Evaluating Parameter Transfer in FALQON Across Graph Families

• Alisson dos Passos Fumaco Instituto de Pesquisas Eldorado https://orcid.org/0009-0003-3258-5146
• Marcos Vinicius Reballo Instituto de Pesquisas Eldorado https://orcid.org/0009-0003-6396-9302
• Fernando Augusto Caletti de Barros Instituto de Pesquisas Eldorado https://orcid.org/0009-0008-5152-7036
• Gabriel Fernandes Thomaz Instituto de Pesquisas Eldorado https://orcid.org/0009-0007-7410-5189
• Eduardo I. Duzzioni Instituto de Pesquisas Eldorado / UFSC https://orcid.org/0000-0002-8971-2033

DOI: https://doi.org/10.5753/sbccq.2026.23365

Resumo

We evaluate FALQON parameter transfer for Max-Cut, transferring sequences from small donors (n ∈ {8, 10, 12}) to 14-node recipients. Using 3-regular and Erdős–Rényi families, we show transfer success is dictated by the recipient graph, not the donor. Transfer excels for dense recipients—achieving high approximation ratios regardless of the donor—but remains challenging in sparse cross-family cases. Crucially, performance is highly resilient to donor size, with 8-node donors matching larger instances. Thus, cheap small graphs can provide robust parameters for larger targets, significantly reducing the measurement overhead of the feedback loop.

Referências

Bollobás, B. (2001). Random Graphs, volume 73 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge.

Brif, C., Chakrabarti, R., and Rabitz, H. (2010). Control of quantum phenomena: past, present and future. New Journal of Physics, 12(7):075008.

Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., and Coles, P. J. (2021). Variational quantum algorithms. Nature Reviews Physics, 3:625–644.

Dong, D. and Petersen, I. R. (2013). A survey of quantum lyapunov control methods. Annual Reviews in Control, 37(1):1–17.

Egger, D. J., Mareček, J., and Woerner, S. (2021). Warm-starting quantum optimization. Quantum, 5:479.

Falla, J., Langfitt, Q., Alexeev, Y., and Safro, I. (2024). Graph representation learning for parameter transferability in the quantum approximate optimization algorithm. Quantum Machine Intelligence, 6(46).

Farhi, E., Goldstone, J., and Gutmann, S. (2014). A quantum approximate optimization algorithm. arXiv:1411.4028.

Galda, A., Gupta, E., Falla, J., Liu, X., Lykov, D., Alexeev, Y., and Safro, I. (2023). Similarity-based parameter transferability in the quantum approximate optimization algorithm. Frontiers in Quantum Science and Technology, 2:1200975.

Grivopoulos, S. and Bamieh, B. (2003). Lyapunov-based control of quantum systems. Proceedings of the 42nd IEEE Conference on Decision and Control, pages 434–438.

Herrman, R., Treffert, L., Ostrowski, J., Lotshaw, P. C., Humble, T. S., and Siopsis, G. (2021). Impact of graph structures for qaoa on maxcut. arXiv:2102.05997.

Jing, H., Wang, Y., and Li, Y. (2023). Data-driven quantum approximate optimization algorithm for power systems. Communications Engineering, 2(1):12.

Lucas, A. (2014). Ising formulations of many np problems. Frontiers in Physics, 2:5.

Lyngfelt, I. and García-Álvarez, L. (2025). Symmetry-informed transferability of optimal parameters in the quantum approximate optimization algorithm. Physical Review A, 111:022418.

Magann, A. B., Rudinger, K. M., Grace, M. D., and Sarovar, M. (2022a). Feedback-based quantum optimization. Physical Review Letters, 129:250502.

Magann, A. B., Rudinger, K. M., Grace, M. D., and Sarovar, M. (2022b). Lyapunov-control-inspired strategies for quantum combinatorial optimization. Physical Review A, 106:062414.

McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., and Neven, H. (2018). Barren plateaus in quantum neural network training landscapes. Nature Communications, 9(1).

Okada, K. N., Nishi, H., Kosugi, T., and Matsushita, Y.-i. (2023). Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions. Scientific Reports, 13:50406.

Pérez, V. P., Grace, M. D., Arenz, C., and Magann, A. B. (2026). Learning parameter curves in feedback-based quantum optimization algorithms. arXiv preprint arXiv:2601.08085.

Self, C. N., Khosla, K. E., Smith, A. W. R., Sauvage, F., Haynes, P. D., Knolle, J., Mintert, F., and Kim, M. S. (2021). Variational quantum algorithm with information sharing. npj Quantum Information, 7(1):116.

Shaydulin, R., Lotshaw, P. C., Larson, J., Ostrowski, J., and Humble, T. S. (2023). Parameter transfer for quantum approximate optimization of weighted maxcut. ACM Transactions on Quantum Computing, 4(3):1–15.

Wang, Z., Hadfield, S., Jiang, Z., and Rieffel, E. (2018). Quantum approximate optimization algorithm for maxcut: A fermionic view. Physical Review A, 97(2):022304.

Zhou, L., Wang, S.-T., Choi, S., Pichler, H., and Lukin, M. D. (2020). Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near-term devices. Physical Review X, 10:021067.