發(fā)布時(shí)間：2021-08-17 16:29

　　量子計(jì)算機(jī)能夠解決經(jīng)典研究無法解決的問題。量子電路是這種計(jì)算機(jī)的主要構(gòu)建模塊。任何具有任意精度的量子電路都可以通過使用CNOT和單量子位門的組合來實(shí)現(xiàn),其中包括Hadamard門。單個(gè)和多個(gè)耦合量子門的完全和精確控制被認(rèn)為是量子物理學(xué)中強(qiáng)烈認(rèn)知以及量子計(jì)算等現(xiàn)代應(yīng)用的首要任務(wù)。本文的主要目的是準(zhǔn)備兩個(gè)重要的量子門,Hadamard和CNOT門,當(dāng)由于與環(huán)境或相鄰量子位的相互作用而消散時(shí)具有高保真度和快速收斂性。然后,當(dāng)它們?cè)诹孔与娐纺Ｐ椭薪M合在一起時(shí),證明Hadamard和CNOT門的評(píng)估產(chǎn)生最大糾纏態(tài)Bell狀態(tài)。要實(shí)現(xiàn)這些個(gè)目標(biāo),需要在系統(tǒng)的時(shí)間演化和控制中進(jìn)行高精度的研究。在系統(tǒng)時(shí)間演化方面,提出了一種用于制備Hadamard門的新技術(shù),該技術(shù)在存在環(huán)境耗散的情況下實(shí)現(xiàn)了將酉時(shí)間動(dòng)力學(xué)演化轉(zhuǎn)換為向量空間。針對(duì)CNOT門的制備,提出了一種分解方法的實(shí)現(xiàn)。在該方法中,系統(tǒng)的時(shí)間演化是由有限時(shí)間片上的通過一系列分解的算子通過有限的時(shí)間片設(shè)計(jì)的。在控制方面,基于Lyapunov穩(wěn)定性定理,設(shè)計(jì)了兩種新的Lyapunov函數(shù),以保證系統(tǒng)的穩(wěn)定性。因此,控制律被設(shè)計(jì)用于引導(dǎo)時(shí)間演化達(dá)到所期望... 

【文章來源】：中國科學(xué)技術(shù)大學(xué)安徽省 211工程院校 985工程院校

【文章頁數(shù)】：96 頁

【學(xué)位級(jí)別】：博士

【文章目錄】：
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



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