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

Fuente: arXiv
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Main Authors: Bourreau, E., Fleury, G., Lacomme, P.
Format: Preprint
Published: 2025
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author Bourreau, E.
Fleury, G.
Lacomme, P.
author_facet Bourreau, E.
Fleury, G.
Lacomme, P.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_01214
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Warm-start QAOA based approach using a swap-based mixer for the TSP: theoretical considerations,implementation and experiments
Bourreau, E.
Fleury, G.
Lacomme, P.
Quantum Physics
Mathematical Physics
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.
title A Warm-start QAOA based approach using a swap-based mixer for the TSP: theoretical considerations,implementation and experiments
topic Quantum Physics
Mathematical Physics
url https://arxiv.org/abs/2505.01214