Architecture for fast implementation of quantum low-density parity-check codes with optimized Rydberg gates

Abstract

We propose an implementation of bivariate bicycle codes [S. Bravyi et al., Nature (London) 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 nonlocal parity-check operators. An optimized Rydberg gate pulse design enables $\mathsf{CZ}$ entangling operations with fidelity $\mathcal{F}>0.999$ at a distance greater than $12\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{m}$. The combination of optimized layout and gate design leads to a quantum error correction cycle time of $\ensuremath{\sim}1.28\phantom{\rule{0.28em}{0ex}}\mathrm{ms}$ for a [[144,12,12]] code, which is nearly a factor-of-two improvement over previous designs.