Optimizing Tourism Routes: A Quantum Approach to the Profitable Tour Problem.

Area of Science:

• Quantum Computing
• Optimization Theory
• Computational Science

Background:

• The Profitable Tour Problem (PTP) is an NP-hard optimization problem crucial for tourism planning.
• Classical heuristic methods for PTP often yield approximate solutions, failing to guarantee global optimality.
• Existing quantum approaches may face challenges with complex constraint handling in optimization problems.

Purpose of the Study:

• To explore the application of near-term quantum computing for solving the Profitable Tour Problem.
• To develop a novel quantum framework utilizing the Variational Quantum Eigensolver (VQE).
• To introduce a constraint-aware variational ansatz for direct encoding of PTP constraints.

Main Methods:

• Implementation of a Variational Quantum Eigensolver (VQE) framework.
• Development of a novel constraint-aware variational ansatz tailored for the PTP.
• Formulation of the problem Hamiltonian, avoiding large penalty terms.
• Numerical simulations on tourism scenarios using up to 25 qubits.

Main Results:

• Demonstrated the viability of the VQE approach for the PTP.
• Achieved high solution accuracy comparable to brute-force methods for smaller problem instances.
• Validated the effectiveness of the constraint-aware ansatz in simplifying the optimization landscape.
• Showcased the potential for quantum computing in complex tourism optimization.

Conclusions:

• The proposed VQE framework offers a promising approach for tackling the Profitable Tour Problem.
• The constraint-aware ansatz represents a significant advancement in applying quantum algorithms to constrained optimization.
• This work serves as a proof-of-concept for future research on quantum hardware for tourism optimization.