Quantum-Assisted Vehicle Routing: Realizing QAOA-based Approach on Gate-Based Quantum Computer

TL;DR

This paper presents a quantum-assisted framework using QAOA for solving Vehicle Routing Problems on gate-based quantum computers, demonstrating practical implementation and analyzing hardware noise effects.

Contribution

It introduces a novel QAOA-based approach for VRP that encodes problem constraints directly into the quantum cost Hamiltonian and implements the full pipeline on real quantum hardware.

Findings

Successful implementation of VRP on IBM Quantum hardware

Analysis of penalty scaling and circuit depth effects

Identification of challenges due to hardware noise and decoherence

Abstract

The Vehicle Routing Problem (VRP) is a fundamental combinatorial optimization challenge with broad applications in logistics and transportation. In this work, we present a quantum-assisted framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) with a link-based formulation of VRP. Our approach encodes flow conservation and subtour elimination directly into the cost Hamiltonian, preserving graph structure while minimizing resource requirements for practical hardware implementation. We design and implement the full pipeline on a gate-based quantum computer, including problem formulation, encoding, circuit synthesis, and execution on IBM Quantum System One. Experimental results on small VRP instances highlight the effects of penalty scaling, coefficient normalization, and circuit depth on solution feasibility under hardware noise. While scalability remains constrained by circuit complexity and decoherence, the study demonstrates a practical pathway for implementing VRP on quantum hardware and identifies methodological directions for advancing near-term quantum optimization.