Quantum Theory from Principles, Quantum Software from Diagrams

This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical problems in quantum computing. The main results of the first part include a reconstruction of quantum theory from principles related to properties of sequential measurement and a reconstruction based on properties of pure maps and the mathematics of effectus theory. It also includes a detailed study of JBW-algebras, a type of infinite-dimensional Jordan algebra motivated by von Neumann algebras. In the second part we find a new model for measurement-based quantum computing, study how measurement patterns in the one-way model can be simplified and find a new algorithm for extracting a unitary circuit from such patterns. We use these results to develop a circuit optimisation strategy that leads to a new normal form for Clifford circuits and reductions in the T-count of Clifford+T circuits.Comment: PhD Thesis. Part A is 135 pages. Part B is 95 page

Bifurcation analysis of the Topp model

In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS

We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement

William Hope Hodgson's borderlands: monstrosity, other worlds, and the future at the fin de siècle

William Hope Hodgson has generally been understood as the author of several atmospheric sea-horror stories and two powerful but flawed horror science fiction novels. There has been no substantial study analysing the historical and cultural context of his fiction or its place in the Gothic, horror, and science fiction literary traditions. Through analysing the theme of borderlands, this thesis contextualises Hodgson’s novels and short stories within these traditions and within late Victorian cultural discourse. Liminal other world realms, boundaries of corporeal monstrosity, and the imagined future of the world form key elements of Hodgson’s fiction, reflecting the currents of anxiety and optimism characterising fin-de-siècle British society.Hodgson’s early career as a sailor and his interest in body-building and physical culture colour his fiction. Fin-de-siècle discourses of evolution, entropy, spiritualism, psychical research, and the occult also influence his ideas. In The House on the Borderland (1908) and The Night Land (1912), the known world brushes against other forms of reality, exposing humanity to incomprehensible horrors. In The Ghost Pirates (1909), the sea forms a liminal region on the borderland of materiality and immateriality in which other world encounters can take place. In The Night Land and The Boats of the ‘Glen Carrig’ (1907), evolution gives rise to strange monstrous forms existing on the borderlines of species and identity. In Hodgson’s science fiction—The House on the Borderland and The Night Land—the future of the earth forms a temporal borderland of human existence shaped by fin-de-siècle fears of entropy and the heat-death of the sun. Alongside the work of other writers such as H. G. Wells and Arthur Machen, Hodgson’s four novels respond to the borderland discourses of the fin de siècle, better enabling us to understand the Gothic literature of the period as well as Hodgson’s position as a writer who offers a unique imaginative perspective on his contemporary culture