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This thesis investigates techniques for the automated optimization of quantum circuits. In the first part we develop an exponential time algorithm for synthesizing minimal depth quantum circuits. We combine this with effective heuristics for reducing the search space, and show how it can be extended to different optimization problems. We then use the algorithm to compute circuits over the Clifford group and T gate for many of the commonly used quantum gates, improving upon the former best known circuits in many cases. In the second part, we present a polynomial time algorithm for the re-synthesis of CNOT and T gate circuits while reducing the number of phase gates and parallelizing them. We then describe different methods for expanding this algorithm to optimize circuits over Clifford and T gates.

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The design of modern integrated circuits is overwhelmingly complicated due to the enormous number of cells in a typical modern circuit. To deal with this difficulty, the design procedure is broken down into a set of disjoint tasks. Circuit layout is the task that refers to the physical realization of a circuit from its functional description. In circuit layout, a connection-list called netlist of cells and nets is given. Placement and routing are subtasks associated with circuit layout and involve determining the geometric locations of the cells within the placement area and connecting cells sharing common nets. In performing the placement and the routing of the cells, minimum placement area, minimum delay and other performance constraints need to be observed. In this work, we propose and investigate new approaches to placement and routing problems. Specifically, for the placement subtask, we propose new convex programming formulations to estimate wirelength and force cells to spread within the placement area. As opposed to previous approaches, our approach is partitioning free and requires no hard constraints to achieve cell spreading within the placement area. The result of the global optimization of the new convex models is a global placement which is further improved using a Tabu search based iterative technique. The effectiveness, robustness and superiority of the approach are demonstrated on a set of nine benchmark industrial circuits. With regard to the routing subtask, we propose a hybrid methodology that combines Tabu search and Stochastic Evolution as a search engine in a new channel router. We also propose a new scheme based on Utility Theory for selecting and assigning nets to tracks in the channel. In this scheme, problem-domain information expressed in the form of utility functions is used to guide the search engine to explore the search space effectively. The effectiveness and robustness of the approach is demonstrated on five industrial benchmarks.

Ongoing efforts to quantify changes in quality of life attributable to low vision rehabilitation have focused on the utility of a single test instrument to measure this multidimensional concept. It is hypothesized that quality of life is best assessed using multiple instruments to capture some of its component facets, including functional status and psychosocial impact. Low vision devices have a predictably spontaneous impact on functional vision status, but associated psychosocial impact occurs with different magnitudes and over more protracted time intervals. The National Eye Institute Visual Function Questionnaire (NEI VFQ-25) measures the functional status of individuals in key vision areas that are associated with quality of life. The Psychosocial Impact of Assistive Devices Scale (PIADS) is an instrument that measures the psychosocial impact of assistive device intervention in three quality of life domains: competence, adaptability, and self-esteem. 68 participants were obtained from an ongoing parent study. These participants were recruited through the Low Vision Clinic at the University of Waterloo. They had a primary diagnosis of age-related macular degeneration (ARMD) and were obtaining a CCTV system for the first time. Assessments from the parent study used in this thesis included follow-up from 2 weeks, 1 month, 3 months, and 6 months post-adoption of the CCTV. The two tests administered were to measure functional vision status (NEI VFQ-25) and perceived psychosocial impact (PIADS), according the framework outlined by the Consortium for Assistive Technology Outcomes Research (CATOR). Multivariate repeated-measures ANVOA results confirmed that CCTV systems have an immediate and robust effect on the daily visual functioning of their users, and that this effect is stable over long periods of device use. The psychosocial impact of CCTV device use peaks in the shorter term and then seems to wane in the longer term for reasons that are not yet understood. The NEI VFQ-25 and the PIADS appear to have differential sensitivity to important influences on low vision rehabilitation outcomes. This project has demonstrated the value of longitudinal outcomes research in low vision rehabilitation. After obtaining a CCTV, visual function status remains static while psychosocial impact is dynamic during 6-months of follow-up.

Today’s advances in communication systems and VLSI circuits increases the performance requirements and complexity of circuits. The performance of RF and mixed-signal circuits is normally limited by the nonlinear behavior of the transistors used in the design. This makes simulation of nonlinear circuits more important. Volterra series is a method used for simulation of mildly nonlinear circuits. Using Volterra series the response of the nonlinear circuit is converted into a sum of multiple linear circuit responses. Thus, using Volterra series, simulation of nonlinear circuits in frequency-domain analysis becomes possible. However, Volterra series is not able to simulate strongly nonlinear circuits such as saturated Power Amplifiers. In this thesis, a new time-varying Volterra analysis is presented. The time-varying Volterra analysis is the generalization of conventional Volterra analysis where instead of using a DC expansion point a time-varying waveform has been used. Employing a time-varying expansion waveform for Volterra analysis, time-varying Volterra achieves better accuracy than conventional Volterra. The time-varying expansion waveforms are derived using a fast pre-analysis of the circuit. Using numerical examples, it has been shown that the time-varying Volterra is capable of simulating nonlinear circuits with better accuracy than conventional Volterra analysis. The time-varying Volterra analysis in both time and frequency domains are discussed in this thesis. The time-varying Volterra analysis has been used to simulate a saturated Class-F Power Amplifier in frequency-domain. The simulation results show good agreement with ELDO® steady-state and Harmonic Balance simulation results. The proposed method manages to simulate nonlinear circuits, such as saturated Power Amplifier, mixers and nonlinear microwave circuits, with good accuracy. Also, this method can be used to simulate circuit with large number of nonlinear elements without the convergence issues of Harmonic Balance.

This thesis has been written at Linköping University for the company Instrument Control Sweden AB (ICS). ICS is a small company located in Linköping that develops software and hardware for Unmanned Aerial Vehicles, UAV. At present, ICS has a fully functional autopilot called EasyPilot but they want to reduce the autopilot’s size to make it more attractive. The purpose of this thesis was to investigate if it was possible to reduce the size of the autopilot and how, in that case, it would be done. It was also necessary to examine whether the old processors should be replaced by new ones and how hard it would be to convert the old software to these new processors. To succeed with the goals many of the old components had to be changed for new, smaller ones. Some less necessary parts were also completely removed. The results showed that the size could be reduced quite a bit, exactly how much is hard to say since no PCB-layout were done. By doing some programming tests on the new components it could be shown that some parts of the old code could be reused on the new design. It was mainly algorithms and other calculations. However, a lot of new code still had to be written in order to successfully convert the old software to the new hardware.