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

TL;DR

This paper introduces a genetic algorithm-based method to embed p-body quantum models onto 2-body quantum annealers, reducing the need for many ancilla qubits and enabling simulation of more complex systems.

Contribution

It develops a novel approximate embedding technique using evolutionary strategies to decouple p-body interactions into 2-body interactions for quantum annealing.

Findings

Feasibility demonstrated for ferromagnetic p-spin models

Reduces ancilla qubit requirements compared to traditional methods

Paves the way for applying evolutionary strategies to complex quantum systems

Abstract

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 pave the way towards the application of evolutionary strategies to more complex quantum models.