An evolutionary strategy for finding effective quantum 2-body Hamiltonians of p-body interacting systems

Embedding p-body interacting models onto the 2-body networks implemented on commercial quantum annealers is a relevant issue. For highly interacting models, requiring a number of ancilla qubits, that can be sizable and make unfeasible (if not impossible) to simulate such systems. In this manuscript, we propose an alternative to minor embedding, developing a new approximate procedure based on genetic algorithms, allowing to decouple the p-body in terms of 2-body interactions. A set of preliminary numerical experiments demonstrates the feasibility of our approach for the ferromagnetic p-spin model and paves the way towards the application of evolutionary strategies to more complex quantum models.