Architecture for fast implementation of qLDPC codes with optimized Rydberg gates

Abstract: 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 $\sf CZ$ entangling operations with fidelity ${\mathcal F}>0.999$ at a distance greater than $12~\mu\rm m$. The combination of optimized layout and gate design leads to a quantum error correction cycle time of $\sim 1.28~\rm ms$ for a $[[144,12,12]]$ code, nearly a factor of two improvement over previous designs.