Architecting Early Fault Tolerant Neutral Atoms Systems with Quantum Advantage

Recent advancements in neutral atom platforms have enabled exploration of early fault-tolerant (FT) architectures for applications with quantum advantage, such as quantum dynamics simulations. An efficient fault-tolerant architecture has both spatially efficient quantum error correction codes (low qubit overhead), and efficient methodologies (transversal based gates, extractor based gates, etc.) for logical computation, to minimize overall execution time. Achieving the right balance between space and time can be critical for enabling early FT demonstrations of quantum advantage. In this work, we identify bottlenecks in existing spatially efficient schemes, which tend to be very serial, and do not take advantage of unutilized space. We introduce a teleportation-based scheme that leverages the reconfigurable connectivity of neutral atoms to parallelize logical operations. Our approach achieves up to \textbf{$\mathbf{\sim 3 \times}$ speedup} over extractor architectures at no extra space cost and achieves the best spacetime performance among other viable architectures before accounting for external \textit{resource-states}. To rigorously evaluate performance, we construct explicit quantum advantage benchmarks and \textit{simulate} compilation to a fault-tolerant instruction set, including low-level gate scheduling and shuttling patterns, and resource-state nondeterminism. We find that our speedups still apply and report exact space-time cost along with success probabilities, identifying architectures capable of achieving quantum advantage \textbf{with as little as $\mathbf{11,495}$ atoms and a runtime of $\mathbf{\sim 15}$ hours}.