# Implementation of a Hybrid Classical-Quantum Annealing Algorithm for Logistic Network Design

## TL;DR

This paper presents a hybrid classical-quantum annealing approach implemented on a D-Wave quantum annealer to solve complex logistic network design problems more efficiently than classical methods, with high accuracy.

## Contribution

The paper introduces a novel hybrid quantum-classical annealing algorithm for logistic network design, demonstrating its effectiveness on real problems using a quantum annealer.

## Key findings

- Average error below 1% compared to optimal solutions
- Significant reduction in iterations over classical algorithms
- Quantum approach feasible for complex supply-chain problems

## Abstract

The logistic network design is an abstract optimization problem that, under the assumption of minimal cost, seeks the optimal configuration of the supply chain's infrastructures and facilities based on customer demand. Key economic decisions are taken about the location, number, and size of manufacturing facilities and warehouses based on the optimal solution. Therefore, improvements in the methods to address this question, which is known to be in the NP-hard complexity class, would have relevant financial consequences. Here, we implement in the D-Wave quantum annealer a hybrid classical-quantum annealing algorithm. The cost function with constraints is translated to a spin Hamiltonian, whose ground state encodes the searched result. As a benchmark, we measure the accuracy of results for a set of paradigmatic problems against the optimal published solutions (the error is on average below $1\%$), and the performance is compared against the classical algorithm, showing a remarkable reduction in the number of iterations. This work shows that state-of-the-art quantum annealers may codify and solve relevant supply-chain problems even still far from useful quantum supremacy.