Fast collisional $\sqrt{\mathrm{SWAP}}$ gate for fermionic atoms in an optical superlattice

TL;DR

The paper tackles the slow operation of two-qubit gates in neutral-atom quantum computing due to tunneling limitations. It introduces a dynamic, collision-driven approach using time-dependent control of optical superlattice depths to create a quasi-harmonic confinement between sites, enabling a fast $\sqrt{\mathrm{SWAP}}$ gate validated by continuum Schrödinger simulations and benchmarking against tunneling-based protocols. The main result is a $\sqrt{\mathrm{SWAP}}$ gate achieved in about $21.2\ \mu\mathrm{s}$ with fidelities approaching $99\%$, along with a faster, robust variant and a pathway to further robustness via composite sequences like $\mathrm{SWAP}^{3/4}$ and $\mathrm{SWAP}^{3/2}$. This work provides a practical, scalable building block for neutral-atom quantum computation, compatible with existing optical-superlattice experiments and extendable to three-dimensional architectures.

Abstract

Collisional gates in optical superlattices have recently achieved record fidelities, but their operation times are typically limited by tunneling. Here we propose and analyze an alternative route to a fast $\sqrt{\mathrm{SWAP}}$ gate for two fermionic atoms in an optical superlattice based on optimized, time-dependent control of the short and long lattice depths. The gate is implemented by transiently releasing the atoms into a quasi-harmonic confinement centered between the two sites. With an appropriately chosen contact interaction strength, a controlled collision accumulates the exchange phase required for $\sqrt{\mathrm{SWAP}}$ and generates entanglement. We employ a continuum, time-dependent Schrödinger-equation simulation that goes beyond a two-site Fermi--Hubbard description and benchmark it against experimentally implemented tunneling-based protocols, reproducing the observed single-particle tunneling and spin-exchange dynamics. For experimentally accessible lattice depths, we find that the proposed gate operates in $\sim 21\,μ\mathrm{s}$, more than an order of magnitude faster than tunneling-based implementations, while achieving fidelities $\gtrsim 99\%$. We further analyze sensitivity to lattice-depth variations and show that a composite sequence improves robustness. Our results establish fast, collision-mediated entangling gates in superlattices as a promising building block for scalable neutral-atom quantum computation.

Figures (8)

• Figure 1: Single-particle tunneling: simulation versus experiment. Tunneling frequency as a function of the short-lattice depth $V_S$. Simulation (solid black) compared with the experimental data (red circles) from Figure S1 of Ref. Bloch_new.
• Figure 2: Simulation of spin-exchange (left) and pair-tunneling (right) oscillations for several holding times $\tau_h$. The fit to a sinusoidal form is shown as well as a solid line.
• Figure 3: Pair tunneling waveform evolution. Panels (a)-(d) depict the absolute value of the two-particle waveform, $|\psi_{\uparrow \downarrow}(x_1,x_2,\tau)$, for different times during the operation of the sequence. $\tau_r = 0.5\mathrm{ms}$ -the ramping time, and $\tau_h = 0.2\mathrm{ms}$ - the holding time. $x_1$ and $x_2$ are the horizontal and vertical axes, respectively (each is $3\mathrm{\mu m}$ wide).
• Figure 4: Spin-exchange oscillations -- simulation versus experiment. The tunneling frequency is extracted from a series of simulations in which the short-lattice depth $V_S$ is varied while the interaction strength $\gamma$ is kept fixed. The on-site interaction $U$ is computed from Eq. \ref{['eq:U_g']}; however, to quantitatively match the experimental data, it must be rescaled by a constant factor of $0.82$. This rescaling yields the solid black curve, which shows excellent agreement with the experimental results (red circles) reported in Figure S2 of Ref. Bloch_new and follows the expected scaling $J = 4t^2/U$.
• Figure 5: $\sqrt{\mathrm{SWAP}}$ gate with fast ramping of amplitudes. Panels (a)-(d) depict the absolute value of the two-particle waveform distribution, $|\psi_{\uparrow \downarrow}(x_1,x_2,\tau)|$, for different times during the operation of the sequence, with $x_1$ and $x_2$ being the horizontal and vertical axes, respectively (each is $3\mathrm{\mu m}$ wide).