Physical and Logical Quantum Circuit Implementation in Neutral-Atom Arrays: Probing the Break-Even Regime with Quantum Kernel

Neutral-atom quantum processors combine long coherence times with native reconfigurability and scalable two-dimensional architectures, making them a strong candidate for fault-tolerant quantum computing. In this work, we encode qubits in the magnetically insensitive clock states of the $^{87}$Rb ground-state manifold and implement high-fidelity single-qubit gates using Raman transitions at 795 nm, enabling precise phase control and parallel global operations across large registers. Entangling operations are realized via Rydberg excitation and blockade-based controlled-Z (CZ) gates, providing strong, fast interactions compatible with scalable array geometries. By combining local addressability with global control fields and in-circuit atom movement while preserving coherence, our architecture enables the execution of nontrivial quantum circuits beyond static register operation. Using this gate set, we implement a quantum kernel application on both physical qubits and on an equivalent error-detecting logical encoding, allowing a direct, circuit-level comparison between physical and logical performance. This approach provides an experimentally relevant pathway to assess the benefits of quantum error correction under realistic noise and control constraints. Our results demonstrate encouraging first indications toward the break-even regime, where logical qubits begin to outperform their physical counterparts, marking an important milestone toward scalable fault-tolerant quantum computation with neutral atoms.