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Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms

Eneko Osaba, Pablo Miranda-Rodriguez, Andreas Oikonomakis, Matic Petrič, Alejandra Ruiz, Sebastian Bock, Michail-Alexandros Kourtis

TL;DR

Q4DR tackles drone routing under real-world constraints by a two-phase hybrid quantum program: a QAOA-based clustering stage partitions $N$ visiting points for two drones, followed by a routing phase solved via quantum annealing on D-Wave hardware. EclipseQrisp enables high-level MaxCut formulation and quantum-variable programming, while D-Wave's HSS and NL-Hybrid/CQM-Hybrid methods provide scalable hybrid solvers for ATSP and open-route problems, respectively. The three demonstrated use cases (including itinerant charging with $M = N/3$ charging points) show reliability against classical baselines for simpler scenarios and establish a path toward larger, more realistic deployments, despite current hardware constraints. The work highlights practical implications for quantum optimization in logistics and outlines future directions such as broader constraints, heterogeneous fleets, problem-size reductions, and comprehensive benchmarking.

Abstract

This paper presents a novel hybrid approach to solving real-world drone routing problems by leveraging the capabilities of quantum computing. The proposed method, coined Quantum for Drone Routing (Q4DR), integrates the two most prominent paradigms in the field: quantum gate-based computing, through the Eclipse Qrisp programming language; and quantum annealers, by means of D-Wave System's devices. The algorithm is divided into two different phases: an initial clustering phase executed using a Quantum Approximate Optimization Algorithm (QAOA), and a routing phase employing quantum annealers. The efficacy of Q4DR is demonstrated through three use cases of increasing complexity, each incorporating real-world constraints such as asymmetric costs, forbidden paths, and itinerant charging points. This research contributes to the growing body of work in quantum optimization, showcasing the practical applications of quantum computing in logistics and route planning.

Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms

TL;DR

Q4DR tackles drone routing under real-world constraints by a two-phase hybrid quantum program: a QAOA-based clustering stage partitions visiting points for two drones, followed by a routing phase solved via quantum annealing on D-Wave hardware. EclipseQrisp enables high-level MaxCut formulation and quantum-variable programming, while D-Wave's HSS and NL-Hybrid/CQM-Hybrid methods provide scalable hybrid solvers for ATSP and open-route problems, respectively. The three demonstrated use cases (including itinerant charging with charging points) show reliability against classical baselines for simpler scenarios and establish a path toward larger, more realistic deployments, despite current hardware constraints. The work highlights practical implications for quantum optimization in logistics and outlines future directions such as broader constraints, heterogeneous fleets, problem-size reductions, and comprehensive benchmarking.

Abstract

This paper presents a novel hybrid approach to solving real-world drone routing problems by leveraging the capabilities of quantum computing. The proposed method, coined Quantum for Drone Routing (Q4DR), integrates the two most prominent paradigms in the field: quantum gate-based computing, through the Eclipse Qrisp programming language; and quantum annealers, by means of D-Wave System's devices. The algorithm is divided into two different phases: an initial clustering phase executed using a Quantum Approximate Optimization Algorithm (QAOA), and a routing phase employing quantum annealers. The efficacy of Q4DR is demonstrated through three use cases of increasing complexity, each incorporating real-world constraints such as asymmetric costs, forbidden paths, and itinerant charging points. This research contributes to the growing body of work in quantum optimization, showcasing the practical applications of quantum computing in logistics and route planning.

Paper Structure

This paper contains 12 sections, 4 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Quantum Computing for the drone mission planning
  4. Eclipse Qrisp programming language
  5. Method
  6. Clustering phase
  7. Routing Phase
  8. Demonstration
  9. UC1: Two drones and a single depot
  10. UC2: Two drones and two depots
  11. UC3: Two drones, two depots and itinerant charging stations
  12. Conclusions & Further Work

Figures (5)

  • Figure 1: Workflow of the implemented hybrid solver.
  • Figure 2: D-Wave's HSS schemes. CM = Classical Module. QM = Quantum Module.
  • Figure 3: Results obtained by Q4RD in the UC1.
  • Figure 4: Results obtained by Q4RD in the UC2. The depots are colored black.
  • Figure 5: Results obtained by Q4RD in the UC3. The depots are colored black.