馬爾可夫開放量子系統(tǒng)無消相干子空間和目標態(tài)的穩(wěn)定化控制
發(fā)布時間：2018-08-19 11:58
【摘要】：近年來,量子信息技術的發(fā)展十分迅速。在進行量子信息處理的過程中,環(huán)境引起的耗散或消相干效應會使所考慮的量子系統(tǒng)成為開放系統(tǒng)。對于開放量子系統(tǒng)而言,其動力學演化不再是幺正的,這將導致存儲在系統(tǒng)中的量子信息發(fā)生錯誤甚至丟失。研究開放量子系統(tǒng)的控制方法,使其盡可能免受消相干的影響,同時實現(xiàn)系統(tǒng)狀態(tài)的高效操縱,對于量子信息技術的發(fā)展具有重要意義。論文針對馬爾可夫開放量子系統(tǒng),研究基于李雅普諾夫方法的消相干控制和基于哈密頓量設計的狀態(tài)控制,主要內(nèi)容包括以下幾個方面:1)概述量子控制的起源和發(fā)展,重點介紹開放量子系統(tǒng)控制的國內(nèi)外研究現(xiàn)狀,包括開放量子系統(tǒng)的消相干控制和狀態(tài)控制。2)馬爾可夫開放量子系統(tǒng)無消相干子空間的快速李雅普諾夫控制。無消相干子空間是量子系統(tǒng)進行幺正演化的所有量子態(tài)張成的一個子空間,將系統(tǒng)狀態(tài)驅動至無消相干子空間中是一種有效避免消相干的方法。論文借助李雅普諾夫方法,提出了一個將馬爾可夫開放量子系統(tǒng)快速驅動至無消相干子空間的控制方案。在該方案中,我們首先設計基于李雅普諾夫方法的控制律,特別是要設計具有快速性的近似棒棒控制律。然后,從數(shù)學上嚴格證明控制場作用下整個系統(tǒng)對于無消相干子空間的收斂性。在此基礎上,通過分析系統(tǒng)的LaSalle最大不變集與無消相干子空間之間的關系,獲得使系統(tǒng)對于無消相干子空間快速收斂的控制哈密頓量的構造方法。最后,在一個三維開放量子系統(tǒng)上進行仿真實驗,以便驗證方案的控制效果。3)開放量子系統(tǒng)的狀態(tài)收斂控制。基于哈密頓量的構造,論文提出了一個使得開放量子系統(tǒng)收斂至目標態(tài)的哈密頓控制方法。首先,針對一個耗散項已知不變的開放量子系統(tǒng),求解含有未知哈密頓量的系統(tǒng)方程以便得到系統(tǒng)的穩(wěn)定解,通過將穩(wěn)定解與期望目標態(tài)進行比較構造出哈密頓量的形式。其次,借助相干矢量體系將原系統(tǒng)的非線性模型轉化為仿射線性模型,繼而對后者的穩(wěn)定性進行分析,由此導出原系統(tǒng)的穩(wěn)定性條件。最后,我們在一個兩能級系統(tǒng)上進行仿真實驗,以驗證所提出的哈密頓控制方案的有效性。
[Abstract]:In recent years, quantum information technology has developed rapidly. In the process of quantum information processing, the dissipative or decoherence effect caused by environment will make the quantum system under consideration as an open system. For open quantum systems, the dynamical evolution is no longer unitary, which will lead to errors or even loss of quantum information stored in the system. It is of great significance for the development of quantum information technology to study the control method of open quantum system so that it can avoid the influence of decoherence as much as possible and realize the efficient manipulation of system state at the same time. In this paper, for Markov open quantum systems, we study the decoherence control based on Lyapunov method and the state control based on Hamiltonian design. The main contents include the following aspects: 1) Overview of the origin and development of quantum control. The research status of open quantum system control at home and abroad is introduced, including the decoherence control and state control of open quantum system. 2) the fast Lyapunov control of Markov open quantum system without coherent subspace is introduced. Non-decoherence subspace is a subspace of Zhang Cheng of all quantum states in which the quantum system is unitary. Driving the state of the system to the non-decoherence subspace is an effective method to avoid decoherence. With the help of Lyapunov method, a control scheme is proposed in which Markov open quantum system is rapidly driven to a non-coherent subspace. In this scheme, we first design the control law based on Lyapunov method, especially the approximate rod control law with rapidity. Then, the convergence of the whole system to the non-coherent subspace under the action of the control field is proved mathematically. On this basis, by analyzing the relationship between the maximum LaSalle invariant set of the system and the non-coherent subspace, a construction method of the control Hamiltonian is obtained to make the system converge rapidly for the non-decoherence subspace. Finally, simulation experiments are carried out on a three-dimensional open quantum system to verify the control effect of the proposed scheme. 3) the state convergence control of the open quantum system. Based on the construction of Hamiltonian, a Hamiltonian control method is proposed to converge the open quantum system to the target state. Firstly, for an open quantum system with known invariant dissipative terms, the system equation with unknown Hamiltonian is solved to obtain the stable solution of the system, and the form of Hamiltonian is constructed by comparing the stable solution with the desired target state. Secondly, the nonlinear model of the original system is transformed into an affine linear model by means of the coherent vector system, and then the stability of the latter is analyzed, and the stability conditions of the original system are derived. Finally, simulation experiments are carried out on a two-level system to verify the effectiveness of the proposed Hamiltonian control scheme.
【學位授予單位】：中國科學技術大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O413
本文編號：2191589
[Abstract]:In recent years, quantum information technology has developed rapidly. In the process of quantum information processing, the dissipative or decoherence effect caused by environment will make the quantum system under consideration as an open system. For open quantum systems, the dynamical evolution is no longer unitary, which will lead to errors or even loss of quantum information stored in the system. It is of great significance for the development of quantum information technology to study the control method of open quantum system so that it can avoid the influence of decoherence as much as possible and realize the efficient manipulation of system state at the same time. In this paper, for Markov open quantum systems, we study the decoherence control based on Lyapunov method and the state control based on Hamiltonian design. The main contents include the following aspects: 1) Overview of the origin and development of quantum control. The research status of open quantum system control at home and abroad is introduced, including the decoherence control and state control of open quantum system. 2) the fast Lyapunov control of Markov open quantum system without coherent subspace is introduced. Non-decoherence subspace is a subspace of Zhang Cheng of all quantum states in which the quantum system is unitary. Driving the state of the system to the non-decoherence subspace is an effective method to avoid decoherence. With the help of Lyapunov method, a control scheme is proposed in which Markov open quantum system is rapidly driven to a non-coherent subspace. In this scheme, we first design the control law based on Lyapunov method, especially the approximate rod control law with rapidity. Then, the convergence of the whole system to the non-coherent subspace under the action of the control field is proved mathematically. On this basis, by analyzing the relationship between the maximum LaSalle invariant set of the system and the non-coherent subspace, a construction method of the control Hamiltonian is obtained to make the system converge rapidly for the non-decoherence subspace. Finally, simulation experiments are carried out on a three-dimensional open quantum system to verify the control effect of the proposed scheme. 3) the state convergence control of the open quantum system. Based on the construction of Hamiltonian, a Hamiltonian control method is proposed to converge the open quantum system to the target state. Firstly, for an open quantum system with known invariant dissipative terms, the system equation with unknown Hamiltonian is solved to obtain the stable solution of the system, and the form of Hamiltonian is constructed by comparing the stable solution with the desired target state. Secondly, the nonlinear model of the original system is transformed into an affine linear model by means of the coherent vector system, and then the stability of the latter is analyzed, and the stability conditions of the original system are derived. Finally, simulation experiments are carried out on a two-level system to verify the effectiveness of the proposed Hamiltonian control scheme.
【學位授予單位】：中國科學技術大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O413
【參考文獻】
相關期刊論文 前1條
1 張為;謝廷;黃寅;王高仁;叢書林;;Stabilizing photoassociated Cs_2 molecules by optimal control[J];Chinese Physics B;2013年01期
相關博士學位論文 前2條
1 楊潔;開放量子系統(tǒng)的建模及其控制[D];中國科學技術大學;2011年
2 李明;開放量子系統(tǒng)量子態(tài)相干保持的控制策略研究[D];中國科學技術大學;2008年
，本文編號：2191589
本文鏈接：http://sikaile.net/shoufeilunwen/benkebiyelunwen/2191589.html
最近更新
教材專著
