Optimizing two-qubit gates for ultracold atoms using Fermi-Hubbard models

Ultracold atoms trapped in optical lattices have emerged as a scalable and promising platform for quantum simulation and computation; however, gate speeds remain a significant limitation for practical applications. In this work, we employ quantum optimal control to design fast, collision-based two-qubit gates within a superlattice based on a Fermi-Hubbard description, reaching errors in the range 10-3 for realistic parameters. Numerically optimizing the lattice depths and the scattering length, we effectively manipulate hopping and interaction strengths intrinsic to the Fermi-Hubbard model. Our results provide five times shorter gate durations by allowing for higher energy bands in the optimization, suggesting that standard modeling with a two-band Fermi-Hubbard model is insufficient for describing the dynamics of fast gates, and we find that four to six bands are required. Additionally, we achieve nonadiabatic gates by employing time-dependent lattice depths rather than using only fixed depths. The optimized control pulses not only maintain high efficacy in the presence of laser-intensity and phase noise but also result in negligible interwell couplings.