Multi-body flux-qubit couplers for quantum annealing

Despite the enormous progress achieved in the field of quantum annealing over the last decade, the demonstration of a computational advantage over classical methods remains elusive. One possible solution is to provide quantum annealers with qualitatively new features, such as higher-order terms in the driver and/or problem Hamiltonians and error-suppression. These capabilities both rely on the physical implementation of multi-body interactions. While interactions between pairs of flux qubits can be achieved rather easily, multi-body interactions require more sophisticated constructions. Some of these use ancillary qubits, while others are based on coupling loops with carefully-engineered flux non-linearities. Here we present a comparative analysis of a few such proposed implementations and propose a quantitative way to compare their performances, with specific focus on their possibility to generate the correct quantum energy spectrum during the annealing process.