Optimizing two-qubit gates for ultracold fermions in optical lattices

TL;DR

This work presents a 1D-confinement simulation framework for ultracold fermions in optical lattices to optimize fast, high-fidelity two-qubit collision gates. By coupling a leapfrog time-evolution method with gradient-based optimal control and a transfer-function model of the optical path, the authors reveal momentum-dependent interactions that differ for atoms starting in the same versus opposite subwells. Case-specific optimizations and robustness analyses demonstrate near-1% gate infidelity is achievable under realistic constraints, with significant gains when treating initial-state configurations separately. The approach extends beyond Fermi-Hubbard models and offers a practical route to robust, scalable quantum gates for quantum computing and quantum simulation with fermionic atoms.

Abstract

Ultracold neutral atoms in optical lattices are a promising platform for simulating the behavior of complex materials and implementing quantum gates. We optimize collision gates for fermionic Lithium atoms confined in a double-well potential, controlling the laser amplitude and keeping its relative phase constant. We obtain high-fidelity gates based on a one-dimensional confinement simulation. Our approach extends beyond earlier Fermi-Hubbard simulations by capturing a momentum dependence in the interaction energy. This leads to a higher interaction strength when atoms begin in separate subwells compared to the same subwell. This momentum dependence might limit the gate fidelity under realistic experimental conditions, but also enables tailored applications in quantum chemistry and quantum simulation by optimizing gates for each of these cases separately.

Figures (12)

• Figure 1: Optical lattice from a tilted laser field. On the left, intensity of the laser field acting on the short lattice in the $xy$-plane with a characteristic angle of $\beta_{x}=26.7^\circ$ between the two laser beams. On the right, a magnified version details the $\cos^2(k_x x)$ lattice.
• Figure 2: The maximally localized Wannier states. The atoms are prepared in either the left or the right Wannier state. Both states are a superposition of the two lowest Bloch bands of the corresponding optical potential in the $x$-direction.
• Figure 3: Wannier states of interacting atoms. (a) shows the decoupled two-atom Wannier state with the first atom in the left state $w_L(x_1)$ and the second one in the right state $w_R(x_2)$. (b) shows the coupled two-atom Wannier state $w_{LL}(x_1,x_2)$, where the interaction energy at $x_1=x_2$ divides the wave packet in two symmetric parts. We have recoil energies $V_s=40 E_{r,s}$, $V_l=30 E_{r,l}$, and a scattering length of $a_{1\mathrm{D}}=-6675 a_0$ with Bohr radius $a_0 \approx 52.9p m$.
• Figure 4: The optimization process as a flow chart. In the first three steps, we optimize the laser intensities $V_s$, $V_l$ and the effective scattering length $a_{1\mathrm{D}}$. In the last step, we check of the robustness of the gate optimization (see Sec. \ref{['Robustness against system impurities']}). This optimization procedure is tailored to minimize the total time of the optimization (see text).
• Figure 5: Benchmark 1. Simulated Rabi oscillations of non-interacting atoms between the left and the right side of a double-well lattice. The blue line is calculated using Eq. \ref{['eq. leapfrog']} while the orange line uses the method from Ref. Singh2025. The black line corresponds the experimental data Chalopin2025 which is almost superimposed with the blue line. The damping of the oscillation amplitude is caused by atoms hopping out of their initial well.