# Optimization by a quantum reinforcement algorithm

## TL;DR

This paper introduces a quantum reinforcement algorithm that uses feedback to enhance quantum optimization, demonstrating potential improvements in solving complex problems by increasing the energy gap during quantum annealing.

## Contribution

It proposes a novel quantum reinforcement strategy that modifies the energy landscape to improve optimization performance in quantum systems.

## Key findings

- Reinforcement increases the minimal energy gap in quantum annealing.
- Numerical simulations show potential for solving hard optimization problems.
- The method localizes the wave function on optimal configurations.

## Abstract

A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use this strategy to concentrate (localize) preferentially the wave function of a quantum particle, which explores the configuration space of the problem, on an optimal configuration. We examine the method by solving numerically the equations governing the evolution of the system, which are similar to the nonlinear Schr\"odinger equations, for small problem sizes. In particular, we observe that reinforcement increases the minimal energy gap of the system in a quantum annealing algorithm. Our numerical simulations and the latter observation show that such kind of quantum feedbacks might be helpful in solving a computationally hard optimization problem by a quantum reinforcement algorithm.