---
author:
- 'Davide Venturelli$^{1}$'
- Alexei Kondratyev$^2$
date: |
    \
    \
title: |
    Reverse Quantum Annealing Approach\
    to Portfolio Optimization Problems
---

  -------------------------------------------------------------------------- --
  **[Keywords:]{}& Portfolio Optimization, Quadratic Unconstrained Binary\   
  & Optimization, Quantum Annealing, Genetic Algorithm,\                     
  & Reverse Quantum Annealing\                                               
  &\                                                                         
  **[JEL classification:]{} & C61, C63, G11\                                 
  ****                                                                       
  -------------------------------------------------------------------------- --

Introduction {#sec:intro}
============

One reason behind the current massive investment in quantum computing is that this computational paradigm has access to resources and techniques that are able to circumvent several bottlenecks of state-of-the-art digital algorithms. Much research is today devoted to understanding how to exploit this power to deliver high quality solutions to discrete optimization problems at a fraction of the time required using the best classical methods on high-end hardware.

Quantum annealers are special-purpose machines inspired by the adiabatic quantum computing paradigm. These machines are manufactured by D-Wave Systems and appeared on the market in 2011, and while being limited in programmability with respect to other experimental devices under testing by other companies, are still the only available quantum devices that feature a sufficient amount of quantum memory (qubits) to be applied to non-trivial problems at the time of writing. For this reason they are subject to extensive 