New optimization tutorial: Drone Route Optimization with QAOA

[Jnan-py]

Summary

This PR introduces a new tutorial: Drone Route Optimization using QAOA, added to the optimization folder.
The tutorial demonstrates how to map a real-world drone delivery routing problem into the combinatorial optimization problem Traveling Salesman Problem (TSP), formulate it as a QUBO/Ising Hamiltonian, and solve it using the Quantum Approximate Optimization Algorithm (QAOA) in Qiskit.

Objectives

• Understand how to formulate the drone delivery problem as a combinatorial optimization problem.
• Learn the mapping from TSP → QUBO → Ising Hamiltonian.
• Explore how QAOA can be used for approximate route optimization.
• Gain insights into penalty parameter scaling, ansatz design, and decoding of quantum solutions.
• Compare classical and quantum-inspired approaches for optimization.
• Demonstrate how quantum-inspired optimization can provide heuristics for logistics and routing tasks.

Prerequisites

• Basic familiarity with Qiskit and quantum circuits.
• Knowledge of combinatorial optimization and the TSP.
• Understanding of QUBO formulations and binary variable mappings.

Details and comments

• Added full mathematical derivation:
  • Objective function
  • One-hot constraints
  • QUBO with penalty terms
  • Mapping to Pauli-(Z) Hamiltonian
• Tutorial includes:
  • Explanations of QAOA ansatz and mixers
  • Decoding measurement results into valid tours
  • Practical notes on penalty scaling and optimizer settings
• Notebook is structured in the Qiskit Community Tutorials style with Introduction, Background, Implementation, and Conclusion.

Changelog

• Added new tutorial: Drone Route Optimization using QAOA under optimization/.

Checklist

• Tutorial notebook is added in the correct folder.
• Mathematical formulations and background theory are included.
• Notebook runs fully without execution errors.
• Documentation has been updated accordingly.
• CONTRIBUTING document has been read and followed.
• Tutorial notebook includes references/links to related Qiskit Optimization and QAOA resources.

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