Browsing Mathematics (Faculty of) by Title
Now showing items 19161935 of 2621

Quantitative Analyses of Software Product Lines
(University of Waterloo, 20220118)A software productline (SPL) is a family of related software systems that are jointly developed and reuse a set of shared assets. Each individual software system in an SPL is called a software product and includes a set ... 
Quantitative Analysis of Extreme Risks and Extremal Dependence in Insurance and Finance
(University of Waterloo, 20190925)In this thesis, we aim at a quantitative understanding of extreme risks and extremal depen dence in insurance and finance. We use regularly varying distribution functions in extreme value theory (EVT) to model extreme ... 
Quantitative Approaches to the Cancer Stem Cell Hypothesis
(University of Waterloo, 20150508)In this thesis, phenotype switching in cancer cell populations is modeled. We focus on the behavior of cells at the phenotypic level and present mathematical models to capture the results of available experiments. The ... 
Quantitative Testing of Probabilistic Phase Unwrapping Methods
(University of Waterloo, 2001)The reconstruction of a phase surface from the observed principal values is required for a number of applications, including synthetic aperture radar (SAR) and magnetic resonance imaging (MRI). However, the process of ... 
Quantum algorithms for searching, resampling, and hidden shift problems
(University of Waterloo, 20120921)This thesis is on quantum algorithms. It has three main themes: (1) quantum walk based search algorithms, (2) quantum rejection sampling, and (3) the Boolean function hidden shift problem. The first two parts deal with ... 
Quantum Cellular Automata: Theory and Applications
(University of Waterloo, 20070926)This thesis presents a model of Quantum Cellular Automata (QCA). The presented formalism is a natural quantization of the classical Cellular Automata (CA). It is based on a lattice of qudits, and an update rule consisting ... 
Quantum Compression and Quantum Learning via Information Theory
(University of Waterloo, 20201221)This thesis consists of two parts: quantum compression and quantum learning theory. A common theme between these problems is that we study them through the lens of information theory. We first study the task of visible ... 
Quantum Cost Models for Cryptanalysis of Isogenies
(University of Waterloo, 20190501)Isogenybased cryptography uses keys large enough to resist a farfuture attack from Tani’s algorithm, a quantum random walk on Johnson graphs. The key size is based on an analysis in the query model. Queries do not ... 
Quantum fields and machine learning
(University of Waterloo, 20200925)In this thesis, we use detector models to study various properties of quantum fields. One such property is the correlations present in fields. It is known that two uncorrelated detectors, upon coupling to a quantum field, ... 
Quantum Indefinite Spacetime: Part II
(University of Waterloo, 20180910)We adopt an operational mode of thinking to study spacetime fluctuations and their impacts on questions of quantum gravity. Particular emphasis is put on studying causal structure fluctuations. The study is guided by the ... 
Quantum independence and chromatic numbers
(University of Waterloo, 20190828)In this thesis we are studying the cases when quantum independence and quantum chromatic numbers coincide with or differ from their classical counterparts. Knowing about the relation of chromatic numbers separation to the ... 
Quantum Information and Variants of Interactive Proof Systems
(University of Waterloo, 20110824)For nearly three decades, the model of interactive proof systems and its variants have been central to many important and exciting developments in computational complexity theory such as exact characterization of some well ... 
Quantum information in security protocols
(University of Waterloo, 20220118)Information security deals with the protection of our digital infrastructure. Achieving meaningful realworld security requires powerful cryptographic models that can give strong security guarantees and it requires ... 
Quantum Information Processing with Adversarial Devices
(University of Waterloo, 20100609)We consider several applications in blackbox quantum computation in which untrusted physical quantum devices are connected together to produce an experiment. By examining the outcome statistics of such an experiment, and ... 
Quantum Random Access Codes with Shared Randomness
(University of Waterloo, 20090522)We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This ... 
Quantum Reference Frames and The Poincaré Symmetry
(University of Waterloo, 20140919)The concept of a reference frame has been a part of the physical formalism since the early days of physics. The reference frame was always understood as a physical system with respect to which states of other physical ... 
Quantum Rejection Sampling
(University of Waterloo, 20150121)Let H be a finite dimensional Hilbert space and ρ, σ ∈ D(H) be quantum states in H such that S(ρσ) is finite. In this thesis, we consider the following communication task involving two parties Alice and Bob. Suppose ... 
Quantum Snake Walk on Graphs
(University of Waterloo, 20100113)Quantum walks on graphs have been proven to be a useful tool in quantum algorithm construction for various problems. In this thesis we introduce a new type of continuoustime quantum walk on graphs called the quantum snake ... 
Quantum Speedups for Boolean Satisfiability and DerivativeFree Optimization
(University of Waterloo, 20140421)In this thesis, we have considered two important problems, Boolean satisfiability (SAT) and derivative free optimization in the context of large scale quantum computers. In the first part, we survey well known classical ... 
Quantum State Local Distinguishability via Convex Optimization
(University of Waterloo, 20150824)Entanglement and nonlocality play a fundamental role in quantum computing. To understand the interplay between these phenomena, researchers have considered the model of local operations and classical communication, or LOCC ...