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Abstract: Demonstrating quantum computation beyond the capabilities of classical methods has been one of the most important challenges in the quantum computing effort. I will present a scalable fault-tolerant approach to quantum advantage, whose smallest interesting instances have recently been demonstrated using reconfigurable atom arrays [Nature 626, 7997 (2024)]. The centerpiece of our approach is the transversal gate-set of the [[2^D,D,2]] color code, which we show can realize arbitrary degree-D instantaneous quantum polynomial (IQP) computation in a hardware-efficient manner. I will first give an overview of our results, and then dive into some details of the complex IQP circuits, in particular, their scrambling properties, simulation complexity, and behavior under noise. I will show a statistical model that can be used to analyze two-copy average properties of random IQP circuits with CNOT gates in arbitrary geometries. I will give an outlook towards increasing the code distance, and using Bell measurements for efficiently validated quantum advantage demonstrations.