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Abstract: Quantum computation and simulation rely on long-lived qubits with controllable interactions. Early work in quantum computing made use of molecules because of their readily available intramolecular nuclear spin coupling and chemical shifts, along with mature nuclear magnetic resonance techniques. Trapped polar molecules have been proposed as a promising quantum computing platform, offering scalability and single-particle addressability while still leveraging inherent complexity and strong couplings of molecules. Recent progress in the single quantum state preparation and coherence of the hyperfine-rotational states of individually trapped molecules allows them to serve as promising qubits, with intermolecular dipolar interactions creating entanglement. Here, we harness intrinsic molecular resources to implement a universal two-qubit iSWAP gate using individually trapped $X^{1}\Sigma^{+}$ NaCs molecules. By allowing the molecules to interact for 664 us at a distance of 1.9 um, we create a maximally entangled Bell state with a fidelity of 94(3)% in trials where both molecules are present. Using motion-rotation coupling, we measure residual excitation of the lowest few motional states along the axial trapping direction and find them to be the primary source of decoherence. Finally, we identify two non-interacting hyperfine states within the ground rotational level in which we encode a qubit. The interaction is toggled by transferring between interacting and non-interacting states to realize an iSWAP gate, which, together with single-qubit rotations, forms a universal set of gates. 

Entanglement and iSWAP Gate between Molecular Qubits
Lewis R.B. Picard*, Annie J. Park*, Gabriel E. Patenotte, Samuel Gebretsadkan, David Wellnitz, Ana Maria Rey, Kang-Kuen Ni
arXiv:2406.15345 (2024) Nature (in press)