Architecture for fast implementation of qLDPC codes with optimized Rydberg gates

TL;DR

The paper addresses the challenge of implementing fast, high-distance qLDPC bicycle codes with non-local parity checks. It combines a dilation-folding planar qubit layout with optimized long-range Rydberg CZ gates to reduce the QEC cycle time, achieving ${F}>0.999$ at inter-atomic distances around $R approx 12 μm$ and a cycle time near ${1.28}$ ms for the [[144,12,12]] code. The approach yields a substantial improvement over transport-based methods and demonstrates feasible operation up to code distance $d=12$ (potentially $d=18$), highlighting a path toward space-time efficient quantum memory using neutral-atom qubits. The work emphasizes the role of fast optical beam switching and detailed gate-design to realize practical, scalable quantum error correction for high-rate memory systems.

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 $12~μ\rm m$. 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.

Figures (5)

• Figure 1: Optimized layout of the [[144,12,12]] code with a maximum communication distance of 7.21 lattice spacings. The check operations are shown for a few ancilla qubits with color coded connections corresponding to the Cs Rydberg levels shown on the right. The qubit color coding is $L$ data = green circle, $R$ data = blue circle, $\sf X$ check = red square, $\sf Z$ check = yellow square.
• Figure 2: a) A grid of nearest-neighbor connected qubits on a torus has long range connections when mapped onto a planar grid with open boundary connections. b) A dilation and remapping procedure converts long-range connections into nearest-neighbors, and neighboring connections into nearest- or next-nearest neighbors EMa1993. c) This remapping is achieved by "folding" the plane in a) once vertically and again horizontally and expanding each quadruplet of overlapping qubits into a square as in panel b). Only a few connections are shown for clarity.
• Figure 3: Rydberg gate simulation at low interaction strength $V/(2\pi)=3.8~\rm MHz$ and Rydberg lifetime $\tau_{\rm R}=252~\mu\rm s$, corresponding to Cs $90s_{1/2}$ giving error $\epsilon=7.\times 10^{-4}$. Panels show (a) Rabi drive $(\Omega_{\rm max}/2\pi=7.3~\rm MHz)$ and phase profile, (b) corresponding detuning, (c) ground $P_{\rm g}$ and Rydberg $P_{\rm R}$ populations for one atom coupled to the Rydberg state, and (d) ground $P_{\rm gg}$, singly excited $P_{\rm gR}+P_{\rm Rg}$ and double Rydberg $P_{\rm RR}$ populations for two atoms coupled to the Rydberg state. Gate parameters are given in row 17 of Table \ref{['tab.distances2']} in Appendix \ref{['sec.App.gate']}.
• Figure 4: Duration of a single round of QEC for the optimized layout of the $[[144,12,12]]$ code as a function of the overhead time due to optical beam switching. The different curves include the time for optical pumping for ancilla reset ($t_{\rm op}$) and ancilla measurement ($t_{\rm meas}$). The curves are labeled with $(t_{\rm op},t_{\rm meas})$ in $\mu\rm s.$ The dashed lines show the cycle time with the assumption of $1.5~\mu\rm s$ switching time assumed in the main text.
• Figure 5: Optimized layout of the [[144,12,12]] code with a maximum communication distance of 7.21 lattice spacings. All nodes are labeled. Edges can be generated via the rules for the [[144,12,12]] code.