Performance enhancement of quantum annealing under the Lechner-Hauke-Zoller scheme by non-linear driving of the constraint term

TL;DR

This paper demonstrates that non-linear driving of the constraint term in the LHZ quantum annealing scheme can avoid first-order phase transitions, leading to exponential speedup in solving complex optimization problems.

Contribution

It introduces a non-linear driving protocol for the constraint term in the LHZ quantum annealing scheme, improving performance and avoiding phase transitions.

Findings

Non-linear driving prevents first-order phase transitions.

Exponential speedup achieved in ferromagnetic and spin glass models.

Performance enhancement applicable to complex optimization problems.

Abstract

We analyze the performance of quantum annealing as formulated by Lechner, Hauke, and Zoller (LHZ), by which a Hamiltonian with all-to-all two-body interactions is reduced to a corresponding Hamiltonian with local many-body interactions. Mean-field analyses show that problematic first-order quantum phase transitions that exist in the original LHZ formulation can be avoided, and thus an exponential speedup is achieved, if we drive the coefficient of the many-body term, which represents the constraint, non-linearly as a function of time. This result applies not only to a simple ferromagnetic model but also to the spin glass problem if a parameter in the spin glass model is chosen appropriately.