The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. Despite the large body of literature in quantum coding theory, many important questions, especially those centering on the issue of "good codes" are unresolved. In this dissertation the dominant underlying theme is that of constructing good quantum codes. It approaches this problem from three rather different but not exclusive strategies. Broadly, its contribution to the theory of quantum error correction is threefold. Firstly, it extends the framework of an important class of quantum codes - nonbinary stabilizer codes. It clarifies the connections of stabilizer codes to classical codes over quadratic extension fields, provides many new constructions of quantum codes, and develops further the theory of optimal quantum codes and punctured quantum codes. In particular it provides many explicit constructions of stabilizer codes, most notably it simplifies the criteria by which quantum BCH codes can be constructed from classical codes. Secondly, it contributes to the theory of operator quantum error correcting codes also called as subsystem codes. These codes are expected to have efficient error recovery schemes than stabilizer codes. Prior to our work however, systematic methods to construct these codes were few and it was not clear how to fairly compare them with other classes of quantum codes. This dissertation develops a framework for study and analysis of subsystem codes using character theoretic methods. In particular, this work established a close link between subsystem codes and classical codes and it became clear that the subsystem codes can be constructed from arbitrary classical codes. Thirdly, it seeks to exploit the knowledge of noise to design efficient quantum codes and considers more realistic channels than the commonly studied depolarizing channel. It gives systematic constructions of asymmetric quantum stabilizer codes that exploit the asymmetry of errors in certain quantum channels. This approach is based on a Calderbank- Shor-Steane construction that combines BCH and finite geometry LDPC codes.

In this thesis we study quantum-like representation and simulation of quantum algorithms by using classical computers.The quantum--like representation algorithm (QLRA) was  introduced by A. Khrennikov (1997) to solve the ``inverse Born's rule problem'', i.e. to construct a representation of probabilistic data-- measured in any context of science-- and represent this data by a complex or more general probability amplitude which matches a generalization of Born's rule.The outcome from QLRA matches the formula of total probability with an additional trigonometric, hyperbolic or hyper-trigonometric interference term and this is in fact a generalization of the familiar formula of interference of probabilities. We study representation of statistical data (of any origin) by a probability amplitude in a complex algebra and a Clifford algebra (algebra of hyperbolic numbers). The statistical data is collected from measurements of two dichotomous and trichotomous observables respectively. We see that only special statistical data (satisfying a number of nonlinear constraints) have a quantum--like representation. We also study simulations of quantum computers on classical computers.Although it can not be denied that great progress have been made in quantum technologies, it is clear that there is still a huge gap between the creation of experimental quantum computers and realization of a quantum computer that can be used in applications. Therefore the simulation of quantum computations on classical computers became an important part in the attempt to cover this gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. Of course, it can not be expected that quantum algorithms would help to solve NP problems for polynomial time on classical computers. However, this is not at all the aim of classical simulation.  The second part of this thesis is devoted to adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulations on classical computers. Concretely we represent Simon's algorithm, Deutsch-Josza algorithm, Shor's algorithm, Grover's algorithm and quantum error-correcting codes in the Mathematica symbolic language. We see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include future algorithms in this framework.

Quantum mechanics is the physics of the very small. Quantum computers are devices that utilize the power of quantum mechanics for their computational primitives. Associated to each quantum system is an abstract space known as the Hilbert space. A subspace of the Hilbert space is known as a quantum code. Quantum codes allow to protect the computational state of a quantum computer against decoherence errors. The well-known classes of quantum codes are stabilizer or additive codes, non-additive codes and Clifford codes. This thesis aims at demonstrating a general approach to the construction of the various classes of quantum codes. The framework utilized is the Fourier transform over finite groups. The thesis is divided into four chapters. The first chapter is an introduction to basic quantum mechanics, quantum computation and quantum noise. It lays the foundation for an understanding of quantum error correction theory in the next chapter. The second chapter introduces the basic theory behind quantum error correction. Also, the various classes and constructions of active quantum error-control codes are introduced. The third chapter introduces the Fourier transform over finite groups, and shows how it may be used to construct all the known classes of quantum codes, as well as a class of quantum codes as yet unpublished in the literature. The transform domain approach was originally introduced in (Arvind et al., 2002). In that paper, not all the classes of quantum codes were introduced. We elaborate on this work to introduce the other classes of quantum codes, along with a new class of codes, codes from idempotents in the transform domain. The fourth chapter details the computer programs that were used to generate and test for the various code classes. Code was written in the GAP (Groups, Algorithms, Programming) computer algebra package. The fifth and final chapter concludes, with possible directions for future work. References cited in the thesis are attached at the end of the thesis.

It is my belief that theatre is the telling of stories, and that playwrighting is the creation of those stories. Regardless of the underlying motives (to make the audience think, to make them feel, to offend them or to draw them in,) the core of the theatre world is the storyline. Some critics write of the importance of audience effect and audience reception; after all, a performance can only be so named if at least one person is there to witness it. So much of audience effect is based the storyline itself - that structure of which is created by the power characters have over others. Theatre generalists learn of Aristotle's well-made play structure. Playwrights quickly learn to distinguish between protagonists and antagonists. Actors are routinely taught physicalizations of creating "status" onstage. A plotline is driven by the power that people, circumstances, and even fate exercise over protagonists. Most audience members naturally sympathize with the underdog or victim in a given storyline, and so the submissive or oppressed character becomes (largely) the most integral. By what process, then, is this sense of oppression created in a play? How can oppression/victimization be analyzed with regard to character development? With emerging criticism suggesting that the concept of character is dying, what portrayals of victim have we seen in the late 20th century? What framework can we use to fully understand this complex concept? What are we to see in the future, and how will the concept evolve? In my attempt to answer these questions, I first analyze the definition of "victim" and what categories of victimization exist - the victim of a crime, for example, or the victim of psychological oppression. "Victim" is a word with an extraordinarily complex definition, and so for the purposes of this study, I focus entirely on social victimization - that is, oppression or harm inflicted on a character by their peers or society. I focus on three major elements of this sort of victimization: harm inflicted on a character by another (not by their own actions), harm inflicted despite struggle or protest, and a power or authority endowed on the victimizer by the victim. After defining these elements, I analyze the literary methods by which playwrights can represent or create victimization - blurred lines of authority, expressive text, and the creation of emotion through visual and auditory means. Once the concept of victim is defined and a framework established for viewing it in the theatre, I analyze the victimization of one of American theatre's most famous sufferers - Eugene O'Neill's Yank in The Hairy Ape. To best contextualize this character, I explore the theories of theatre in this time period - reflections of social struggles, the concept of hierarchy, and clearly drawn class lines. I also position The Hairy Ape in its immediate historical and theoretical time period, to understand if O'Neill created a reflection on or of his contemporaries. Finally, I look at the concept of victim through the nonrealistic and nonlinear plays of the 20th century - how it has changed, evolved, or even (as Eleanor Fuchs may suggest) died. I found that my previously established framework for "making victim" has change dramatically to apply to contemporary nonlinear theatre pieces. Through this study, I have found that the lines of victimization and authority are as blurred today in nonrealistic and nonlinear theatre as they were in the seemingly "black and white" dramas of the 1920s and 30s. In my research, I have found the very beginnings of an extraordinarily complex definition of "victim".

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.