Quantum annealing and the Schr\"odinger-Langevin-Kostin equation

TL;DR

This paper explores how the nonlinear Schr"odinger-Langevin-Kostin equation can enhance quantum annealing by guiding systems toward ground states and preventing quantum localization issues.

Contribution

It introduces a novel approach using the Schr"odinger-Langevin-Kostin equation to improve quantum annealing efficiency and avoid localization problems.

Findings

The nonlinear equation can effectively drive systems to their ground states.

Kostin-type friction prevents quantum localization phenomena.

The approach offers potential improvements in quantum optimization algorithms.

Abstract

We show, in the context of quantum combinatorial optimization, or quantum annealing, how the nonlinear Schr\"odinger-Langevin-Kostin equation can dynamically drive the system toward its ground state. We illustrate, moreover, how a frictional force of Kostin type can prevent the appearance of genuinely quantum problems such as Bloch oscillations and Anderson localization which would hinder an exhaustive search.