Title:Â Quantum advantage of transversal IQP sampling with logical qubits
Abstract:Â Quantum computational advantage and quantum error correction are important frontiers in modern quantum information science. I will present a scalable fault-tolerant approach to quantum advantage that is hardware-efficient for reconfigurable atom arrays, with initial demonstrations on up to 48 logical qubits realized in Bluvstein et al. [Nature 626, 7997 (2024)]. The centerpiece of our approach is using the transversal gate-set of the [[2^D,D,2]] color code to 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.