Architecture for fast implementation of qLDPC codes with optimized Rydberg gates

We propose an implementation of bivariate bicycle codes (Nature {\bf 627}, 778 (2024)) based on long-range Rydberg gates between stationary neutral atom qubits. An optimized layout of data and ancilla qubits reduces the maximum Euclidean communication distance needed for non-local parity check operators. An optimized Rydberg gate pulse design enables $\mathsf{C}\mathsf{Z}$ entangling operations with fidelity $\mathcal{F}>0.999$ at a distance greater than $12\mu \mathrm{m}$. The combination of optimized layout and gate design leads to a quantum error correction cycle time of $\sim 1.28\mathrm{m}\mathrm{s}$ for a $[[144,12,12]]$ code, nearly a factor of two improvement over previous designs.