A Warm-start QAOA based approach using a swap-based mixer for the TSP: theoretical considerations,implementation and experiments

• URL: http://arxiv.org/abs/2505.01214v2
• Date: Thu, 05 Jun 2025 08:38:30 GMT
• Title: A Warm-start QAOA based approach using a swap-based mixer for the TSP: theoretical considerations,implementation and experiments
• Abstract summary: We introduce a swap-based mixer tailored to the Traveling Salesman Problem (TSP)<n>We propose a warm-start technique that initializes QAOA with a solution generated by any classical solution.<n> Experimental results on a custom TSP instance involving five customers demonstrate the effectiveness of this approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper investigates quantum heuristics based on Mixer Hamiltonians, which allow the search to be restricted to a specific subspace and enable warm-start strategies for solving the Traveling Salesman Problem (TSP). Approaches involving Mixer Hamiltonians can be integrated into the Quantum Approximate Optimization Algorithm (QAOA), where the Mixer acts as a mapping function that transforms qubit strings into feasible solution sets. We first introduce a swap-based mixer tailored to the TSP, which ensures that only qubit strings representing valid TSP solutions are explored during the QAOA process. Second, we propose a warm-start technique that initializes QAOA with a solution generated by any classical heuristic, thereby promoting faster convergence. These two contributions are combined into a Warm-Start QAOA framework with a Swap-Based Mixer, leveraging both structural and initialization advantages. Experimental results on a custom TSP instance involving five customers demonstrate the effectiveness of this approach, providing, for the first time, a viable integration of warm-start and swap-based mixers for the TSP within a quantum optimization framework.

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