fields in quantum control theory.This implies that optimizing quantum control schemes through machine learning is desirable.Hence,based on the quantum open system theory,this thesis will investigate environment-influenced quantum control schemes and discuss quantum control schemes combined with machine learning.The specific research contents are as follows.We study the influence of the memory effect of non-Markovian Bose baths on the simulated Raman adiabatic quantum control(STIRAP).The theoretical model is based on a ?-type threelevel atomic system coupled to two independent non-Markovian Bose baths.In the adiabatic frame,we analytically derive the non-Markovian master equation under adiabatic condition by using the quantum-state diffusion(QSD).By comparing the STIRAP under non-Markovian Bose baths and Markovian Bose baths,we find that the former can suppress the decoherence of the system.Besides,we prove that the memory effect of two independent non-Markovian Bose baths is stronger than a single non-Markovian Bose bath under the same parameters,which makes the former more effective in suppressing decoherence.In this theoretical scheme,if the memory effect of the non-Markovian Bose baths is strong,the external driving intensity can be reduced appropriately,so that it can be applied to more realistic physical systems.We study the interference effect in a globally coupled quantum network.The network is composed of optical cavities with high-quality factor(" good”cavity)and low-quality factor(“bad”cavity),respectively.By eliminating the bad-cavity,we obtain the effective master equation with additional interference terms.We propose that one can use the interference terms to control the quantum phenomena in the system.Then we manipulate the strength and direction of heat flow between heat reservoirs as an example.The numerical results show that heat flow can be flexibly adjusted,which provides theoretical support for constructing some quantum thermal devices.We propose a quantum control scheme to manipulate the preparation of quantum state and the mean-value of the Hermitian operator for multi-level quantum systems by using supervised machine learning.The control scheme is robust against the random noise of the system;the control fields are continuous and smooth.We take the manipulation of the preparing quantum state in a two-level system and the expected value of Hermite operators in a four-level system as examples,and numerically verify the control scheme is effective.We propose a scheme to detect phonon blockade in a quadratically coupled optomechanical system by using supervised machine learning.In this scheme,the detected cavity field is the input of the neural network.The outputs are the logarithm of the equal-time second-order correlation function of the acoustic mode.The numerical results demonstrate that the trained neural network can find out the nonlinear map between the input and output with high precision.Taking some examples to test the scheme,we find that the scheme can effectively detect the strong phonon blockade,even for existing internal noise.To sum up,this thesis solves some quantum control problems in open systems with new ideas,enriches the control methods of open quantum systems,amplifies the application of machine learning in quantum systems,and further promotes the development of quantum information and control.