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Solving Higher Order Binary Optimization Problems on NISQ Devices: Experiments and Limitations

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Computational Science – ICCS 2023 (ICCS 2023)

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Abstract

With the recent availability of Noisy Intermediate-Scale Quantum devices, the potential of quantum computers to impact the field of combinatorial optimization lies in quantum variational and annealing-based methods. This paper further compares Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) in solving Higher Order Binary Optimization (HOBO) problems. This case study considers the hypergraph partitioning problem, which is used to generate custom HOBO problems. Our experiments show that D-Wave systems quickly reach limits solving dense HOBO problems. Although the QAOA demonstrates better performance on exact simulations, noisy simulations reveal that the gate error rate should remain under \(10^{-5}\) to match D-Wave systems’ performance, considering equal compilation overheads for both device.

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References

  1. Akshay, V., Rabinovich, D., Campos, E., Biamonte, J.: Parameter concentrations in quantum approximate optimization. Phys. Rev. A 104(1), L010401 (2021)

    Article  MathSciNet  Google Scholar 

  2. Basso, J., Gamarnik, D., et al.: Performance and limitations of the qaoa at constant levels on large sparse hypergraphs and spin glass models. arXiv preprint arXiv:2204.10306 (2022)

  3. Bunyk, P., et al.: Architectural considerations in the design of a superconducting quantum annealing processor. IEEE Trans. Appl. Supercond. 24(4), 1–10 (2014)

    Article  Google Scholar 

  4. Cai, J., Macready, W.G., Roy, A.: A practical heuristic for finding graph minors. arXiv preprint arXiv:1406.2741 (2014)

  5. Campbell, C., Dahl, E.: Qaoa of the highest order. In: 2022 IEEE 19th International Conference on Software Architecture Companion (ICSA-C), pp. 141–146. IEEE (2022)

    Google Scholar 

  6. Djidjev, H.N., Chapuis, G., Hahn, G., Rizk, G.: Efficient combinatorial optimization using quantum annealing. arXiv preprint arXiv:1801.08653 (2018)

  7. Farhi, E., et al.: A quantum approximate optimization algorithm (2014)

    Google Scholar 

  8. Gao, F., Han, L.: Implementing the nelder-mead simplex algorithm with adaptive parameters. Comput. Optim. Appl. 51(1), 259–277 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lucas, A.: Ising formulations of many np problems. Front. Phys., 5 (2014)

    Google Scholar 

  10. Md Sajid, A., et al.: Qiskit: An open-source framework for quantum computing (2022). https://doi.org/10.5281/zenodo.2573505

  11. Pelofske, E., Bärtschi, A., Eidenbenz, S.: Quantum annealing vs. qaoa: 127 qubit higher-order ising problems on nisq computers. arXiv preprint arXiv:2301.00520 (2023)

  12. Pudenz, K.L.: Parameter setting for quantum annealers. In: 2016 IEEE High Performance Extreme Computing Conference (HPEC), pp. 1–6 (2016)

    Google Scholar 

  13. Rodriguez, J.: Quantum algorithms for hypergraph bi-partitioning. In: 23ème congrès annuel de la Société Française de Recherche Opérationnelle et d’Aide à la Décision. INSA Lyon, Villeurbanne - Lyon, France (Feb 2022), https://hal.archives-ouvertes.fr/hal-03595234

  14. Rosenberg, I.G.: Reduction of bivalent maximization to the quadratic case. Cahiers du Centre d’Etudes de Recherche Operationnelle 17, 71–74 (1975)

    MathSciNet  MATH  Google Scholar 

  15. Tabi, Z., et al.: Quantum optimization for the graph coloring problem with space-efficient embedding. In: 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 56–62. IEEE (2020)

    Google Scholar 

  16. Ushijima-Mwesigwa, H., Negre, C.F., Mniszewski, S.M.: Graph partitioning using quantum annealing on the d-wave system. In: Proceedings of the Second International Workshop on Post Moores Era Supercomputing, pp. 22–29 (2017)

    Google Scholar 

  17. Willsch, D., et al.: Benchmarking advantage and d-wave 2000q quantum annealers with exact cover problems. Quantum Inf. Process. 21(4), 1–22 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhou, L., Wang, S.T., Choi, S., Pichler, H., Lukin, M.D.: Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near-term devices. Phys. Rev. X 10(2), 021067 (2020)

    Google Scholar 

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Acknowledgment

The work presented in this paper has been supported by AIDAS - AI, Data Analytics and Scalable Simulation - which is a Joint Virtual Laboratory gathering the Forschungszentrum Jülich (FZJ) and the French Alternative Energies and Atomic Energy Commission (CEA). We thank D. Vert for useful advice and fruitful discussions.

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Authors and Affiliations

  1. Université Paris-Saclay, CEA-List, 91120, Palaiseau, France

    Valentin Gilbert, Julien Rodriguez, Stéphane Louise & Renaud Sirdey

  2. Université de Bordeaux, INRIA, Palaiseau, France

    Julien Rodriguez

Authors
  1. Valentin Gilbert
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  2. Julien Rodriguez
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  3. Stéphane Louise
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  4. Renaud Sirdey
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Corresponding author

Correspondence to Valentin Gilbert .

Editor information

Editors and Affiliations

  1. Czech Technical University in Prague, Prague, Czech Republic

    Jiří Mikyška

  2. University of Amsterdam, Amsterdam, The Netherlands

    Clélia de Mulatier

  3. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  4. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  5. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  6. University of Amsterdam, Amsterdam, The Netherlands

    Peter M.A. Sloot

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Gilbert, V., Rodriguez, J., Louise, S., Sirdey, R. (2023). Solving Higher Order Binary Optimization Problems on NISQ Devices: Experiments and Limitations. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 10477. Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_18

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  • DOI: https://doi.org/10.1007/978-3-031-36030-5_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-36029-9

  • Online ISBN: 978-3-031-36030-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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