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Quantum Approximate Optimisation for Not-All-Equal SAT

Published 5 Jan 2024 in quant-ph | (2401.02852v1)

Abstract: Establishing quantum advantage for variational quantum algorithms is an important direction in quantum computing. In this work, we apply the Quantum Approximate Optimisation Algorithm (QAOA) -- a popular variational quantum algorithm for general combinatorial optimisation problems -- to a variant of the satisfiability problem (SAT): Not-All-Equal SAT (NAE-SAT). We focus on regimes where the problems are known to have solutions with low probability and introduce a novel classical solver that outperforms existing solvers. Extensively benchmarking QAOA against this, we show that while the runtime of both solvers scales exponentially with the problem size, the scaling exponent for QAOA is smaller for large enough circuit depths. This implies a polynomial quantum speedup for solving NAE-SAT.

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References (35)
  1. Quantum algorithms: A survey of applications and end-to-end complexities, 2023.
  2. Variational quantum algorithms. Nature Reviews Physics, 3(9):625–644, August 2021.
  3. A quantum approximate optimization algorithm, 2014. Available from https://arxiv.org/abs/1411.4028.
  4. Evaluating quantum approximate optimization algorithm: A case study. In 2019 Tenth International Green and Sustainable Computing Conference (IGSC). IEEE, oct 2019. Available from https://doi.org/10.1109%2Figsc48788.2019.8957201.
  5. Training variational quantum algorithms is np-hard. Physical Review Letters, 127(12), September 2021.
  6. The quantum approximate optimization algorithm needs to see the whole graph: A typical case, 2020.
  7. The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size. Quantum, 6:759, July 2022.
  8. Performance and limitations of the qaoa at constant levels on large sparse hypergraphs and spin glass models, 2022.
  9. Limitations of local quantum algorithms on random max-k-xor and beyond. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2022.
  10. Solving boolean satisfiability problems with the quantum approximate optimization algorithm, 2022. Available from https://arxiv.org/abs/2208.06909.
  11. Stephen A. Cook. The complexity of theorem-proving procedures. In Proceedings of the Third Annual ACM Symposium on Theory of Computing, STOC ’71, page 151–158, New York, NY, USA, 1971. Association for Computing Machinery. Available from https://doi.org/10.1145/800157.805047.
  12. Qed: Quick error detection tests for effective post-silicon validation. In 2010 IEEE International Test Conference, pages 1–10, 2010. Available from https://ieeexplore.ieee.org/document/5699215.
  13. Planning as satisfiability. In Bernd Neumann, editor, 10th European Conference on Artificial Intelligence, ECAI 92, Vienna, Austria, August 3-7, 1992. Proceedings, pages 359–363. John Wiley and Sons, 1992. Available from https://www.cs.cornell.edu/selman/papers/pdf/92.ecai.satplan.pdf.
  14. Finding bugs with a constraint solver. In Proceedings of the 2000 ACM SIGSOFT International Symposium on Software Testing and Analysis, ISSTA ’00, page 14–25, New York, NY, USA, 2000. Association for Computing Machinery. Available from https://doi.org/10.1145/347324.383378.
  15. The quest for efficient boolean satisfiability solvers. In Proceedings of the 14th International Conference on Computer Aided Verification, CAV ’02, page 17–36, Berlin, Heidelberg, 2002. Springer-Verlag. Available from https://www.princeton.edu/~chaff/publication/cade_cav_2002.pdf.
  16. The Nature of Computation. Oxford University Press, 2011. Available from https://www.amazon.co.uk/Nature-Computation-Cristopher-Moore/dp/0199233217.
  17. Amin Coja-Oghlan. Random constraint satisfaction problems. In S. Barry Cooper and Vincent Danos, editors, Proceedings Fifth Workshop on Developments in Computational Models–Computational Models From Nature, DCM 2009, Rhodes, Greece, 11th July 2009, volume 9 of EPTCS, pages 32–37, 2009. Available from https://doi.org/10.4204/EPTCS.9.4.
  18. Improving WalkSAT By Effective Tie-Breaking and Efficient Implementation. The Computer Journal, 58(11):2864–2875, 11 2014. Available from https://doi.org/10.1093/comjnl/bxu135.
  19. Reachability deficits in quantum approximate optimization. Physical Review Letters, 124(9), March 2020.
  20. Quantum computational phase transition in combinatorial problems. npj Quantum Information, 8(1):1–11, 2022.
  21. Bernard ME Moret. Planar nae3sat is in p. ACM SIGACT News, 19(2):51–54, 1988.
  22. Satisfiability threshold for random regular nae-sat, 2013.
  23. The number of solutions for random regular nae-sat, 2016. Available from https://arxiv.org/abs/1604.08546.
  24. Quantum computation by adiabatic evolution, 2000. Available from https://arxiv.org/abs/quant-ph/0001106.
  25. Noise strategies for improving local search. Proceedings of the National Conference on Artificial Intelligence, 1, 09 1999. Available from https://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=EA15D3B4A4BA9334625A14FC12A28742?doi=10.1.1.319.7660&rep=rep1&type=pdf.
  26. One-step replica symmetry breaking of random regular nae-sat i, 2021. Available form https://arxiv.org/abs/2011.14270.
  27. Python satellite data analysis toolkit (pysat) vx.y.z, 2021. Available from https://doi.org/10.5281/zenodo.1199703.
  28. Comprehensive score: Towards efficient local search for sat with long clauses. In International Joint Conference on Artificial Intelligence, 2013. Available from https://www.ijcai.org/Proceedings/13/Papers/080.pdf.
  29. Lov K. Grover. A fast quantum mechanical algorithm for database search, 1996. Available from https://arxiv.org/abs/quant-ph/9605043.
  30. Limits to quantum gate fidelity from near-field thermal and vacuum fluctuations, 2023. Available from https://arxiv.org/abs/2207.09441.
  31. Full-state quantum circuit simulation by using data compression. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. ACM, nov 2019. Available from https://doi.org/10.1145%2F3295500.3356155.
  32. Stuart Hadfield. On the representation of boolean and real functions as hamiltonians for quantum computing. ACM Transactions on Quantum Computing, 2(4):1–21, dec 2021. Available from https://doi.org/10.1145%2F3478519.
  33. Qiskit contributors. Qiskit: An open-source framework for quantum computing, 2023. Available from https://doi.org/10.5281/zenodo.2573505.
  34. Pytorch: An imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32, pages 8024–8035. Curran Associates, Inc., 2019. Available from http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf.
  35. John Bent. Data-Driven Batch Scheduling. PhD thesis, University of Wisconsin, Madison, May 2005. Available from https://research.cs.wisc.edu/wind/Publications/thesis_johnbent.pdf.

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