Polar molecules are an emerging platform for quantum technologies based on their long-range electric dipole-dipole interactions, which open new possibilities for quantum information processing and the quantum simulation of strongly correlated systems. Here, we use magnetic and microwave fields to design a fast entangling gate with >0.999 fidelity and which is robust with respect to fluctuations in the trapping and control fields and to small thermal excitations. These results establish the feasibility to build a scalable quantum processor with a broad range of molecular species in optical-lattice and optical-tweezers setups.

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Recent experimental progress in magnetic atoms and polar molecules has created the prospect of simulating dipolar Hubbard models with off-site interactions. When applied to real-space cylindrical optical lattices, these anisotropic dipole-dipole interactions acquire a tunable spatially dependent component while they remain translationally invariant in the axial direction, creating a sublattice structure in the azimuthal direction. We numerically study how the coexistence of these classes of interactions affects the ground state of hard-core dipolar bosons at half filling in a finite-size cylindrical optical lattice with octagonal rings. When these two interaction classes cooperate, we find a solid state where the density order is determined by the azimuthal sublattice structure and builds smoothly as the interaction strength increases. For dipole polarizations where the axial interactions are sufficiently repulsive, the repulsion competes with the sublattice structure, significantly increasing entanglement and creating two distinct ordered density patterns. The spatially varying interactions cause the emergence of these ordered states in small lattices as a function of interaction strength to be staggered according to the azimuthal sublattices.