Spin degrees of freedom have been extensively explored in the context of quantum information processing. Many proposals of quantum computation architectures use spins as carriers of quantum of information. A central problem is to efficiently generate quantum entanglement between spin qubits which proves to be a crucial resource for quantum information tasks. On the other hand, uncontrollable spin degrees of freedom in the environment of spin qubits are the major causes of errors at low temperature, for example, the lattice nuclear spins hyperfine coupled to single electron spin qubit localized in semiconductor nano-structures. An outstanding problem for scalable quantum computation is to suppress the collective fluctuations from such spin baths so that the coherence time of the spin qubit can be improved. With these two motivations, the problems of suppressing collective spin fluctuations and generating entanglement in various spin ensembles are addressed in this thesis. In the first half of the thesis, two approaches are introduced for suppressing the collective fluctuations in the nuclear spin bath so that the quantum coherence time of electron spin qubit in semiconductor quantum dots can be improved. The first approach works for a coupled double dot system. A theory for the interaction with the nuclear spins is developed when the two-electron singlet state is in resonance with one of the triplet state in moderate external magnetic field. At this resonance condition, the nuclear-electron flip-flop process caused by the hyperfine interaction can lead to a feedback mechanism, which can be used to suppress the nuclear hyperfine field. The second approach works for a single dot system. It is shown that strong pumping of the nuclear spins in dynamic nuclear polarization processes can saturate the nuclear spin bath towards the collective “dark states”. In such dark states, the transverse nuclear field fluctuation can be substantially suppressed compared to the value at thermal equilibrium. Two physical schemes are proposed to realize the nuclear dark states for suppression of the nuclear field fluctuations. In the second half of the thesis, schemes are presented for generating large scale quantum entanglement in two types of spin qubit systems. For atomic spin qubits in optical lattices, schemes are proposed on how to prepare pure spin coherent state (SCS) with low collective spin by incoherent pumping with collective spin raising and lowering operations. Such SCS realize networks of mutually entangled spins which can be idea resources for the quantum telecloning algorithm. For donor nuclear spin qubits in silicon architecture, proposals are shown on how to deterministic prepare Dicke states which constitute an important class of multipartite entangled states. Our scheme is capable of preparing both symmetric and asymmetric Dicke states which form a complete basis set of the spin Hilbert space. The required controls are in situ to the prototype Kane’s quantum computer. The preparation is robust because each desired Dicke state is the steady state under designed pumping process. The schemes presented here also make possible the construction of decoherence free subspaces where quantum information is protected from collective noises. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

動力學解耦(DD) 是一種源於核磁共振(NMR) 的技術。通過快速地控制量子系統， DD可以把不需要的耦合抑制。它可以用來保護處於噪音環境中的量于系統或者用來測量環境噪音譜，甚至它可以用來測量單分子的核磁共振信號。 / 在論文的第一部分，我們主要研究和設計DD技術來保護量子系統。(i)我們提出最套DD來保護量子算符，例如嵌套Uhrig DD (NUDD)。NUDD保護一個相互正交算符集(MOOS); 通過保護這個MOOS算符集， NUDD可以保護所有由MOOS生成的算符。對於量子比特系統，任何一個物理量都可以由NUDD保護;而且，NUDD可以通過單量子比特的操作實現。由於對於單量子比特系統， NUDD 剛好是內層含有偶數階UDD 的quadratic DD (QDD). 所以我們證明了內層含有偶數階UDD 的QDD可以達到設計上所期待的效能。隨著解耦階數的增長， NUDD 只需要多項式增長的脈衝數目，而以前的最套DD(CDD)則要指數增長的脈衝數目。基於保護MOOS 的DD可以用一種通用的有限寬度的服衝代替理想的瞬時脈衝，這種非瞬時的脈衝只會引起正比於脈衝寬度的二階小量的誤差。(ii) 我們也證明了，如果一個動態操控方法能夠以一定的控制精度O(TN +1 )控制一個與不依賴於時間的通屬量子庫耦合的量子系統，那麼它也能夠以同樣階數的精度控制含時的這類系統。這裡T是很短的控制時間。這個結果拓展了各種普適量子控制方法的應用範圍，使它們也可以用於含時系統。(iii) 一個量子系統如果和一個無限大的環境耦合，它會受到馬科夫噪音的影響。這種噪音的關聯函數對於時間的級數展開會有奇數項。我們證明，對於這種噪音， DD不會特別有效，因為退相干只能被DD抑制到一定的階數(以時間的級數展開的階數計算)。在這種噪音下，我們做了DD 的脈衝優化。我們發現，當脈衝比較少的時候，它和UDD序列一樣，但當脈衝比較多的時候，它接近於Carr-Purcell-Meiboom-Gill(CPMG)序列 。對於關聯函數對時間的級數展開含有線性項的情況， CPMG序列在時間很短的情況下是最優的。我們也得到了外加約束條件的做衝序列優化方程組，通過解這方程組，我們得到了一些DD序列，它們可以完全消去由非均勻展寬導致的退相干。(iv) 我們通過一個例子演示了，如果我們不能解析地優化量子控制方案，遺傳算法是很有用的。遺傳算法可以有效地得到優化的控制方案。對比以前的控制方案，我們通過遺傳算法得到的控制方案在性能上好很多。 / 在論文的第二部分，我們提出用原子干涉技術和動力學解捐助〈衝技術來選擇性地測量隨時間變化的引力場。通過惆整脈衝序列的時間，我們可以提取特定頻率下的信號或者噪音譜。我們得到了通用的相移公式。這些公式對於任意的π 脈衝序列都適用。當引力場的漲落對於光子的頻率的變化可以忽略的時候，由引力場引起的相位差和序列時間T的二次方成正比，或者對於某個測量頻率，相位差和脈衝數N成正比。對於引力波探測，這個相位差和自永衝數N的平方成正比，所以，對比於以前的π/2一π一π/2序列，我們的方法提供了額外的N²倍信號放大。 / Dynamical decoupling (DD) is a technique originated from the spin echo techniques in nuclear magnetic resonance (NMR). DD can average out unwanted couplings through fast control on the quantum systems. It has applications in protection of quantum systems from noisy environments, measurements of environmental noise spectra, and even NMR of single molecule. / In the first part of this thesis, we study and design DD techniques for quantum system preservation. (i) We propose nested DD, such as nested Uhrig DD (NUDD), for protection of system operators. NUDD protects a set of mutually orthogonal operators (a MOOS) and hence all system operators generated by the MOOS. For multiqubit systems, any physical quantities can be protected, and NUDD can be implemented by single-qubit operations. For single-qubit systems NUDD reduces to quadratic DD (QDD) with even-order UDD on the inner level. Thus we have proved the validity of QDD with even-order DD on the inner level. NUDD achieves a desired decoupling order with only a polynomial increase in the number of pulses, with exponential saving of the number of pulses as compared with concatenated DD (CDD) of the same decoupling order. DD based on protection of a MOOS can be implemented with pulses of finite amplitude, up to an error in the second order of the pulse durations. (ii) We also establish that if a scheme can control a time-independent system arbitrarily coupled to a generic finite bath over a short period oftime T with control precision O(T[superscript N]⁺¹), it can also realize the control with the same order of precision on smoothly time-dependent systems. This result extends the validity of various universal dynamical control schemes to arbitrary analytically time-dependent systems. (iii) A quantum systems coupled to infinite baths feels a Markovian noise. The short-time correlation function expansion of this noise has odd-order expansion terms. We proof that in this case DD is not very efficient and the decoherence can be suppressed only to some order in short-time T. In the optimization of pulse sequence for a qubit under dephasing due to Markovian noise, the optimal sequences coincide the Uhrig DD sequence when the number N of pulses is small, and they resemble Carr-Purcell-Meiboom-Gill (CPMG) sequences when N is large. For a special case, if the short-time correlation function expansion has a linear term in time, the CPMG sequences are optimal in short-time limit. We have also derived the optimizing equations for suppressing decoherence with arbitrary constraints, and have obtained optimized sequences that can also perfectly eliminate the decoherence due to inhomogeneous broadening. (iv) When analytic results is not possible, we demonstrate that genetic algorithm may be useful by showing an optimized quantum control which has much better performance than the previous results. / In the second part, we combine atom interferometry and dynamical decoupling pulse sequences to selectively measure time-dependent gravitational fields. Using the pulse sequences, we can extract signals or noise with certain frequencies by tuning the timing of the sequences. We obtain the general phase-shift formulas for arbitrary π pulse sequences. When the effect of gravity fluctuations on the light is not considered in the interferometers, the phase shift due to gravitational fields scales quadratically with the duration time T of pulse sequences or linearly with the number N of pulses for a given detection frequency. For gravitational wave detection, the phase shift due to the spacetime fluctuations scales quadratic ally with the number N of pulses, N²-fold enhancement over the traditional π/2-π-π/2 sequences. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Zhenyu = 信息處理和頻譜測定中的量子相干動態操控 / 王振宇. / "December 2011." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 100-112). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Wang, Zhenyu = Xin xi chu li he pin pu ce ding zhong de liang zi xiang gan dong tai cao kong / Wang Zhenyu. / Abstract --- p.iii / Acknowledgment --- p.vii / List of Figures --- p.xiii / List of Appendices --- p.xiv / Chapter 1 --- Introduction and Outline --- p.1 / Chapter I --- Dynamical Control of Quantum Coherence / Chapter 2 --- Introduction --- p.5 / Chapter 3 --- Decoherence and Dynamical Control --- p.11 / Chapter 3.1 --- Quantum decoherence --- p.11 / Chapter 3.1.1 --- Semiclassical picture of decoherence --- p.12 / Chapter 3.1.2 --- Quantum picture of decoherence --- p.13 / Chapter 3.2 --- Dynamical control of open quantum systems --- p.14 / Chapter 3.3 --- Protection of system operators --- p.15 / Chapter 4 --- Dynamical Oecoupling for Quantum Systems --- p.19 / Chapter 4.1 --- Dynamical decoupling for a qubit --- p.19 / Chapter 4.1.1 --- A semiclassical model --- p.19 / Chapter 4.1.1.1 --- Filter functions --- p.21 / Chapter 4.1.2 --- Geometrical view of decoherence and control --- p.22 / Chapter 4.1.3 --- Uhrig dynamical decoupling (UDD) --- p.25 / Chapter 4.2 --- Nested dynamical decoupling for quantum systems --- p.26 / Chapter 4.2.1 --- Mutually orthogonal operation set --- p.26 / Chapter 4.2.2 --- Lowest-order protection of system operators --- p.29 / Chapter 4.2.3 --- Higher-order protection by nesting and concatenation --- p.31 / Chapter 4.2.4 --- Higher-order protection by nested UDD (NUDD) --- p.33 / Chapter 4.2.4.1 --- A theorem on UDD control of time-dependent systerns --- p.34 / Chapter 4.2.4.2 --- Nested Uhrig dynamical decoupling (NUDD) --- p.37 / Chapter 4.2.5 --- Pulses of finite amplitude --- p.39 / Chapter 5 --- Dynamical Control for Time-Dependent Hamiltonians --- p.43 / Chapter 5.1 --- Universal control of time-independent systems --- p.44 / Chapter 5.2 --- Time-dependence in interaction frames --- p.44 / Chapter 5.3 --- Generalization to time-dependent systems --- p.45 / Chapter 6 --- Dynamical Decoupling for Noise Spectra with Soft Cutoff --- p.49 / Chapter 6.1 --- Decoherence functions in frequency domain --- p.50 / Chapter 6.2 --- Performance of dynamical decoupling against noise with soft highfrequency cutoff --- p.53 / Chapter 6.3 --- Relation between noise correlation and high-frequency cutoff --- p.54 / Chapter 6.4 --- Sequence optimization --- p.57 / Chapter 6.4.1 --- Short-time optimization --- p.57 / Chapter 6.4.2 --- Optimization with constraints --- p.59 / Chapter 7 --- Design of Optimal Control by Genetic Algorithm --- p.64 / Chapter 8 --- Summary and Discussions --- p.69 / Chapter II --- Dynamical Decoupling for Gravitational Spectrometry / Chapter 9 --- Introduction --- p.73 / Chapter 10 --- Selective Detection of Gravitational Field by Dynamical Decoupling --- p.75 / Chapter 10.1 --- Atom interferometry --- p.75 / Chapter 10.2 --- Phase shift calculation --- p.76 / Chapter 10.2.1 --- Path phase Δφ[subscript path] --- p.79 / Chapter 10.2.2 --- Laser phase Δφ[subscript laser] --- p.80 / Chapter 10.3 --- Spectroscopy by dynamical decoupling --- p.82 / Chapter 10.4 --- Effects due to gravity gradient --- p.85 / Chapter 11 --- Gravitational Wave Antenna by Dynamical Decoupling --- p.89 / Chapter 11.1 --- Configuration and simple understanding --- p.89 / Chapter 11.1.1 --- Path phase --- p.93 / Chapter 11.1.2 --- Laser phase --- p.95 / Chapter 11.2 --- Gravitational wave signal --- p.96 / Chapter 12 --- Summary and Discussions --- p.99 / Bibliography --- p.100

Chan Yuk-Lin = 並行機上量子自旋模型的對角化 / 陳玉蓮. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 121-123). / Text in English; abstracts in English and Chinese. / Chan Yuk-Lin = Bing xing ji shang liang zi zi xuan mo xing de dui jiao hua / Chen Yulian. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Development of Theory of Magnetism --- p.2 / Chapter 1.3 --- Heisenberg Model --- p.5 / Chapter 1.4 --- Thesis Organization --- p.9 / Chapter 2 --- Introduction to Parallel Computing --- p.11 / Chapter 2.1 --- Architecture of Parallel Computer --- p.12 / Chapter 2.2 --- Symmetric Multiprocessors and Clusters --- p.16 / Chapter 2.2.1 --- Symmetric Multiprocessors --- p.16 / Chapter 2.2.2 --- Cluster --- p.18 / Chapter 2.2.3 --- Clusters versus SMP --- p.19 / Chapter 2.3 --- Hybrid Architectures (Cluster of SMPs) --- p.20 / Chapter 2.4 --- Hardware Platform for Parallel Computing --- p.21 / Chapter 2.4.1 --- SGI Origin 2000 (Origin) --- p.21 / Chapter 2.4.2 --- IBM RS/6000 SP (Orbit) --- p.22 / Chapter 3 --- Parallelization --- p.23 / Chapter 3.1 --- Models of Parallel Programming --- p.24 / Chapter 3.2 --- Parallel Programming Paradigm --- p.26 / Chapter 3.2.1 --- Programming for Distributed Memory Systems: MPI --- p.26 / Chapter 3.2.2 --- Programming for Shared Memory Systems: OpenMP --- p.31 / Chapter 3.2.3 --- Programming for Hybrid Systems: MPI + OpenMP --- p.39 / Chapter 4 --- Performance --- p.42 / Chapter 4.1 --- Writing a Parallel Program --- p.42 / Chapter 4.2 --- Performance Analysis --- p.43 / Chapter 4.3 --- Synchronization and Communication --- p.47 / Chapter 4.3.1 --- Communication modes --- p.47 / Chapter 5 --- Exact Diagonalization --- p.50 / Chapter 5.1 --- Symmetry Invariance --- p.52 / Chapter 5.2 --- Lanczos Method --- p.53 / Chapter 5.2.1 --- Basic Lanczos Algorithm --- p.54 / Chapter 5.2.2 --- Modified Lanczos Method --- p.56 / Chapter 5.3 --- Dynamic Memory Allocation --- p.58 / Chapter 6 --- Parallelization of Exact Diagonalization --- p.62 / Chapter 6.1 --- Parallelization of Lanczos Method --- p.62 / Chapter 6.2 --- Hamiltonian Matrix Decomposition --- p.66 / Chapter 6.2.1 --- Row-Wise Block Decomposition --- p.67 / Chapter 6.2.2 --- Column-Wise Block Decomposition --- p.69 / Chapter 7 --- Results and Discussion --- p.71 / Chapter 7.1 --- Lattice structure --- p.71 / Chapter 7.2 --- Definition of Timing --- p.72 / Chapter 7.3 --- Rowwise vs Columnwise --- p.73 / Chapter 7.4 --- SGI Origin 2000(0rigin) --- p.77 / Chapter 7.4.1 --- Timing Results --- p.77 / Chapter 7.4.2 --- Performance --- p.79 / Chapter 7.5 --- IBM RS/6000 SP(Orbit) --- p.82 / Chapter 7.5.1 --- MPI vs Hybrid --- p.82 / Chapter 7.5.2 --- Timing and Performance --- p.84 / Chapter 7.6 --- Timing on Origin vs Orbit --- p.89 / Chapter 8 --- Conclusion --- p.91 / Chapter A --- Basic MPI Concepts --- p.95 / Chapter A.1 --- Message Passing Interface --- p.95 / Chapter A.2 --- MPI Routine Format --- p.96 / Chapter A.3 --- Start writing a MPI program --- p.96 / Chapter A.3.1 --- The First MPI Program --- p.97 / Chapter A.3.2 --- Sample MPI Program #1 --- p.100 / Chapter A.3.3 --- Sample MPI Program #2 --- p.106 / Chapter B --- Compiling and Running Parallel Jobs in IBM SP --- p.111 / Chapter B.1 --- Compilation --- p.111 / Chapter B.1.1 --- Compiler Options --- p.112 / Chapter B.2 --- Running Jobs --- p.114 / Chapter B.2.1 --- Loadleveler --- p.114 / Chapter B.2.2 --- Serial Job Script --- p.114 / Chapter B.2.3 --- Parallel Job Script : MPI Program --- p.115 / Chapter B.2.4 --- Parallel Job Script: OpenMP Program --- p.117 / Chapter B.2.5 --- Parallel Job Script: Hybrid MPI/OpenMP Program . . --- p.118 / Chapter B.2.6 --- LoadLeveler Commands --- p.120 / Bibliography --- p.123

Yan, Changqing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 92-97). / Abstracts in English and Chinese. / ABSTRACT (ENGLISH) --- p.iii / ABSTRACT (CHINESE) --- p.iv / ACKNOWLEDGMENTS --- p.v / LIST OF ABBREVIATIONS --- p.vi / TABLE OF CONTENTS --- p.vii / LIST OF FIGURES --- p.ix / LIST OF TABLES --- p.x / Chapter CHAPTER ONE: --- BACKGROUND INFORMATION --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Deoxyribonucleic Acid --- p.2 / Chapter 1.3 --- DNA Studies --- p.9 / Chapter 1.4 --- Cisplatin Studies --- p.11 / Chapter 1.5 --- Scope of the Thesis --- p.13 / Chapter CHAPTER TWO: --- METHODOLOY AND COMPUTATION --- p.16 / Chapter 2.1 --- Introduction --- p.16 / Chapter 2.2 --- Molecular Dynamics Simulation --- p.16 / Chapter 2.3 --- Quantum Mechanics Calculation --- p.23 / Chapter 2.4 --- Verification of Methodology --- p.25 / Chapter 2.4.1 --- Backbone Torsion Angles --- p.25 / Chapter 2.4.2 --- N7-N7 Distance --- p.30 / Chapter 2.4.3 --- Location of HOMO --- p.33 / Chapter 2.5 --- Summary --- p.35 / Chapter CHAPTER THREE: --- UNDERSTANDING OF THE CISPLATIN-DNA CROSSLINKS --- p.36 / Chapter 3.1 --- Introduction --- p.36 / Chapter 3.2 --- MO Analysis --- p.37 / Chapter 3.3 --- Potential Binding Products with the Ligand --- p.37 / Chapter 3.3.1 --- "1,2-d(GpG) Intrastrand Crosslink" --- p.43 / Chapter 3.3.2 --- "l,2-d(ApG) Intrastrand Crosslink" --- p.43 / Chapter 3.3.3 --- "l,3-d(GpXpG) Intrastrand Crosslink" --- p.44 / Chapter 3.3.4 --- d(GpC)d(GpC) Interstrand Crosslink --- p.44 / Chapter 3.3.5 --- d(GpXpC)d(GpXpC) Interstrand Crosslink --- p.44 / Chapter 3.3.6 --- Summary --- p.45 / Chapter 3.4 --- Potential Binding Products Analysis --- p.47 / Chapter 3.4.1 --- Site Identification Convention --- p.47 / Chapter 3.4.2 --- Potential Binding Products Analysis --- p.48 / Chapter 3.4.3 --- Applications --- p.53 / Chapter 3.5 --- Cisplatin-DNA Crosslink Products Analysis --- p.56 / Chapter 3.5.1 --- "1,2-d(GpG) and l,2-d(ApG) Intrastrand Crosslinks" --- p.61 / Chapter 3.5.2 --- "l,3-d(GpXpG) Intrastrand and d(GpXpC)d(GpXpC) Interstrand Crosslinks" --- p.62 / Chapter 3.5.3 --- d(GpC)d(GpC) Interstrand Crosslinks --- p.63 / Chapter 3.5.4 --- Platination at Terminal Positions --- p.65 / Chapter 3.6 --- Summary --- p.65 / Chapter CAHPTER FOUR: --- CONCLUDING REMARKS --- p.67 / APPENDIX I: BACKBONE TORSION ANGLES AND SUGAR RING CONFORMATIONS OF THE OPTIMIZED GEOMETRIES --- p.69 / APPENDIX II: BACKBONE TORSION ANGLES OF THE EXPERIMENTAL SEQUENCES FROM NUCLEIC ACID DATABASE (NDB) --- p.77 / REFERENCES --- p.92

Le développement de la Théorie du Calcul Quantique provient de l'idée qu'un ordinateur est avant tout un système physique, de sorte que ce sont les lois de la Nature elles-mêmes qui constituent une limite ultime sur ce qui peut être calculé ou non. L'intérêt pour cette discipline fut stimulé par la découverte par Peter Shor d'un algorithme quantique rapide pour factoriser un nombre, alors qu'actuellement un tel algorithme n'est pas connu en Théorie du Calcul Classique. Un autre résultat important fut la construction par Lov Grover d'un algorithme capable de retrouver un élément dans une base de donnée non-structurée avec un gain de complexité quadratique par rapport à tout algorithme classique. Alors que ces algorithmes quantiques sont exprimés dans le modèle ``standard' du Calcul Quantique, où le registre évolue de manière discrète dans le temps sous l'application successive de portes quantiques, un nouveau type d'algorithme a été récemment introduit, où le registre évolue continûment dans le temps sous l'action d'un Hamiltonien. Ainsi, l'idée à la base du Calcul Quantique Adiabatique, proposée par Edward Farhi et ses collaborateurs, est d'utiliser un outil traditionnel de la Mécanique Quantique, à savoir le Théorème Adiabatique, pour concevoir des algorithmes quantiques où le registre évolue sous l'influence d'un Hamiltonien variant très lentement, assurant une évolution adiabatique du système. Dans cette thèse, nous montrons tout d'abord comment reproduire le gain quadratique de l'algorithme de Grover au moyen d'un algorithme quantique adiabatique. Ensuite, nous montrons qu'il est possible de traduire ce nouvel algorithme adiabatique, ainsi qu'un autre algorithme de recherche à évolution Hamiltonienne, dans le formalisme des circuits quantiques, de sorte que l'on obtient ainsi trois algorithmes quantiques de recherche très proches dans leur principe. Par la suite, nous utilisons ces résultats pour construire un algorithme adiabatique pour résoudre des problèmes avec structure, utilisant une technique, dite de ``nesting', développée auparavant dans le cadre d'algorithmes quantiques de type circuit. Enfin, nous analysons la résistance au bruit de ces algorithmes adiabatiques, en introduisant un modèle de bruit utilisant la théorie des matrices aléatoires et en étudiant son effet par la théorie des perturbations. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished