Transversal Surface-Code Game Powered by Neutral Atoms

Neutral atom technologies have opened the door to novel theoretical advances in surface-code protocols for fault-tolerant quantum computation (FTQC), offering a compelling alternative to lattice surgery by leveraging transversal gates. However, a crucial gap remains between the theory of FTQC and its practical realization on neutral atom systems; most critically, a key theoretical requirement -- that syndrome extraction must be performed frequently enough to keep error accumulation below a threshold constant -- is difficult to satisfy in a scalable manner in conventional zoned approach. In this work, we develop a comprehensive theoretical framework that closes such a gap, bridging theoretical advances in surface-code fault-tolerant protocols with capabilities of neutral atoms. Building on the "game of surface code" framework originally developed for superconducting qubits, we introduce an alternative game-based paradigm for transversal-gate FTQC that harnesses the unique strengths of neutral atom arrays. The game rules are designed to enable syndrome extraction at any intermediate step during logical gate implementation, ensuring compatibility with the threshold theorem. We further present an efficient method for designing resource state factories tailored to transversal-gate FTQC. As an application, our framework offers a systematic methodology and high-level abstraction for resource estimation and optimization, demonstrating that space-time performance competitive with a baseline lattice-surgery-based approach on superconducting qubits is possible, even when physical operations on neutral atoms are orders of magnitude slower. These results establish a solid foundation that bridges the theory and experiment of FTQC powered by neutral atoms, charting a well-founded pathway toward scalable, fault-tolerant quantum computers and setting practical directions for technological development.