Optimizing Stabilizer Measurements on Rydberg Atoms

Rydberg atom quantum computers are starting to enter the era of fault tolerance. As two qubit gate fideltities surpass the threshold for quantum error correction, the the logical error rate that can be achieved with a given gate protocol becomes a more important metric than the gate fidelity itself. Here, we estimate the logical error rates that different implementations of a controlled-Z (CZ) gate on Rydberg atoms can achieve when used in the stabilizer measurements of a surface code. We focus on errors induced by Rydberg decay, which is a dominant error source in most experimental implementations. Interestingly, we find that the time-optimal implementation of the CZ gate, which has the lowest possible infidelity in the presence of Rydberg decay, does not offer the best performance in terms of the logical error rate. This arrises because the time-optimal gate introduces correlated errors, which effectively reduce the code distance. We overcome this issue by proposing a new gate protocol in which atoms spend slightly more time in the Rydberg state, but correlations in the errors are reduced, effectively reducing the logical error rate.