Quantum Hopfield networks with higher order interactions

Hopfield networks are models of Ising spins with long-range interactions which exhibit associative memory. They can be generalized to modern Hopfield networks with higher order interactions, which have a larger memory capacity scaling as higher powers of its system size. In this work, we consider a quantum generalization of modern Hopfield networks, by considering a system of qubits instead of Ising spins and allowing the patterns being retrieved to be general separable states of the qubits. We numerically analyze such models using computer simulations and compare their behavior with that of classical networks.