  Quantum error detection relies primarily on precise measurement of qubit
parity, a fundamental operation in quantum information processing. Here, we
introduce a resilient parity-controlled gate tailored for detecting quantum
errors within a 2D Rydberg atom array. Our method enables the discrimination
between even and odd parities of virtually excited control atoms by tracking
the dynamic evolution of an auxiliary atom. Using spin-exchange dipolar
interactions of Rydberg states and single- and two-photon driving between
ground states and Rydberg states, our method speeds up Rydberg-parity
measurements by a large amount compared to previous methods. In practical
application, we explore three-qubit repetition codes, standard surface codes
featuring stabilizers in the forms $ZZZZ$ and $XXXX$, as well as rotated
surface codes in the $XZZX$ configuration, facilitating the measurement of
stabilizers with a single-shot readout. We carry out thorough numerical
simulations to evaluate the feasibility of our strategy, considering potential
experimental imperfections such as undesired interactions between Rydberg
states, fluctuations in atomic positions, dephasing noise, and laser amplitude
inhomogeneities. Particular emphasis is placed on ensuring the reliability and
advantages of the physical mechanisms of the parity meter. These results affirm
the robustness and viability of our protocol, positioning it as a promising
candidate for quantum error detection employing the Rydberg atom system in the
foreseeable future.
