Studies in matrix perturbation and robust statistics

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.Includes bibliographical references (p. 124-132).by Yanyuan Ma.Ph.D

Resource optimization for fault-tolerant quantum computing

In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error correction procedures, circumventing existing no-go theorems. We then show how to simplify ancilla preparation, reducing the cost of error correction by more than a factor of four. Using this optimized ancilla preparation, we develop improved techniques for proving rigorous lower bounds on the noise threshold. Additional overhead can be incurred because quantum algorithms must be translated into sequences of gates that are actually available in the quantum computer. In particular, arbitrary single-qubit rotations must be decomposed into a discrete set of fault-tolerant gates. We find that by using a special class of non-deterministic circuits, the cost of decomposition can be reduced by as much as a factor of four over state-of-the-art techniques, which typically use deterministic circuits. Finally, we examine global optimization of fault-tolerant quantum circuits under physical connectivity constraints. We adapt techniques from VLSI in order to minimize time and space usage for computations in the surface code, and we develop a software prototype to demonstrate the potential savings.Comment: 231 pages, Ph.D. thesis, University of Waterlo

The ambivalence of urban obsolescence: questioning emancipatory design practices in Phnom Penh, Cambodia

The research draws on the transdisciplinary debate, emerging within urban studies, which highlights the proliferation of fenced environments in the contemporary city. The research considers such environments to be tangible manifestations of dynamics of securitisation, control, privatisation, commodification, exclusion, depoliticisation. The research analyses therefore the production of the fenced city as essentially revolving around two archetypes: the gated community and the camp, as expressions respectively of phenomena of voluntary seclusion and forced confinement. The research interprets such archetypes from a twofold perspective: drawing, on one side, from governmental studies; and on the other side, from urban design studies. Expanding the trans-disciplinary character of the research (drawing from disciplines such as urban history, political economy, gender studies, performative arts), the research constructs a debate on urbanisms characterised by obsolescing phenomena: spaces of abandonment and dereliction, but also apparently leftover spaces, or interstitial and marginal ones. The analysis of such debate highlights a latent ambivalence: on one side, obsolescence is seen to partake into the production of the fenced city, through cycles of ruination, demolition, displacement; on the other side, obsolescence is read as emancipating from such production, creating the conditions for opening up, decommodifying, repoliticising the contemporary fenced city. Do camp-like or gated-community-like dynamics emerge even within obsolescing urbanisms? Or, conversely, do emancipatory practices emerge? The research attempts to answer such questions, challenging both sides of the debate. It does so investigating, at multiple scales, the reality of several obsolescing urbanisms in Phnom Penh, Cambodia. The research concludes suggesting an epistemological shift, that would place obsolescence at the centre of the understanding of the current dynamics of urban transformation. In so doing, the research questions the relevance of its (theory-driven) method in framing and guiding urban research; and the relevance of its reflections on emancipatory practices – for the current debate on the social agency of urban design and architecture; and for the current dynamics of transformation in Phnom Penh