Doctor of Philosophy

dissertationWith the ever-increasing amount of available computing resources and sensing devices, a wide variety of high-dimensional datasets are being produced in numerous fields. The complexity and increasing popularity of these data have led to new challenges and opportunities in visualization. Since most display devices are limited to communication through two-dimensional (2D) images, many visualization methods rely on 2D projections to express high-dimensional information. Such a reduction of dimension leads to an explosion in the number of 2D representations required to visualize high-dimensional spaces, each giving a glimpse of the high-dimensional information. As a result, one of the most important challenges in visualizing high-dimensional datasets is the automatic filtration and summarization of the large exploration space consisting of all 2D projections. In this dissertation, a new type of algorithm is introduced to reduce the exploration space that identifies a small set of projections that capture the intrinsic structure of high-dimensional data. In addition, a general framework for summarizing the structure of quality measures in the space of all linear 2D projections is presented. However, identifying the representative or informative projections is only part of the challenge. Due to the high-dimensional nature of these datasets, obtaining insights and arriving at conclusions based solely on 2D representations are limited and prone to error. How to interpret the inaccuracies and resolve the ambiguity in the 2D projections is the other half of the puzzle. This dissertation introduces projection distortion error measures and interactive manipulation schemes that allow the understanding of high-dimensional structures via data manipulation in 2D projections

The architecture of a quantum programming environment

University of Technology Sydney. Faculty of Engineering and Information Technology.This thesis presents the architecture of quantum programming environment, called QSI, along with its related modules and several quantum experiments. The environment is based on one specific quantum language, namely quantum while-language. Some partial experimental results are also presented within QSI. The first part relates to the architecture, the designing and the implementation of quantum programming environment which provides a new, powerful and flexible environment for developing and implementing quantum programs. First, we study the possible structure of the programming environment which supports a measurement-based case statement and a measurement-based while-loop. These two program constructs are extremely convenient for describing large-scale quantum algorithms, such as quantum random walk-based algorithms. We also define a new assembly language called f-QASM (Quantum Assembly Language with feedback) as an interactive command set. The assembly language is compatible with other low-level instruction sets and can be used to directly drive quantum hardware. Moreover, the simulation of syntax of quantum program and the behaviours within the architecture on the classical computer are discussed. Finally, we consider the work-flow which contains the decomposition of unitary matrix to achieve the goal that executing on Noisy Intermediate-Scale Quantum Computer. The second part concerns the modules based on quantum programming environment: termination analysis module, detective separable unitary module and quantum control module. Along with the architecture, we bring an essential module - termination analysis module for the loop structure. It can analyze sub-bodies of quantum program and suggest the critical termination information. In addition, we improve the Jordan decomposition step in the original algorithm which consumes extended period for analyzing. This improvement also makes the module more robust on executing. A fast permutation algorithm module clarifies the re-ordering algorithm in case of qubits system. It regenerates the program (unitary operator) which is not in pre-ordered sequence. In the detective separable unitary module, we prove sufficient conditions for separable unitary and its approximate scenario. The result shows there does not exist a universal algorithm for potential parallel executing quantum programs without communications (classical or quantum communications). However, in approximate, there exists a scheme for parallel computing without the help of communication. In this part, two examples for parallel computing are given. Last, in quantum control module, an algorithm is suggested towards automatically generating quantum circuits for quantum case-statement. We believe these analysis modules can help the compiler to optimize the implementation of quantum algorithms. The third part is devoted to quantum experiment. First, we focus several experiments which can be operated directly by QSI : Qloop, BB84 protocol and Grover search algorithm. After that, with the help of IBM’s QISKit, two impressive experiments: distinguishing unitary gates and Bell states are given on real quantum computer. Finally, we combine QSI with Microsoft’s LIQUi|> to implement quantum case-statement. These experiments significantly show the quantum power and the scalable framework of the quantum programming environment in practice

Multivariate volume visualization through dynamic projections

pre-printWe propose a multivariate volume visualization framework that tightly couples dynamic projections with a high-dimensional transfer function design for interactive volume visualization. We assume that the complex, high-dimensional data in the attribute space can be well-represented through a collection of low-dimensional linear subspaces, and embed the data points in a variety of 2D views created as projections onto these subspaces. Through dynamic projections, we present animated transitions between different views to help the user navigate and explore the attribute space for effective transfer function design. Our framework not only provides a more intuitive understanding of the attribute space but also allows the design of the transfer function under multiple dynamic views, which is more flexible than being restricted to a single static view of the data. For large volumetric datasets, we maintain interactivity during the transfer function design via intelligent sampling and scalable clustering. Using examples in combustion and climate simulations, we demonstrate how our framework can be used to visualize interesting structures in the volumetric space

Distinguishing unitary gates on the IBM quantum processor

An unknown unitary gates, which is secretly chosen from several known ones, can always be distinguished perfectly. In this paper, we implement such a task on IBM's quantum processor. More precisely, we experimentally demonstrate the discrimination of two qubit unitary gates, the identity gate and the 23π-phase shift gate, using two discrimination schemes -- the parallel scheme and the sequential scheme. We program these two schemes on the \emph{ibmqx4}, a 5-qubit superconducting quantum processor via IBM cloud, with the help of the QSI modules [S. Liu et al.,~arXiv:1710.09500, 2017]. We report that both discrimination schemes achieve success probabilities at least 85%

EP-GIG Priors and Applications in Bayesian Sparse Learning

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases include Gaussian scale mixtures and Laplace scale mixtures. Furthermore, Laplace scale mixtures can subserve a Bayesian framework for sparse learning with nonconvex penalization. The densities of EP-GIG can be explicitly expressed. Moreover, the corresponding posterior distribution also follows a generalized inverse Gaussian distribution. These properties lead us to EM algorithms for Bayesian sparse learning. We show that these algorithms bear an interesting resemblance to iteratively re-weighted $\ell_2$ or $\ell_1$ methods. In addition, we present two extensions for grouped variable selection and logistic regression.Comment: 33 pages, 10 figure