- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Optimizing QAOA circuit transpilation with parity twine and SWAP network encodings

J. A. Montañez-Barrera1,*, Yanjun Ji2, Michael R. von Spakovsky3, David E. Bernal Neira4, and Kristel Michielsen1,5,6

  • *Contact author: j.montanez-barrera@fz-juelich.de
PDF

Phys. Rev. Applied 26, 024012 – Published 7 August, 2026

DOI: https://doi.org/10.1103/sjqb-b1h4

Abstract

Mapping quantum approximate optimization algorithm (QAOA) circuits with nontrivial connectivity in fixed-layout quantum platforms, such as superconducting quantum processing units (QPUs), requires a transpilation process to match the circuit to the hardware layout. This step is critical for reducing error rates on noisy QPUs. Two approaches that improve the resources required for such transpilation are the SWAP network and parity twine chains (PTC), which reduce the two-qubit gate count and circuit depth needed to represent fully connected circuits. In this work, we introduce a simulated annealing-based method that further reduces the encoding overhead of PTC and SWAP networks for QAOA circuits with nonfully connected two-qubit interactions. The method is benchmarked against various transpilers, including the Qiskit SAT mapper, demonstrating that beyond specific connectivity thresholds it achieves significant reductions in both two-qubit gate count and circuit depth. For example, for a 120-qubit QAOA instance with 25% connectivity, our method achieves an 87% reduction in depth and a 29% reduction in two-qubit gates compared with the Qiskit transpiler. Finally, the practical impact of PTC encoding is validated by benchmarking QAOA on the ibm_fez and ibm_kingston devices, showing improved performance for systems of up to 20 qubits.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (36)

  1. Y. Ge, W. Wenjie, C. Yuheng, P. Kaisen, L. Xudong, Z. Zixiang, W. Yuhan, W. Ruocheng, and Y. Junchi, Quantum circuit synthesis and compilation optimization: Overview and prospects, arXiv:2407.00736.
  2. J. Kusyk, S. M. Saeed, and M. U. Uyar, Survey on quantum circuit compilation for noisy intermediate-scale quantum computers: Artificial intelligence to heuristics, IEEE Trans. Quantum Eng. 2, 1 (2021).
  3. Y. Ji, S. Brandhofer, and I. Polian, Calibration-aware transpilation for variational quantum optimization, in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE Computer Society, Los Alamitos, CA, USA, 2022), pp. 204–214.
  4. Q. Fu, J. Wu, and X. Wang, Decoherence in exchange-coupled quantum spin-qubit systems: Impact of multiqubit interactions and geometric connectivity, Phys. Rev. A 109, 052628 (2024).
  5. R. E. Throckmorton and S. Das Sarma, Crosstalk- and charge-noise-induced multiqubit decoherence in exchange-coupled quantum dot spin qubit arrays, Phys. Rev. B 105, 245413 (2022).
  6. M. Y. Siraichi, V. F. d. Santos, C. Collange, and F. M. Q. Pereira, Qubit allocation, in Proceedings of the 2018 International Symposium on Code Generation and Optimization, CGO ’18 (Association for Computing Machinery, New York, NY, USA, 2018), pp. 113–125.
  7. V. R. Pascuzzi, A. He, C. W. Bauer, W. A. de Jong, and B. Nachman, Computationally efficient zero-noise extrapolation for quantum-gate-error mitigation, Phys. Rev. A 105, 042406 (2022).
  8. G. E. Crooks, Performance of the quantum approximate optimization algorithm on the maximum cut problem, arXiv:1811.08419.
  9. I. D. Kivlichan, J. McClean, N. Wiebe, C. Gidney, A. Aspuru-Guzik, G. K.-L. Chan, and R. Babbush, Quantum simulation of electronic structure with linear depth and connectivity, Phys. Rev. Lett. 120, 110501 (2018).
  10. B. O’Gorman, W. J. Huggins, E. G. Rieffel, and K. B. Whaley, Generalized swap networks for near-term quantum computing, arXiv:1905.05118.
  11. T. Hagge, Optimal fermionic swap networks for hubbard models, arXiv:2001.08324.
  12. J. Weidenfeller, L. C. Valor, J. Gacon, C. Tornow, L. Bello, S. Woerner, and D. J. Egger, Scaling of the quantum approximate optimization algorithm on superconducting qubit based hardware, Quantum 6, 870 (2022).
  13. Y. Ji, X. Chen, I. Polian, and Y. Ban, Algorithm-oriented qubit mapping for variational quantum algorithms, Phys. Rev. Appl. 23, 034022 (2025).
  14. A. Holmes, S. Johri, G. G. Guerreschi, J. S. Clarke, and A. Y. Matsuura, Impact of qubit connectivity on quantum algorithm performance, Quantum Sci. Technol. 5, 025009 (2020).
  15. E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028.
  16. F. Dreier, C. Fleckenstein, G. Aigner, M. Fellner, R. Stahn, M. Lanthaler, and W. Lechner, Connectivity-aware synthesis of quantum algorithms, arXiv:2501.14020.
  17. B. Klaver, S. Rombouts, M. Fellner, A. Messinger, K. Ender, K. Ludwig, and W. Lechner, Swap-less implementation of quantum algorithms, Phys. Rev. A 113, 012443 (2024)..
  18. L. Vinet and A. Zhedanov, A “missing” family of classical orthogonal polynomials, J. Phys. A: Math. Theor. 44, 085201 (2011).
  19. D. Coppersmith, An approximate fourier transform useful in quantum factoring, arXiv:quant-ph/0201067.
  20. A. Matsuo, S. Yamashita, and D. J. Egger, A sat approach to the initial mapping problem in swap gate insertion for commuting gates, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E106.A, 1424 (2023).
  21. Qiskit Community, QAOA best practices for quantum optimization (2025) https://github.com/qiskit-community/qopt-best-practices. accessed: 2026-04-17.
  22. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by simulated annealing, Science 220, 671 (1983) 10.1126/science.220.4598.671.
  23. J. A. Montanez-Barrera and K. Michielsen, Towards a universal QAOA protocol: Evidence of a scaling advantage in solving some combinatorial optimization problems (2024) arXiv:2405.09169.
  24. J. A. Montanez-Barrera, K. Michielsen, and D. E. B. Neira, Evaluating the performance of quantum process units at large width and depth, arXiv:2502.06471.
  25. A. Hashim, R. Rines, V. Omole, R. K. Naik, J. M. Kreikebaum, D. I. Santiago, F. T. Chong, I. Siddiqi, and P. Gokhale, Optimized swap networks with equivalent circuit averaging for QAOA, Phys. Rev. Res. 4, 033028 (2022).
  26. Y. Ji, K. F. Koenig, and I. Polian, Improving the performance of digitized counterdiabatic quantum optimization via algorithm-oriented qubit mapping, Phys. Rev. A 110, 032421 (2024).
  27. Y. Ji and I. Polian, Synergistic dynamical decoupling and circuit design for enhanced algorithm performance on near-term quantum devices, Entropy 26, 586 (2024).
  28. Y. Ji, K. F. Koenig, and I. Polian, Optimizing quantum algorithms on bipotent architectures, Phys. Rev. A 108, 022610 (2023).
  29. IBM Quantum, Qiskit: An open-source quantum SDK (2025). accessed: 2025-03-19.
  30. Qiskit Development Team, Qiskit transpiler API documentation (2025). accessed: 2025-05-13.
  31. IBM Quantum, AI-powered transpiler passes (2025). accessed: 2025-03-19.
  32. Quantinuum, Tket documentation, https://docs.quantinuum.com/tket/ accessed: 2025-03-19.
  33. P. D. Nation and M. Treinish, Suppressing quantum circuit errors due to system variability, PRX Quantum 4, 010327 (2023).
  34. P. D. Nation, A. A. Saki, S. Brandhofer, L. Bello, S. Garion, M. Treinish, and A. Javadi-Abhari, Benchmarking the performance of quantum computing software, Nat. Comput. Sci. 5, 427 (2025).
  35. D. Bertsimas and J. Tsitsiklis, Simulated annealing, Stat. Sci. 8, 10 (1993).

  36. https://github.com/alejomonbar/QAOA-efficient-circuit-transpilation.

Outline

Information

Phys. Rev. Applied 26, 024012– Published 7 August, 2026
  • Received 29 January 2026
  • Revised 4 May 2026
  • Accepted 30 June 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation