Experimental roadmap for performing optimal state transfer and entanglement generation in power-law interacting systems

Experimental systems with power-law interactions have attracted interest as promising platforms for quantum information processing. Such systems are capable of spreading entanglement superballistically and achieving an asymptotic speed-up over locally interacting systems, as shown in Eldredge et al. (PRL '17) and Tran et al. (PRX '19). In this work, we provide an experimental roadmap towards realizing two protocols for transferring quantum states in subpolynomial time in three classes of atomic and molecular systems with dipolar interactions: polar molecules composed of alkali-metal dimers, neutral atoms in excited Rydberg states, and atoms with strong magnetic moments. We also numerically evaluate the tradeoffs between the two protocols for small system sizes as a guide to near-term experimental implementation.