Drive-Through Quantum Gate: Non-Stop Entangling a Mobile Ion Qubit with a Stationary One

Abstract

Towards the scalable realization of a quantum computer, a quantum charge-coupled device (QCCD) based on ion shuttling has been considered a promising approach. However, the processes of detaching an ion from an array, reintegrating it, and driving non-uniform motion introduce severe heating, requiring significant time and laser power for re-cooling and stabilization. To mitigate these challenges, we propose a novel entangling scheme between a stationary ion qubit and a continuously transported mobile ion, which remains in uniform motion and minimizes motional heating. We theoretically demonstrate a gate error on the order of 0.01%, within reach of current technology. This approach enables resource-efficient quantum operations and facilitates long-distance entanglement distribution, where stationary trapped-ion arrays serve as memory units and mobile ions act as communication qubits passing beside them. Our results pave the way for an alternative trapped-ion architecture beyond the QCCD paradigm.

Figures (4)

• Figure 1: Drive-through gate scheme. (a) Schematic representation of the drive-through gate scheme for a two-ion system. The local trap of ion $1$ is stationary while the local trap of ion $2$ is shuttled along a straight path in the $x$-$y$ plane. The entangling operation is performed as ion $2$ moves through the operation region. (b) Ion $2$ undergoes uniform motion with speed $v$, leading to a time-dependent Coulomb interaction characterized by $R(t)$, the inter-ion separation. The laser beam, with a spatial width $w$, defines the operation region where the drive-through gate is performed.
• Figure 2: Dynamical normal modes and parameter regimes for the DTG scheme. (a) The dynamical normal mode frequencies. The blue and orange curves correspond to the center-of-mass mode $\Omega_{1}$ and zigzag mode $\Omega_{2}$, respectively. The trapping frequency is $\omega_{x,y}=2\pi\times2.5~{\rm MHz}$ and $\omega_{z}=2\pi\times5~{\rm MHz}$, the closest trap distance is $d=10~\mu{\rm m}$, the shuttling velocity is $v=0.2~{\rm m/s}$ and the laser addressing width is $w=10~\mu{\rm m}$. The two black dashed lines indicate the entry and exit times of the mobile ion within the operation region, corresponding to $t_{0}=-w/(2v)$ and $T=w/v$. (b) Heatmap showing the normalized oscillation amplitude in the $x$-direction, $\xi_{x,{\rm max}}/d$, as a function of the frequency ratios $f_{1}/f_{3}$ and $f_{2}/f_{3}$. The contours indicate specific values of $\xi_{x,{\rm max}}/d$. (c) Maximum displacement of the equilibrium positions of the ions, normalized as $q_{{\rm max}}^{(0)}/d$, plotted as a function of $f_{2}/f_{3}$.
• Figure 3: Optimized pulse shape and phase space trajectory. (a) Optimized pulse shape and (b) phase space trajectories with $v=0.2~{\rm m/s}$ and $\mu=-0.06\omega_{z}$. (c) Optimized pulse shape and (d) phase space trajectories with $v=0.5~{\rm m/s}$ and $\mu=-0.02\omega_{z}$. In both cases, $d=10~\mu{\rm m}$, $w=10~\mu{\rm m}$, $\omega_{x,y}=2\pi\times2.5~{\rm MHz}$ and $\omega_{z}=2\pi\times5~{\rm MHz}$. $\left\langle \tilde{Z}_{n}\right\rangle$ and $\left\langle \tilde{P}_{n}\right\rangle$ denote the normalized expectation values of the position and momentum operators in the interaction picture for the center-of-mass ($n=1$) and zigzag ($n=2$) modes. In (b) and (d), the yellow circle (initial) and red cross (final) indicate the phase-space displacements.
• Figure 4: Scalable architecture. (a) Schematic for generating a distributed $N$-qubit GHZ state using a single moving ion and $N$ stationary ions. The moving ion (Ion $X$) is initialized to a superposition state and sequentially interacts with stationary ions $1$ through $N-1$ via drive-through CNOT gates. A final drive-through SWAP gate with stationary ion $N$ completes the process, creating a GHZ state distributed among the $N$ stationary ions. (b) Linear architecture with static ion arrays serving as memory units. A single moving ion is initialized in the cooling and initialization zone, interacts with the memory ions via drive-through gates, and can be recycled afterward. (c) Race-track architecture where multiple moving ions travel along a closed track, interacting with memory ions via drive-through gates. The moving ions can be re-cooled and re-initialized after completing a cycle.