Analysis of Vehicle Routing Problem in Presence of Noisy Channels

TL;DR

This paper explores applying quantum computing, specifically variational quantum eigensolvers, to vehicle routing problems with an emphasis on robustness in noisy quantum channels.

Contribution

It introduces a quantum algorithm-based VRP solution for small instances and evaluates its robustness under noise using Qiskit simulations.

Findings

Quantum VRP solutions can be implemented for small instances.

Robustness of quantum solutions decreases with increased noise.

Hybrid quantum algorithms show potential for combinatorial optimization.

Abstract

Vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global solution. Quantum computing and quantum machine learning provide a new approach to solving combinatorial optimization of problems faster due to inherent speedups of quantum effects. Many solutions of VRP are offered across different quantum computing platforms using hybrid algorithms such as quantum approximate optimization algorithm and quadratic unconstrained binary optimization. Quantum computers such as IBM-Q experience along with Qiskit framework offer tools to solve combinatorial optimization problems. This work proposed here builds a basic VRP solution for 3 and 4 cities using variational quantum eigensolver on a variable ANSATZ. The work is further extended to evaluate the robustness of the solution in noisy channels available within the ambit of Qiskit framework.