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This book employs end-to-end materials-to-systems modeling to show how topological properties of emerging quantum materials can be useful as low-power accelerators of classical computing hardware in edge intelligence. Skyrmions are ultra-small and topologically protected, so that their self-focusing, notch-driven synchronization and current-driven placement along a racetrack can be used to encode analog thresholds for random forest classifiers and weights in optimization problems for temporal computing such as DNA alignment, image classification, and speech recognition in robotics. A comparable silicon CMOS-based digital framework is estimated to incur 40x more components, 40x more energy, and 1000x more energy-delay product due to data volatility and the need for costly analog-to-digital converters. A second example of topologically stabilized computing discussed in the thesis is the strain-driven rotation of a magnet on a 3D topological insulator to gate its surface states and act as a row-column selector in a crossbar array. Selected rows can then be fed into a sense amplifier to do in-memory-computing, reducing the von Neumann latency associated with costly data transfer between memory and processing cores. The studies reported within combine material models including non-idealities and quantum transport, and circuit models including energy consumption in the overhead circuitry.