Parity-controlled gate in a two-dimensional neutral-atom array

We propose a parity-controlled gate within a two-dimensional Rydberg atom array, enabling efficient discrimination between even and odd parities of virtually excited control atoms by monitoring the dynamic evolution of an auxiliary atom. This is achieved through the use of spin-exchange dipolar interactions between Rydberg states and coupling between ground states and Rydberg states. For practical applications, we explore its implementation in three-qubit repetition codes and rotated surface codes featuring XZZX stabilizers, enabling single-shot readout of stabilizer measurements. Comprehensive numerical simulations are conducted to assess the feasibility of the proposed approach, taking into account potential experimental imperfections such as unwanted interactions between Rydberg states, atomic position fluctuations, laser phase noise, and Rabi amplitude noise. Our study highlights the inherent advantages of the physical mechanisms underlying parity measurement, demonstrating its reliability and practicality. These findings establish our protocol as a highly promising solution for quantum error detection and computation within Rydberg atom systems, with significant potential for future experimental realizations.