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Reusability report: Comparing gradient descent and Monte Carlo tree search optimization of quantum annealing schedules

Nature Machine Intelligence volume 4, pages 810–813 (2022)Cite this article

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The Original Article was published on 14 March 2022

arising from Yu-Qin Chen et al. Nature Machine Intelligence https://doi.org/10.1038/s42256-022-00446-y (2022).

The AI system AlphaZero1,2 famously learned to play complex and strategic games such as Go and chess and achieved super-human performance in these tasks. AlphaZero uses a combination of searching through the possible states of a game (Monte Carlo tree search) and a neural network to guide that search. The result is an algorithm that learns to choose sequences of moves that lead to a victory. Chen and colleagues3 set out to employ this same set of techniques to solve a specific class of combinatorial optimization problems—the 3-satisfiability (3-SAT) problems.

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Fig. 1: Fidelity at the end of the quantum annealing process versus annealing time T for 3-SAT instances with n = 11 variables and M = 5 frequency components in the annealing schedule s(t).
Fig. 2: Effect of the number of frequency components M on the algorithm’s performance.
Fig. 3: Fidelity at the end of the annealing process versus T for unweighted MAX CUT problems on 3-regular graphs with n = 12 vertices.

Data availability

The data for reproducing this work are available at https://github.com/condensedAI/quantumzero (ref. 15).

Code availability

The code can be found at https://github.com/condensedAI/quantumzero (ref. 15).

References

  1. Silver, D. et al. Mastering the game of Go without human knowledge. Nature 550, 354–359 (2017).

    Article  Google Scholar 

  2. Silver, D. et al. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science 362, 1140–1144 (2018).

    Article  MathSciNet  Google Scholar 

  3. Chen, Y.-Q. et al. Optimizing quantum annealing schedules with Monte Carlo tree search enhanced with neural networks. Nat. Mach. Intell. 4, 269–278 (2022).

    Article  Google Scholar 

  4. Kirkpatrick, S. & Selman, B. Critical behavior in the satisfiability of random boolean expressions. Science 264, 1297–1301 (1994).

    Article  MathSciNet  Google Scholar 

  5. Das, A. & Chakrabarti, B. K. Quantum Annealing and Related Optimization Methods Vol. 679 (Springer, 2005).

  6. Morita, S. & Nishimori, H. Mathematical foundation of quantum annealing. J. Math. Phys. 49, 125210 (2008).

    Article  MathSciNet  Google Scholar 

  7. Chen, Y.-Q., Chen, Y., Lee, C.-K., Zhang, S. & Hsieh, C.-Y. QuantumZero Code Repository (GitHub, 2022); https://github.com/yutuer21/quantumzero

  8. Nocedal, J. & Wright, S. Numerical Optimization (Springer, 2006).

  9. Bukov, M. et al. Reinforcement learning in different phases of quantum control. Phys. Rev. X 8, 031086 (2018).

    Google Scholar 

  10. Halperin, E., Livnat, D. & Zwick, U. MAX CUT in cubic graphs. J. Algorithms 53, 169–185 (2004).

    Article  MathSciNet  Google Scholar 

  11. 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, 021067 (2020).

    Google Scholar 

  12. Cerezo, M. et al. Variational quantum algorithms. Nat. Rev. Phys. 3, 625–644 (2021).

    Article  Google Scholar 

  13. Uvarov, A. V. & Biamonte, J. D. On barren plateaus and cost function locality in variational quantum algorithms. J. Phys. A 54, 245301 (2021).

    Article  MathSciNet  Google Scholar 

  14. Mele, A. A., Mbeng, G. B., Santoro, G. E., Collura, M. & Torta, P. Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz. Preprint at https://arxiv.org/abs/2206.01982 (2022).

  15. CondensedAI/Quantumzero Code Repository (GitHub, 2022); https://github.com/condensedAI/quantumzero

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Acknowledgements

M.W. was supported by the Villum Foundation (research grant no. 25310). This project received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement no. 847523 ‘INTERACTIONS’.

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Authors and Affiliations

  1. Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    Matteo M. Wauters & Evert van Nieuwenburg

  2. Lorentz Institute and Leiden Institute of Advanced Computer Science, Leiden University, Leiden, the Netherlands

    Evert van Nieuwenburg

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  1. Matteo M. Wauters
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  2. Evert van Nieuwenburg
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MMW performed the simulations and analyzed the data. Both authors contributed to writing the code and interpreting the data and to the writing.

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Correspondence to Evert van Nieuwenburg.

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Wauters, M.M., van Nieuwenburg, E. Reusability report: Comparing gradient descent and Monte Carlo tree search optimization of quantum annealing schedules. Nat Mach Intell 4, 810–813 (2022). https://doi.org/10.1038/s42256-022-00535-y

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