量子门的制备及最大纠缠态的实现
发布时间：2021-08-17 16:29
量子计算机能够解决经典研究无法解决的问题。量子电路是这种计算机的主要构建模块。任何具有任意精度的量子电路都可以通过使用CNOT和单量子位门的组合来实现,其中包括Hadamard门。单个和多个耦合量子门的完全和精确控制被认为是量子物理学中强烈认知以及量子计算等现代应用的首要任务。本文的主要目的是准备两个重要的量子门,Hadamard和CNOT门,当由于与环境或相邻量子位的相互作用而消散时具有高保真度和快速收敛性。然后,当它们在量子电路模型中组合在一起时,证明Hadamard和CNOT门的评估产生最大纠缠态Bell状态。要实现这些个目标,需要在系统的时间演化和控制中进行高精度的研究。在系统时间演化方面,提出了一种用于制备Hadamard门的新技术,该技术在存在环境耗散的情况下实现了将酉时间动力学演化转换为向量空间。针对CNOT门的制备,提出了一种分解方法的实现。在该方法中,系统的时间演化是由有限时间片上的通过一系列分解的算子通过有限的时间片设计的。在控制方面,基于Lyapunov稳定性定理,设计了两种新的Lyapunov函数,以保证系统的稳定性。因此,控制律被设计用于引导时间演化达到所期望...
【文章来源】：中国科学技术大学安徽省 211工程院校 985工程院校
【文章页数】：96 页
【学位级别】：博士
【文章目录】：
Abstract
中文摘要
Chapter 1 Introduction
1.1 Quantum state
1.2 Quantum gate
1.3 Quantum control tasks and objectives
1.3.1 Quantum gates preparation and suppressing the dissipation caused bythe environment
1.3.2 Quantum gates preparation and deduction the unwanted effects ofcoupling between the qubits
1.4 Thesis overview
Chapter 2 Theory of quantum control systems
2.1 The models of quantum control systems
2.1.1 Schrodinger Equation
2.1.2 Liouville Equation
2.1.3 Markovian Master Equations
2.1.4 Non-Markovian Master Equations
2.2 The formations of quantum control systems
2.3 Control objectives, and performance indices
2.3.1 Control objectives
2.3.2 Performance indices
2.4 Bloch sphere representation
2.4.1 Bloch sphere to show the pure states
2.4.2 Bloch sphere to show the mixed states
2.5 Lie algebra decompositions
2.5.1 Lie Algebras
2.5.2 Semisimple Lie algebras and cartan decomposition
Chapter 3 Quantum gate preparation for a two-level system via dynamical-transferred evolution based on the Lyapunov stability theorem
3.1 The system modeling and dynamical transferring
3.2 Design of Lyapunov-based control laws
3.3 Numerical simulation and performance analysis
3.3.1 Analysis of Preparation the Hadamard Gate via performance indices
3.3.2 The evolution of State-transferring
3.3.3 Comparison and result discussion
Chapter 4 Realization of quantum gates via decomposition method in a four-levelquantum system
4.1 Mathematic model for the two-spin system and description of relatedHamiltonians
4.2 Analysis of quantum CNOT gate via Cartan decomposition
4.2.1 Canonical decomposition of the unitary gate
4.2.2 Realization process of the CNOT gate by Cartan Decomposition
4.3 Design of Lyapunov control fields
4.4 Numerical experiments and result discussions
Chapter 5 Preparing the Hadamard and CNOT gates to realize the maximumentangled states
5.1 Model description of the single-spin and two-spin systems
5.2 Realizing of Hadamard and CNOT gates to achieve the Bell states viadecomposition method
5.2.1 Canonical decomposition of the unitary gates
5.2.2 Realization process of the Hadamard and CNOT gates by CartanDecomposition
5.2.2.1 Cartan Decomposition process in realization of the Hadamard gate
5.2.2.2 Cartan Decomposition process in realization of the CNOT gate
5.3 The design process of control function and control laws
5.4 Experimental simulations and result discussions
Chapter 6 Conclusion
References
Acknowledgement
Published Paper Lists
List of Foundations participation
本文编号：3348106
【文章来源】：中国科学技术大学安徽省 211工程院校 985工程院校
【文章页数】：96 页
【学位级别】：博士
【文章目录】：
Abstract
中文摘要
Chapter 1 Introduction
1.1 Quantum state
1.2 Quantum gate
1.3 Quantum control tasks and objectives
1.3.1 Quantum gates preparation and suppressing the dissipation caused bythe environment
1.3.2 Quantum gates preparation and deduction the unwanted effects ofcoupling between the qubits
1.4 Thesis overview
Chapter 2 Theory of quantum control systems
2.1 The models of quantum control systems
2.1.1 Schrodinger Equation
2.1.2 Liouville Equation
2.1.3 Markovian Master Equations
2.1.4 Non-Markovian Master Equations
2.2 The formations of quantum control systems
2.3 Control objectives, and performance indices
2.3.1 Control objectives
2.3.2 Performance indices
2.4 Bloch sphere representation
2.4.1 Bloch sphere to show the pure states
2.4.2 Bloch sphere to show the mixed states
2.5 Lie algebra decompositions
2.5.1 Lie Algebras
2.5.2 Semisimple Lie algebras and cartan decomposition
Chapter 3 Quantum gate preparation for a two-level system via dynamical-transferred evolution based on the Lyapunov stability theorem
3.1 The system modeling and dynamical transferring
3.2 Design of Lyapunov-based control laws
3.3 Numerical simulation and performance analysis
3.3.1 Analysis of Preparation the Hadamard Gate via performance indices
3.3.2 The evolution of State-transferring
3.3.3 Comparison and result discussion
Chapter 4 Realization of quantum gates via decomposition method in a four-levelquantum system
4.1 Mathematic model for the two-spin system and description of relatedHamiltonians
4.2 Analysis of quantum CNOT gate via Cartan decomposition
4.2.1 Canonical decomposition of the unitary gate
4.2.2 Realization process of the CNOT gate by Cartan Decomposition
4.3 Design of Lyapunov control fields
4.4 Numerical experiments and result discussions
Chapter 5 Preparing the Hadamard and CNOT gates to realize the maximumentangled states
5.1 Model description of the single-spin and two-spin systems
5.2 Realizing of Hadamard and CNOT gates to achieve the Bell states viadecomposition method
5.2.1 Canonical decomposition of the unitary gates
5.2.2 Realization process of the Hadamard and CNOT gates by CartanDecomposition
5.2.2.1 Cartan Decomposition process in realization of the Hadamard gate
5.2.2.2 Cartan Decomposition process in realization of the CNOT gate
5.3 The design process of control function and control laws
5.4 Experimental simulations and result discussions
Chapter 6 Conclusion
References
Acknowledgement
Published Paper Lists
List of Foundations participation
本文编号：3348106
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