Programming higher-order interactions of Rydberg atoms

TL;DR

This paper introduces a method to program higher-order interactions in Rydberg atom systems using graph gadgets, enabling the solution of complex optimization problems with favorable scaling.

Contribution

It presents a novel approach to encode and control higher-order interactions in Rydberg atoms for solving complex optimization problems.

Findings

Effective programming of K-th order interactions using Rydberg-atom graph gadgets

Ground state determination of Ising-type Hamiltonians for hypergraph optimization

Favorable scaling behavior of O(N^K) in atom number for N-vertex problems

Abstract

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 $K$-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.