Cavity-Free Distributed Quantum Computing with Rydberg Ensembles via Collective Enhancement

Abstract

A complete architecture for cavity-free quantum networking based on collective enhancement in Rydberg atom ensembles is presented. The protocol exploits Rydberg blockade and phase-matched directional emission to eliminate optical cavities without sacrificing performance. The architecture comprises three steps: (i) local control-ensemble entanglement via Rydberg blockade with fidelity $F_{\mathrm{gate}} \approx 99.93\%$; (ii) atom-photon conversion via Raman transitions, achieving directional emission ($η_{\mathrm{dir}} \approx 35\%$) and single-node efficiency $η_{\mathrm{node}} \approx 19\%$; and (iii) remote atom-atom entanglement via Hong-Ou-Mandel interference, producing Bell states with fidelity $F > 97.5\%$. With quantum memories enabling retry protocols, entanglement generation rates exceed $600$ Hz at 20 km separation. This cavity-free approach provides a practical and scalable pathway for distributed quantum computing and secure quantum communication.

Figures (3)

• Figure 1: Three-step protocol for cavity-free quantum networking with Rydberg atoms.Step 1: A control atom (red) and atomic ensemble are entangled via Rydberg blockade. Energy levels show the control atom states $|g_c\rangle$ (ground) and $|r_c\rangle$ (Rydberg), and ensemble states $|G_e\rangle$ (collective ground state) and $|W_{\mathrm{Ryd}}\rangle$ (collective Rydberg excitation), generating the entangled state $|\psi_1\rangle$. Step 2: Raman transitions map the collective excitation to a directional photon (green cone). State-selective coupling to Rydberg magnetic sublevels encodes quantum information in photon polarizations $|H\rangle$ and $|V\rangle$, creating the atom-photon state $|\psi_2\rangle$. Step 3: Constructive interference at a beam splitter with heralding detectors (D$_1$, D$_2$) generates the remote Bell state $|\psi_3\rangle$.
• Figure 2: Protocol performance and mechanisms.(a) Step 1 dynamics: $\pi/2$ pulse on control atom (left dashed line) followed by conditional $\pi$ pulse on ensemble (right dashed line) generates Bell state $\ket{\psi_1}$. Blockade suppresses $\ket{r_c,W_{\mathrm{Ryd}}}$ (blue, $<10^{-4}$). (b) Step 2 Raman mapping: Collective Rydberg state $\ket{W_{\mathrm{Ryd}}}$ is transferred to optical collective state with phase $e^{i\mathbf{k}0\cdot\mathbf{r}i}$ for directional emission. State-selective coupling to magnetic sublevels $\ket{r,\pm1/2}$ yields polarization-encoded photons $\ket{H}$, $\ket{V}$ (inset). (c) Angular emission pattern for $L/\lambda = 10$ (black), $5$ (red), $1$ (blue). Elongated clouds ($L=10\lambda$) give narrow cone ($\Delta\theta\approx5.7^\circ$) matching fiber acceptance (green, $\pm6^\circ$). (d) Directional efficiency $\eta_{\mathrm{dir}}$ vs $L/\lambda$ for $R/\lambda = 0.5$ (black), $1.0$ (red), $2.0$ (blue). Operating point ($L=10\lambda$, $R=\lambda$, red dot) yields $\eta_{\mathrm{dir}} \approx 0.35$.
• Figure 3: Remote entanglement performance.(a) Cumulative success probability versus attempts $M$ for $P_E = 0.2\%$ (black), $0.5\%$ (red), $1.0\%$ (blue), and $2.0\%$ (green). Quantum memory enables $M \sim 100$ attempts within $T_2$, yielding $\sim 40\%$ cumulative probability for $P_E = 0.5\%$. (b) Entanglement rate $R$ versus distance for node efficiencies $\eta_{\mathrm{node}} = 0.15$ (black), $0.19$ (red), and $0.25$ (blue). For $\eta_{\mathrm{node}} = 0.19$, $R$ exceeds 600 Hz at 20 km, enabling metropolitan-scale applications.