Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet

TL;DR

This paper investigates how many-body transverse interactions in quantum annealing influence the phase transition order in the p-spin ferromagnetic model, showing they can promote smoother second-order transitions and potentially improve annealing performance.

Contribution

It introduces and analyzes many-body transverse interactions as quantum drivers, extending previous two-body approaches to enhance quantum annealing efficiency.

Findings

Many-body interactions induce second-order phase transitions.

Ground-state overlap may not be critical for success.

Potential for improved quantum annealing performance.

Abstract

We study the performance of quantum annealing for the simple $p$-body infinite-range ferromagnetic Ising model. In particular, we generalize the transverse antiferromagnetic interactions proposed by Seki and Nishimori as a quantum driver to many-body transverse interactions to understand if the two-body interactions are essential to allow the system to avoid troublesome first-order quantum phase transitions. We conclude that the general many-body interactions are effective to let the system evolve only through second-order transitions as long as a few minor conditions are satisfied. It is also discussed whether the overlap of the ground-state wave function of the new driver term with the target ground state is an essential factor for the success.