NEAT: A Neutral-Atom Transpiler for Joint Mapping and Scheduling of Syndrome Extraction Circuits

Abstract

Quantum Error Correction (QEC) demands efficient implementation of syndrome extraction circuits. However, existing compilers for neutral-atom processors largely miss the opportunity to co-optimize these circuits by exploiting both the structural properties of Quantum Error-Correcting Codes (QECCs) and the physical constraints of neutral-atom architectures. In this work, we introduce NEAT, an SMT-based compiler that jointly optimizes qubit mapping and syndrome extraction scheduling for a broad class of stabilizer-based QECCs, achieving depth-optimal execution with minimal shuttling overhead on neutral-atom platforms. Across a wide range of QECCs, NEAT consistently achieves near-optimal circuit depth and reduces atom movement by 3x-30x compared the baseline compiler Enola. Logical-level simulations further demonstrate 2x-20x lower logical error rates under realistic hardware noise. A hierarchical symmetry-breaking formulation and relaxed parallel-motion constraints substantially improve solver scalability, yielding up to 100x speedup in compilation time. Together, these results show that NEAT produces depth-optimal, movement-efficient, and logically robust syndrome extraction schedules, while scaling effectively to large QECCs on neutral-atom hardware.