Programming higher-order interactions of Rydberg atoms

Higher-order interactions in spin-based Hamiltonians are crucial in addressing numerous fundamentally significant physical problems. In this work, Rydberg-atom graph gadgets are introduced to effectively program $K\mathrm{th}$-order interactions within a Rydberg-atom system. This approach facilitates the determination of the ground states of an Ising-type Hamiltonian, encoded to solve higher-order unconstrained optimization problems. A favorable scaling behavior, $O({N}^{K})$, is expected in terms of the number of atoms required for $N$-vertex hypergraph optimization problems.