Thesis (M. Phil.)--University of Hong Kong, 1988.

Includes bibliographical references (p. 62-67).

No description available.

published_or_final_version / Computer Science and Information Systems / Doctoral / Doctor of Philosophy

published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

published_or_final_version / Computer Science / Master / Master of Philosophy

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

With the advancement of Internet technology and the changes in the mode of communications, it is found that much first-hand news have been discussed in Internet forums well before they are reported in traditional mass media. Also, this communication channel provides an effective channel for illegal activities such as dissemination of copyrighted movies, threatening messages and online gambling etc. The law enforcement agencies are looking for solutions to monitor these discussion forums for possible criminal activities and download suspected postings as evidence for investigation. The volume of postings is huge, for 10 popular forums in Hong Kong; we found that there are 300,000 new messages every day. In this thesis, we propose an automatic system that tackles this problem. Our proposed system downloads postings from selected discussion forums continuously and employs data mining techniques to identify hot topics and cluster authors into different groups using word based user profiles. Using these data, we try to locate some useful trends and detect crime from the data, the result is discussed afterward with include advantages and limitations of different approaches and at the end, there is a conclusion of the way to solve those problems and provide future direction of this research. / published_or_final_version / Computer Science / Master / Master of Philosophy

Many computational problems involve massive data. A reasonable solution to those problems should be able to store and process the data in a effective manner. In this thesis, we study sparse representation of data streams and metric spaces, which allows for fast and private computation of heavy hitters from distributed streams, and approximate distance queries between points in a metric space. Specifically, we consider application scenarios where an untrusted aggregator wishes to continually monitor the heavy-hitters across a set of distributed streams. Since each stream can contain sensitive data, such as the purchase history of customers, we wish to guarantee the privacy of each stream, while allowing the untrusted aggregator to accurately detect the heavy hitters and their approximate frequencies. Our protocols are scalable in settings where the volume of streaming data is large, since we guarantee low memory usage and processing overhead by each data source, and low communication overhead between the data sources and the aggregator. We also study fault-tolerant spanners in doubling metrics. A subgraph H for a metric space X is called a k-vertex-fault-tolerant t-spanner ((k; t)-VFTS or simply k-VFTS), if for any subset S _ X with |Sj|≤k, it holds that dHnS(x; y) ≤ t ∙d(x; y), for any pair of x, y ∈ X \ S. For any doubling metric, we give a basic construction of k-VFTS with stretch arbitrarily close to 1 that has optimal O(kn) edges. We also consider bounded hop-diameter, which is studied in the context of fault-tolerance for the first time even for Euclidean spanners. We provide a construction of k-VFTS with bounded hop-diameter: for m ≥2n, we can reduce the hop-diameter of the above k-VFTS to O(α(m; n)) by adding O(km) edges, where α is a functional inverse of the Ackermann's function. In addition, we construct a fault-tolerant single-sink spanner with bounded maximum degree, and use it to reduce the maximum degree of our basic k-VFTS. As a result, we get a k-VFTS with O(k^2n) edges and maximum degree O(k^2). / published_or_final_version / Computer Science / Master / Master of Philosophy

This dissertation presents two circuit simulation techniques to accelerate the simulation time for time-domain transient circuit simulation and circuit thermal analysis. Matrix exponential method is one of the state-of-the-art methods for millionth-order time-domain circuit simulations due to its explicit nature and global stability. The matrix exponential is commonly computed by Krylov subspace methods, which become inefficient when the circuit is stiff, namely when the time constants of the circuit differ by several orders. The truncated Faber series is suitable for accurate evaluation of the matrix exponential even under a highly stiff system matrix arising from practical circuits. Experiments have shown that the proposed approach is globally stable, highly accurate and parallelizable, and avoids excessive memory storage demanded by Krylov subspace methods. Another major issue in circuit simulation is thermal circuit analysis. The use of Hierarchical matrix (H-matrix) in the efficient finite-element-based (FE-based) direct solver implementation for both steady and transient thermal analyses of three-dimensional integrated circuits (3D ICs) is proposed. H-matrix was shown to provide a data-sparse way to approximate the matrices and their inverses with almost linear space and time complexities. This is also true for FE-based transient analysis of thermal parabolic partial differential equations (PDEs). Specifically, the stiffness matrix from a FE-based steady and transient thermal analysis can be represented by H-matrix without approximation, and its inverse and Cholesky factors can be evaluated by H-matrix with controlled accuracy. This thesis shows that the memory and time complexities of the solver are bounded by O(k_1NlogN) and O(K_1^2Nlog〖log〗^2N), respectively, for very large scale thermal systems, where k1 is a small quantity determined by accuracy requirements and N is the number of unknowns in the system. Numerical results validate and demonstrate the effectiveness of the proposed method in terms of predicted theoretical scalability. / published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy