Fast Quantum Gates for Neutral Atoms Separated by a Few Tens of Micrometers

Abstract

We present a theoretical scheme for a family of fast and high-fidelity two-qubit iSWAP gates between neutral atoms separated by more than 20 um, enabled by resonant dipole-dipole spin-exchange interactions between Rydberg states. The protocol harnesses coherent excitation-exchange-deexcitation dynamics between the qubit and the Rydberg states within a single and smooth laser pulse, in the presence of strong dipole-dipole interactions. We utilize optimal control methods to achieve theoretical gate fidelities and durations comparable to blockade-based gates in the presence of relevant noise, while extending the effective interaction range by an order of magnitude. This enables entanglement well beyond the blockade radius, offering a route toward fast, high-connectivity quantum processors.

Figures (6)

• Figure 1: iSWAP gate with Rydberg atoms. (a) Two atoms separated by a distance $R$, irradiated by two laser fields $\Omega_{0,1}$, with a resonant dipolar coupling $J$. Rydberg decay $\Gamma_{0,1}$, atomic motion, and vdW interactions $V_{\text{vdW}}$ are also included. (b) A single optimal laser pulse $\Omega_{0,1}$ is applied, with dipolar and vdW interactions present from the outset. (c) Evolution of the two-atom state populations during the pulse for $\Omega_{\rm{max}}/J=2.1$ (Fig. \ref{['fig:pulses']}), starting from the state $\ket{01}$.
• Figure 2: Time-optimal and vdW-robust pulses. (a) Minimum infidelity $1-F$ found by GRAPE for pulses of different durations $T$, in units of the Rabi frequency $\Omega_{\rm max}$, for the given ratio $\Omega_{\rm{max}}/J=2.1$. The time-optimal pulse has duration $T\Omega_{\rm{max}}=11.95$, while trying to make it robust to vdW interactions the pulse durations is increased to $T\Omega_{\rm{max}}=12.1$ (inset). (b) Optimal duration $T$, in units of $\Omega_{\rm max}$ versus coupling ratio $\Omega_{\max}/J$ of the vdW-robust pulses. The resulting duration $T$, range $R$, and fidelity $F$ obtained for a realistic choice of experimental parameters are shown in Fig. \ref{['fig:fidelity']}. (c) Optimal phase profile $\phi(t)$ of three vdW-robust pulses.
• Figure 3: Infidelity of the vdW-robust pulses for a fixed Rabi frequency $\Omega_{\rm max}/2\pi=10\,\mathrm{MHz}$. (a) Heat map of gate infidelity $1-F$ (color scale on the right) for several coupling ratios $\Omega_{\max}/J$, with $1.5 \leq J \leq 15\,\mathrm{MHz}$. (b)-(d) Fidelity of the vdW-robust pulse for $\Omega_{\max}/J=2.1$ as a function of (b) the principal quantum number $n$, (c) the atomic temperature $T_{\rm temp}$, and (d) the radial trapping frequency $\omega_z/2\pi$, in absence of photon recoil and with the laser orientated along the interatomic direction ($\bar{\ell}=z$).
• Figure S1: (a) Simulation of the fidelity $\pi J \pi$ protocol with $\Omega_{\text{max}}/2\pi=10\,\mathrm{MHz}$, and $n=100$, in absence of decay from the Rydberg states. Each point represents a different ratio $\Omega_{\text{max}}/J$, thus a different gate duration $T$ and range $R$. (b) Same simulation of Fig. \ref{['S_fig:miscellanea']}, including also the Rydberg decay, $\Gamma_0/2\pi=0.88\,\mathrm{kHz}$ and $\Gamma_1/2\pi=0.44\,\mathrm{kHz}$. (c) Time evolution of the population of the state $\ket{10}$ when starting from $\ket{01}$ and applying constant global pulses $\Omega_j(t)=\Omega_{\text{max}}$ ($j=0,1$) with three different ratios $\Omega_{\text{max}}/J$.
• Figure S2: Time-optimal pulses. (a) The time-optimal gate duration $T\Omega_{\text{max}}$ for different ratios $\Omega_{\text{max}}/J$. (b) Phase $\phi(t)$ of the time-optimal pulse for $\Omega_{\text{max}}/J=0.1$, with duration $T\Omega_{\text{max}}=8.84$. (c) Phase $\phi(t)$ of the time-optimal pulse for $\Omega_{\text{max}}/J=0.7$, with duration $T\Omega_{\text{max}}=8.2$. (d.1) Infidelity $1-F$ as a function of the gate time duration $T\Omega_{\text{max}}$ for the ratio $\Omega_{\text{max}}/J=2.1$. In order to achieve a numerical zero infidelity pulses of duration $T\Omega_{\text{max}}\ge 11.95$ are required. (d.2) Phase $\phi(t)$ of the time-optimal pulse for $\Omega_{\text{max}}/J=2.1$, with duration $T\Omega_{\text{max}}=11.95$. (e) Phase $\phi(t)$ of the time-optimal pulse for $\Omega_{\text{max}}/J=3.25$, with duration $T\Omega_{\text{max}}=13.38$. (f) Phase $\phi(t)$ of the time-optimal pulse for $\Omega_{\text{max}}/J=4.5$, with duration $T\Omega_{\text{max}}=13.8$.