量子控制中的量子信息获取研究
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摘要
量子理论自二十世纪初诞生以来,就开始深刻的影响和改变着人类社会:它为人们了解和改造微观世界提供了理论基础,并推动了激光、半导体、核能等高科技的发展。量子理论在快速发展的同时,不断与其他学科交叉融合,量子信息学就是量子理论与信息科学相结合产生的一门新兴学科,它的迅速发展必将带来科学界的又一次革命。
量子信息学以量子态作为信息单元,要处理量子信息就需要对量子态进行操控,因此以研究量子系统主动控制为主要内容的量子控制理论诞生了。随着理论的不断的完善,近些年来量子控制已经成为国际上的研究热点,并取得了很多喜人的成果。闭环控制一直是经典控制中的核心内容,量子控制在不断的发展过程中也开始从最初的开环控制向闭环控制逐步迈进,闭环控制又被称为反馈控制,系统信息的获取是反馈控制中的关键环节,是了解系统状态和做出控制决策的依据。量子系统遵循的量子力学规律与经典力学有着本质上的差别,经典的信息获取方法已经不再适用于量子系统,需要我们探索新的技术和方法来完成量子反馈控制中的信息获取任务。
本文首先综述了量子控制的主要研究内容和量子反馈控制的最新研究进展,结合量子反馈控制的特点,分析了利用量子层析对量子态进行测量的可行性,并进一步提出了基于量子过程层析的量子控制系统辨识方案,设计了基于量子层析的量子反馈控制系统。文章的主要内容包括以下几个方面:
(1)提出了基于量子层析的量子态测量方案。
量子态作为量子信息的承载单元,是量子控制研究的主要对象。由于量子态遵循的是量子力学规律,量子不可克隆定理和不确定性关系使得对量子态的测量会产生“量子塌缩”现象,这给量子信息获取带来了极大的困难,我们试图利用量子层析技术来解决这一难题。量子层析一词来源于医学中的计算机辅助X射线断层摄影术CT,从名字中可以看出,它属于一种统计测量方法。根据量子力学的知识我们知道一个量子系统的密度矩阵包含了该系统的所有可知信息,如果可以得到系统的密度矩阵就可以说我们已经掌握了这个系统的状态信息。量子层析恰好可以通过测量未知量子态的大量全同样本的一组完备可观测量的平均值来重构量子态的密度矩阵,从而获取量子态信息。我们以偏振光子态为研究对象,设计了利用量子层析重构量子态密度矩阵的实验方案,并通过计算机仿真技术对实验的可行性进行了验证。结果表明,量子层析作为获取量子态信息的手段是有效和可行的。
(2)设计了基于量子过程层析的量子控制系统辨识方案
想要更好的设计量子控制系统,实现更为精确的主动控制,设计者需要了解控制系统的性能和参数。为解决这一问题,我们提出了基于量子过程层析的量子控制系统辨识。量子过程层析是一项基于量子层析的主要应用,在量子通讯领域中广泛应用于测定量子信道参数,主要过程如下:首先选择一组完备的输入量子态ρin,让其通过量子信道,然后利用量子层析测定输出量子态ρout,并根据输入与输出之间的关系确定量子信道的参数。借鉴这一思路,我们以电子自旋的控制磁场为对象,设计了控制系统辨识方案,同样利用计算机仿真技术对方案进行了模拟,结果证明,该方案能够有效的对量子控制系统进行参数辨识。
(3)提出了基于量子层析的量子反馈控制策略
随着量子反馈控制研究逐步成为热点,近年来已经取得了一些成果。但已有的反馈控制策略存在着一些缺陷,如马尔可夫量子反馈、贝叶斯量子反馈和含时延非马尔可夫量子反馈,用来反馈的信号都是经典信息,不能视为纯粹的量子反馈控制;而量子相干控制、基于克隆的反馈控制和基于量子隐形传态的反馈控制,虽然是以量子信息作为反馈信号,且在一定程度上可以保持量子系统的相干性,但这些系统的实现条件都是比较苛刻的,实用性不强,要想得到真正的应用还需要实验技术的进一步提高。为此,我们提出了基于量子层析的量子反馈控制策略,利用量子层析和量子过程层析两项技术的结合,可以同时实现量子控制系统中的量子态测量和控制系统参数辨识,形成一个以量子信息为反馈信号的量子反馈控制系统,既能根据被控对象的当前状态调整控制策略,又能按照辨识得到的控制系统参数来矫正控制系统的偏差,从而有效的降低系统外部干扰,完成对量子系统的精确控制。
Since the birth of quantum theory at the beginning of the twentieth century, it has changed and affected human society profoundly: it provides a theoretical basis for people to understand and rebuild the micro-world; also it promotes the laser, semiconductor, nuclear, and other high-tech development. With the rapid development quantum theory has integrated with other subjects. Quantum information science is a new discipline generated from the integration of quantum theory and information science, and its rapid development will bring another revolution in scientific community.
Quantum state is an information unit in quantum information science, which need be manipulated in order to deal with quantum information, so the quantum control theory was born to study the active control of quantum systems. With the continuous improvement, quantum control has become a hot international research focus and many gratifying results have been achieved in recent years. Closed-loop control has been the core of classical control, so quantum control began to gradually move to closed-loop control from the initial open-loop control. Closed-loop control is also known as feedback control, in which the information acquisition, the basis for understanding the system status and making control decision, is the key. Quantum system follows the laws of quantum mechanics which is essentially different from classical mechanics, so the classic information acquisition method is no longer applicable to quantum system. We need to explore new technology and method for information acquisition in quantum feedback control.
The main contents on quantum control and the latest development of quantum feedback control are summarized at the beginning of this paper. Then, combined with the character of quantum feedback control, the feasibility of measuring quantum states by quantum tomography is analyzed, and further quantum control system identification based on the quantum process tomography is proposed and quantum feedback control system based on quantum tomography is designed. This paper includes main aspects as following:
(1) Quantum state measurement based on quantum tomography is proposed.
Quantum state as a unit of quantum information is main research object in quantum control. Since quantum states follow the laws of quantum mechanics, quantum non-cloning theorem and uncertainty relationship result in "quantum collapse" phenomenon when quantum states are measured, which makes quantum information acquisition much difficult. We attempt to solve this problem by quantum tomography technology. The term, quantum tomography, comes from medical X-ray computer-aided tomography (CT), and it is a statistical measurement method. According to quantum mechanics we know that a quantum system density matrix contains all the system information, so the system information is totally obtained if the system density matrix can be acquired. Quantum tomography can reconstruct density matrix by measuring a large number of unknown quantum state in the same status to gain quantum state information. Taking example for polarized photon state, we design the experiment of quantum state density matrix reconstruction through quantum tomography, and validate the feasibility of experiment by computer simulation technology. The results show that quantum tomography is an effective and feasible method to obtain quantum state information.
(2) The scheme for quantum control system identification based on quantum process tomography is designed.
In order to design better quantum control systems and achieve more precise control, the performance and parameters of control system need to be understood well. To solve this problem, we propose a scheme of quantum system identification based on quantum process tomography. Quantum process tomography is a main application based on quantum tomography, which is widely used to determine quantum channel parameter in the field of quantum communication. The main process of quantum process tomography is as follows: first, let a set of selected complete input quantum statesρin pass through the quantum channel, and then quantum output statesρout are measured by quantum tomography, and quantum channel parameter is determined according to relationship between input and output states. Following this idea, taking example for magnetic field control of electron spin, we design the control system identification program which is simulated by computer simulation technology. The simulation results proved that this scheme is able to effectively identify quantum control system parameter.
(3) Quantum feedback control based on quantum tomography is proposed.
Quantum feedback control has gradually become a research focus and achieved some results in recent years. However, these feedback control strategy has some flaws, in Markovian quantum feedback, Bayesian quantum feedback and non-Markovian quantum feedback with delay, feedback signals are all classical information, so they can not be regarded as purely quantum feedback control; and for quantum coherent control, feedback control based on quantum cloning and teleportation, although quantum information is used as feedback signal and coherence of quantum systems is maintained in some extent, these systems are very difficult to realize. The realization of these systems is depended on further improvement of experimental techniques. We propose quantum feedback control strategy based on quantum tomography, in which quantum state measurement and quantum control system identification are realized, and quantum feedback control system using quantum information as feedback is formed. In this system, control strategy can be adjusted according to current system status and deviation of control system can be corrected according to control system parameters form identification so as to effectively reduce external interference and realize more precise control of quantum systems.
量子信息学以量子态作为信息单元,要处理量子信息就需要对量子态进行操控,因此以研究量子系统主动控制为主要内容的量子控制理论诞生了。随着理论的不断的完善,近些年来量子控制已经成为国际上的研究热点,并取得了很多喜人的成果。闭环控制一直是经典控制中的核心内容,量子控制在不断的发展过程中也开始从最初的开环控制向闭环控制逐步迈进,闭环控制又被称为反馈控制,系统信息的获取是反馈控制中的关键环节,是了解系统状态和做出控制决策的依据。量子系统遵循的量子力学规律与经典力学有着本质上的差别,经典的信息获取方法已经不再适用于量子系统,需要我们探索新的技术和方法来完成量子反馈控制中的信息获取任务。
本文首先综述了量子控制的主要研究内容和量子反馈控制的最新研究进展,结合量子反馈控制的特点,分析了利用量子层析对量子态进行测量的可行性,并进一步提出了基于量子过程层析的量子控制系统辨识方案,设计了基于量子层析的量子反馈控制系统。文章的主要内容包括以下几个方面:
(1)提出了基于量子层析的量子态测量方案。
量子态作为量子信息的承载单元,是量子控制研究的主要对象。由于量子态遵循的是量子力学规律,量子不可克隆定理和不确定性关系使得对量子态的测量会产生“量子塌缩”现象,这给量子信息获取带来了极大的困难,我们试图利用量子层析技术来解决这一难题。量子层析一词来源于医学中的计算机辅助X射线断层摄影术CT,从名字中可以看出,它属于一种统计测量方法。根据量子力学的知识我们知道一个量子系统的密度矩阵包含了该系统的所有可知信息,如果可以得到系统的密度矩阵就可以说我们已经掌握了这个系统的状态信息。量子层析恰好可以通过测量未知量子态的大量全同样本的一组完备可观测量的平均值来重构量子态的密度矩阵,从而获取量子态信息。我们以偏振光子态为研究对象,设计了利用量子层析重构量子态密度矩阵的实验方案,并通过计算机仿真技术对实验的可行性进行了验证。结果表明,量子层析作为获取量子态信息的手段是有效和可行的。
(2)设计了基于量子过程层析的量子控制系统辨识方案
想要更好的设计量子控制系统,实现更为精确的主动控制,设计者需要了解控制系统的性能和参数。为解决这一问题,我们提出了基于量子过程层析的量子控制系统辨识。量子过程层析是一项基于量子层析的主要应用,在量子通讯领域中广泛应用于测定量子信道参数,主要过程如下:首先选择一组完备的输入量子态ρin,让其通过量子信道,然后利用量子层析测定输出量子态ρout,并根据输入与输出之间的关系确定量子信道的参数。借鉴这一思路,我们以电子自旋的控制磁场为对象,设计了控制系统辨识方案,同样利用计算机仿真技术对方案进行了模拟,结果证明,该方案能够有效的对量子控制系统进行参数辨识。
(3)提出了基于量子层析的量子反馈控制策略
随着量子反馈控制研究逐步成为热点,近年来已经取得了一些成果。但已有的反馈控制策略存在着一些缺陷,如马尔可夫量子反馈、贝叶斯量子反馈和含时延非马尔可夫量子反馈,用来反馈的信号都是经典信息,不能视为纯粹的量子反馈控制;而量子相干控制、基于克隆的反馈控制和基于量子隐形传态的反馈控制,虽然是以量子信息作为反馈信号,且在一定程度上可以保持量子系统的相干性,但这些系统的实现条件都是比较苛刻的,实用性不强,要想得到真正的应用还需要实验技术的进一步提高。为此,我们提出了基于量子层析的量子反馈控制策略,利用量子层析和量子过程层析两项技术的结合,可以同时实现量子控制系统中的量子态测量和控制系统参数辨识,形成一个以量子信息为反馈信号的量子反馈控制系统,既能根据被控对象的当前状态调整控制策略,又能按照辨识得到的控制系统参数来矫正控制系统的偏差,从而有效的降低系统外部干扰,完成对量子系统的精确控制。
Since the birth of quantum theory at the beginning of the twentieth century, it has changed and affected human society profoundly: it provides a theoretical basis for people to understand and rebuild the micro-world; also it promotes the laser, semiconductor, nuclear, and other high-tech development. With the rapid development quantum theory has integrated with other subjects. Quantum information science is a new discipline generated from the integration of quantum theory and information science, and its rapid development will bring another revolution in scientific community.
Quantum state is an information unit in quantum information science, which need be manipulated in order to deal with quantum information, so the quantum control theory was born to study the active control of quantum systems. With the continuous improvement, quantum control has become a hot international research focus and many gratifying results have been achieved in recent years. Closed-loop control has been the core of classical control, so quantum control began to gradually move to closed-loop control from the initial open-loop control. Closed-loop control is also known as feedback control, in which the information acquisition, the basis for understanding the system status and making control decision, is the key. Quantum system follows the laws of quantum mechanics which is essentially different from classical mechanics, so the classic information acquisition method is no longer applicable to quantum system. We need to explore new technology and method for information acquisition in quantum feedback control.
The main contents on quantum control and the latest development of quantum feedback control are summarized at the beginning of this paper. Then, combined with the character of quantum feedback control, the feasibility of measuring quantum states by quantum tomography is analyzed, and further quantum control system identification based on the quantum process tomography is proposed and quantum feedback control system based on quantum tomography is designed. This paper includes main aspects as following:
(1) Quantum state measurement based on quantum tomography is proposed.
Quantum state as a unit of quantum information is main research object in quantum control. Since quantum states follow the laws of quantum mechanics, quantum non-cloning theorem and uncertainty relationship result in "quantum collapse" phenomenon when quantum states are measured, which makes quantum information acquisition much difficult. We attempt to solve this problem by quantum tomography technology. The term, quantum tomography, comes from medical X-ray computer-aided tomography (CT), and it is a statistical measurement method. According to quantum mechanics we know that a quantum system density matrix contains all the system information, so the system information is totally obtained if the system density matrix can be acquired. Quantum tomography can reconstruct density matrix by measuring a large number of unknown quantum state in the same status to gain quantum state information. Taking example for polarized photon state, we design the experiment of quantum state density matrix reconstruction through quantum tomography, and validate the feasibility of experiment by computer simulation technology. The results show that quantum tomography is an effective and feasible method to obtain quantum state information.
(2) The scheme for quantum control system identification based on quantum process tomography is designed.
In order to design better quantum control systems and achieve more precise control, the performance and parameters of control system need to be understood well. To solve this problem, we propose a scheme of quantum system identification based on quantum process tomography. Quantum process tomography is a main application based on quantum tomography, which is widely used to determine quantum channel parameter in the field of quantum communication. The main process of quantum process tomography is as follows: first, let a set of selected complete input quantum statesρin pass through the quantum channel, and then quantum output statesρout are measured by quantum tomography, and quantum channel parameter is determined according to relationship between input and output states. Following this idea, taking example for magnetic field control of electron spin, we design the control system identification program which is simulated by computer simulation technology. The simulation results proved that this scheme is able to effectively identify quantum control system parameter.
(3) Quantum feedback control based on quantum tomography is proposed.
Quantum feedback control has gradually become a research focus and achieved some results in recent years. However, these feedback control strategy has some flaws, in Markovian quantum feedback, Bayesian quantum feedback and non-Markovian quantum feedback with delay, feedback signals are all classical information, so they can not be regarded as purely quantum feedback control; and for quantum coherent control, feedback control based on quantum cloning and teleportation, although quantum information is used as feedback signal and coherence of quantum systems is maintained in some extent, these systems are very difficult to realize. The realization of these systems is depended on further improvement of experimental techniques. We propose quantum feedback control strategy based on quantum tomography, in which quantum state measurement and quantum control system identification are realized, and quantum feedback control system using quantum information as feedback is formed. In this system, control strategy can be adjusted according to current system status and deviation of control system can be corrected according to control system parameters form identification so as to effectively reduce external interference and realize more precise control of quantum systems.
引文
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