Document Open Access Logo

Local Algorithms and the Failure of Log-Depth Quantum Advantage on Sparse Random CSPs

Authors Antares Chen , Neng Huang , Kunal Marwaha

PDF

File

Thumbnail PDF
PDF
LIPIcs.APPROX-RANDOM.2026.78.pdf
  • Filesize: 3.69 MB
  • 26 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Randomness, geometry and discrete structures
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Random CSP
  • message-passing algorithm

Metrics

Abstract

We construct and analyze a message-passing algorithm for random constraint satisfaction problems (CSPs) at large clause density, generalizing work of El Alaoui, Montanari, and Sellke for Maximum Cut [Alaoui et al., 2023] through a connection between random CSPs and mean-field Ising spin glasses [Alaoui et al., 2021; Jones et al., 2023]. For CSPs with even predicates, the algorithm asymptotically solves a stochastic optimal control problem dual to an extended Parisi variational principle. This gives an optimal fraction of satisfied constraints among algorithms obstructed by the branching overlap gap property of Huang and Sellke [Huang and Sellke, 2025], notably including the Quantum Approximate Optimization Algorithm and all quantum circuits on a bounded-degree architecture of up to ε ⋅ log n depth [Chou et al., 2022].

Cite As Get BibTex

Antares Chen, Neng Huang, and Kunal Marwaha. Local Algorithms and the Failure of Log-Depth Quantum Advantage on Sparse Random CSPs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 78:1-78:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.78

Author Details

Antares Chen
  • University of Chicago, IL, USA
Neng Huang
  • University of Michigan, Ann Arbor, MI, USA
Kunal Marwaha
  • University of Chicago, IL, USA

References

  1. Ahmed El Alaoui, Andrea Montanari, and Mark Sellke. Optimization of mean-field spin glasses. The Annals of Probability, 49(6):2922-2960, 2021. URL: https://arxiv.org/abs/2001.00904.
  2. Ahmed El Alaoui, Andrea Montanari, and Mark Sellke. Sampling from the sherrington-kirkpatrick gibbs measure via algorithmic stochastic localization. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 323-334. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00038.
  3. Ahmed El Alaoui, Andrea Montanari, and Mark Sellke. Local algorithms for maximum cut and minimum bisection on locally treelike regular graphs of large degree, 2023. URL: https://arxiv.org/abs/2111.06813.
  4. Anurag Anshu and Tony Metger. Concentration bounds for quantum states and limitations on the QAOA from polynomial approximations. Quantum, 7:999, May 2023. URL: https://doi.org/10.22331/q-2023-05-11-999.
  5. Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando G. S. L. Brandao, David A. Buell, Brian Burkett, Yu Chen, Zijun Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, Austin Fowler, Craig Gidney, Marissa Giustina, Rob Graff, Keith Guerin, Steve Habegger, Matthew P. Harrigan, Michael J. Hartmann, Alan Ho, Markus Hoffmann, Trent Huang, Travis S. Humble, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Paul V. Klimov, Sergey Knysh, Alexander Korotkov, Fedor Kostritsa, David Landhuis, Mike Lindmark, Erik Lucero, Dmitry Lyakh, Salvatore Mandrà, Jarrod R. McClean, Matthew McEwen, Anthony Megrant, Xiao Mi, Kristel Michielsen, Masoud Mohseni, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Murphy Yuezhen Niu, Eric Ostby, Andre Petukhov, John C. Platt, Chris Quintana, Eleanor G. Rieffel, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Kevin J. Sung, Matthew D. Trevithick, Amit Vainsencher, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, and John M. Martinis. Quantum supremacy using a programmable superconducting processor. Nature, 574(7779):505-510, October 2019. URL: https://doi.org/10.1038/s41586-019-1666-5.
  6. Antonio Auffinger and Wei-Kuo Chen. Parisi formula for the ground state energy in the mixed p-spin model. The Annals of Probability, 45(6B):4617-4631, 2017. URL: https://arxiv.org/abs/1606.05335.
  7. Antonio Auffinger, Andrea Montanari, and Eliran Subag. Optimization of random high-dimensional functions: Structure and algorithms. In Patrick Charbonneau, Enzo Marinari, Giorgio Parisi, Federico Ricci-Tersenghi, Gabriele Sicuro, Francesco Zamponi, and Marc Mézard, editors, Spin Glass Theory and Far Beyond: Replica Symmetry Breaking After 40 Years, chapter 29. World Scientific, 2023. URL: https://arxiv.org/abs/2206.10217.
  8. Boaz Barak and Kunal Marwaha. Classical algorithms and quantum limitations for maximum cut on high-girth graphs. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022), 2022. URL: https://doi.org/10.4230/LIPIcs.ITCS.2022.14.
  9. Boaz Barak, Ankur Moitra, Ryan O'Donnell, Prasad Raghavendra, Oded Regev, David Steurer, Luca Trevisan, Aravindan Vijayaraghavan, David Witmer, and John Wright. Beating the random assignment on constraint satisfaction problems of bounded degree. In APPROX/RANDOM 2015, pages 110-123, 2015. URL: https://arxiv.org/abs/1505.03424.
  10. Aseem Baranwal, Kimon Fountoulakis, and Aukosh Jagannath. Optimality of message-passing architectures for sparse graphs. Advances in Neural Information Processing Systems, 36:40320-40341, 2023. URL: https://doi.org/10.48550/arXiv.2305.10391.
  11. Joao Basso, Edward Farhi, Kunal Marwaha, Benjamin Villalonga, and Leo Zhou. The Quantum Approximate Optimization Algorithm at high depth for MaxCut on large-girth regular graphs and the Sherrington-Kirkpatrick model. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography, 2022. URL: https://arxiv.org/abs/2110.14206.
  12. Joao Basso, David Gamarnik, Song Mei, and Leo Zhou. Performance and limitations of the QAOA at constant levels on large sparse hypergraphs and spin glass models. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS). IEEE, October 2022. URL: https://doi.org/10.1109/focs54457.2022.00039.
  13. Mohsen Bayati and Andrea Montanari. The dynamics of message passing on dense graphs, with applications to compressed sensing. IEEE Transactions on Information Theory, 57(2):764-785, 2011. URL: https://arxiv.org/abs/1001.3448.
  14. Erwin Bolthausen. An iterative construction of solutions of the TAP equations for the Sherrington-Kirkpatrick model. Communications in Mathematical Physics, 325(1):333-366, 2014. URL: https://arxiv.org/abs/1201.2891.
  15. Adam Bouland, Bill Fefferman, Chinmay Nirkhe, and Umesh Vazirani. On the complexity and verification of quantum random circuit sampling. Nature Physics, 15(2):159-163, October 2018. URL: https://doi.org/10.1038/s41567-018-0318-2.
  16. Sami Boulebnane, Abid Khan, Minzhao Liu, Jeffrey Larson, Dylan Herman, Ruslan Shaydulin, and Marco Pistoia. Evidence that the Quantum Approximate Optimization Algorithm optimizes the Sherrington-Kirkpatrick model efficiently in the average case, 2025. URL: https://arxiv.org/abs/2505.07929.
  17. Sami Boulebnane and Ashley Montanaro. Predicting parameters for the Quantum Approximate Optimization Algorithm for MAX-CUT from the infinite-size limit, 2021. URL: https://arxiv.org/abs/2110.10685.
  18. Anne Broadbent, Joseph Fitzsimons, and Elham Kashefi. Universal blind quantum computation. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science. IEEE, October 2009. URL: https://doi.org/10.1109/focs.2009.36.
  19. Houssam El Cheairi and David Gamarnik. Algorithmic universality, low-degree polynomials, and Max-Cut in sparse random graphs, 2024. URL: https://doi.org/10.48550/arXiv.2412.18014.
  20. Wei Kuo Chen. Variational representations for the Parisi functional and the two-dimensional Guerra-Talagrand bound. Annals of Probability, 45(6):3929-3966, 2017. URL: https://arxiv.org/abs/1501.06635.
  21. Wei-Kuo Chen, David Gamarnik, Dmitry Panchenko, and Mustazee Rahman. Suboptimality of local algorithms for a class of max-cut problems. The Annals of Probability, 47(3):1587-1618, 2019. URL: https://arxiv.org/abs/1707.05386.
  22. Wei-Kuo Chen and Dmitry Panchenko. On the TAP free energy in the mixed p-spin models. Communications in Mathematical Physics, 362:219-252, 2018. URL: https://arxiv.org/abs/1709.03468.
  23. Wei-Kuo Chen, Dmitry Panchenko, and Eliran Subag. Generalized TAP free energy. Communications on Pure and Applied Mathematics, 76(7):1329-1415, 2023. URL: https://arxiv.org/abs/1812.05066.
  24. Chi-Ning Chou, Peter J Love, Juspreet Singh Sandhu, and Jonathan Shi. Limitations of local quantum algorithms on random MAX-k-XOR and beyond. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022), 2022. URL: https://doi.org/10.4230/LIPIcs.ICALP.2022.41.
  25. Alexander M Dalzell, Nicola Pancotti, Earl T Campbell, and Fernando GSL Brandão. Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, pages 1131-1144, 2023. URL: https://arxiv.org/abs/2212.01513.
  26. Amir Dembo, Andrea Montanari, and Subhabrata Sen. Extremal cuts of sparse random graphs. The Annals of Probability, 45(2):1190-1217, March 2017. URL: https://doi.org/10.1214/15-AOP1084.
  27. Jian Ding, Allan Sly, and Nike Sun. Maximum independent sets on random regular graphs. Acta Mathematica, 217:263-340, 2016. URL: https://arxiv.org/abs/1310.4787.
  28. Jian Ding, Allan Sly, and Nike Sun. Proof of the satisfiability conjecture for large k. Annals of Mathematics, 196(1):1-388, 2022. URL: https://arxiv.org/abs/1411.0650.
  29. David L Donoho, Arian Maleki, and Andrea Montanari. Message-passing algorithms for compressed sensing. Proceedings of the National Academy of Sciences, 106(45):18914-18919, 2009. URL: https://arxiv.org/abs/0907.3574.
  30. Richard Durrett. Probability: Theory and Examples. Cambridge University Press, fifth edition, 2019. URL: https://doi.org/10.1017/9781108591034.
  31. Sepehr Ebadi, Alexander Keesling, Madelyn Cain, Tout T Wang, Harry Levine, Dolev Bluvstein, Giulia Semeghini, Ahmed Omran, J-G Liu, Rhine Samajdar, et al. Quantum optimization of maximum independent set using rydberg atom arrays. Science, 376(6598):1209-1215, 2022. URL: https://arxiv.org/abs/2202.09372.
  32. Edward Farhi, David Gamarnik, and Sam Gutmann. The Quantum Approximate Optimization Algorithm needs to see the whole graph: A typical case, 2020. URL: https://arxiv.org/abs/2004.09002.
  33. Edward Farhi, David Gamarnik, and Sam Gutmann. The Quantum Approximate Optimization Algorithm needs to see the whole graph: Worst case examples, 2020. URL: https://arxiv.org/abs/2005.08747.
  34. Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A Quantum Approximate Optimization Algorithm, 2014. URL: https://arxiv.org/abs/1411.4028.
  35. Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A Quantum Approximate Optimization Algorithm applied to a bounded occurrence constraint problem, 2015. URL: https://arxiv.org/abs/1412.6062.
  36. Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Leo Zhou. The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick model at infinite size. Quantum, 6:759, July 2022. URL: https://doi.org/10.22331/q-2022-07-07-759.
  37. Edward Farhi, Sam Gutmann, Daniel Ranard, and Benjamin Villalonga. Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA, 2025. URL: https://doi.org/10.48550/arXiv.2503.12789.
  38. Oliver Y Feng, Ramji Venkataramanan, Cynthia Rush, and Richard J Samworth. A unifying tutorial on approximate message passing. Foundations and Trends® in Machine Learning, 15(4):335-536, 2022. URL: https://arxiv.org/abs/2105.02180.
  39. Yaotian Fu and Philip W. Anderson. Application of statistical mechanics to NP-complete problems in combinatorial optimisation. Journal of Physics A: Mathematical and General, 19(9):1605-1620, June 1986. URL: https://doi.org/10.1088/0305-4470/19/9/033.
  40. David Gamarnik. The overlap gap property: A topological barrier to optimizing over random structures. Proceedings of the National Academy of Sciences, 118(41), October 2021. URL: https://doi.org/10.1073/pnas.2108492118.
  41. David Gamarnik. Barriers for the performance of graph neural networks (gnn) in discrete random structures. a comment, 2023. URL: https://arxiv.org/abs/2306.02555.
  42. David Gamarnik, Aukosh Jagannath, and Alexander S. Wein. Circuit lower bounds for the p-spin optimization problem, 2021. URL: https://arxiv.org/abs/2109.01342.
  43. David Gamarnik, Aukosh Jagannath, and Alexander S Wein. Hardness of random optimization problems for boolean circuits, low-degree polynomials, and Langevin dynamics. SIAM Journal on Computing, 53(1):1-46, 2024. URL: https://arxiv.org/abs/2004.12063.
  44. David Gamarnik and Madhu Sudan. Limits of local algorithms over sparse random graphs. In Proceedings of the 5th conference on Innovations in Theoretical Computer Science, pages 369-376, 2014. URL: https://arxiv.org/abs/1304.1831.
  45. M. B. Hastings. Classical and quantum bounded depth approximation algorithms, 2019. URL: https://arxiv.org/abs/1905.07047.
  46. Brice Huang. Computational Hardness in Random Optimization Problems from the Overlap Gap Property. Master’s thesis, Massachusetts Institute of Technology, 2022. URL: https://dspace.mit.edu/handle/1721.1/143164.
  47. Brice Huang and Mark Sellke. Algorithmic threshold for multi-species spherical spin glasses, 2023. URL: https://doi.org/10.48550/arXiv.2303.12172.
  48. Brice Huang and Mark Sellke. Optimization algorithms for multi-species spherical spin glasses. Journal of Statistical Physics, 191(2):29, 2024. URL: https://arxiv.org/abs/2308.09672.
  49. Brice Huang and Mark Sellke. Strong low degree hardness for stable local optima in spin glasses, 2025. URL: https://doi.org/10.48550/arXiv.2501.06427.
  50. Brice Huang and Mark Sellke. Tight Lipschitz hardness for optimizing mean field spin glasses. Communications on Pure and Applied Mathematics, 78(1):60-119, 2025. URL: https://arxiv.org/abs/2110.07847.
  51. Neng Huang, Will Perkins, and Aaron Potechin. Hardness of sampling for the anti-ferromagnetic Ising model on random graphs, 2024. URL: https://doi.org/10.48550/arXiv.2409.03974.
  52. Misha Ivkov and Tselil Schramm. Semidefinite programs simulate approximate message passing robustly. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, pages 348-357, 2024. URL: https://arxiv.org/abs/2311.09017.
  53. Aukosh Jagannath and Ian Tobasco. A dynamic programming approach to the Parisi functional. Proceedings of the American Mathematical Society, 144(7):3135-3150, December 2015. URL: https://doi.org/10.1090/proc/12968.
  54. David Jekel, Juspreet Singh Sandhu, and Jonathan Shi. Potential Hessian ascent: The Sherrington-Kirkpatrick model. In Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 5307-5387. SIAM, 2025. URL: https://arxiv.org/abs/2408.02360.
  55. Chris Jones, Kunal Marwaha, Juspreet Singh Sandhu, and Jonathan Shi. Random Max-CSPs inherit algorithmic hardness from spin glasses. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023), 2023. URL: https://doi.org/10.4230/LIPIcs.ITCS.2023.77.
  56. Stephen P Jordan, Noah Shutty, Mary Wootters, Adam Zalcman, Alexander Schmidhuber, Robbie King, Sergei V Isakov, Tanuj Khattar, and Ryan Babbush. Optimization by decoded quantum interferometry, 2024. URL: https://arxiv.org/abs/2408.08292.
  57. Yoshiyuki Kabashima. A CDMA multiuser detection algorithm on the basis of belief propagation. Journal of Physics A: Mathematical and General, 36(43):11111, 2003. URL: https://doi.org/10.1088/0305-4470/36/43/030.
  58. Daphne Koller and Nir Friedman. Probabilistic Graphical Models: Principles and Techniques. MIT press, 2009. URL: https://dl.acm.org/doi/abs/10.5555/1795555.
  59. Florent Krzakala, Marc Mézard, Francois Sausset, Yifan Sun, and Lenka Zdeborová. Probabilistic reconstruction in compressed sensing: Algorithms, phase diagrams, and threshold achieving matrices. Journal of Statistical Mechanics: Theory and Experiment, 2012(08):P08009, 2012. URL: https://arxiv.org/abs/1206.3953.
  60. Frank R Kschischang, Brendan J Frey, and H-A Loeliger. Factor graphs and the sum-product algorithm. IEEE Transactions on information theory, 47(2):498-519, 2001. URL: https://doi.org/10.1109/18.910572.
  61. Thibault Lesieur, Florent Krzakala, and Lenka Zdeborová. Constrained low-rank matrix estimation: Phase transitions, approximate message passing and applications. Journal of Statistical Mechanics: Theory and Experiment, 2017(7):073403, 2017. URL: https://arxiv.org/abs/1701.00858.
  62. Filip B Maciejewski, Stuart Hadfield, Benjamin Hall, Mark Hodson, Maxime Dupont, Bram Evert, James Sud, M Sohaib Alam, Zhihui Wang, Stephen Jeffrey, et al. Design and execution of quantum circuits using tens of superconducting qubits and thousands of gates for dense Ising optimization problems. Physical Review Applied, 22(4):044074, 2024. URL: https://arxiv.org/abs/2308.12423.
  63. Kunal Marwaha. Local classical MAX-CUT algorithm outperforms p=2 QAOA on high-girth regular graphs. Quantum, 5:437, April 2021. URL: https://doi.org/10.22331/q-2021-04-20-437.
  64. Sohir Maskey, Ron Levie, Yunseok Lee, and Gitta Kutyniok. Generalization analysis of message passing neural networks on large random graphs. Advances in neural information processing systems, 35:4805-4817, 2022. URL: https://arxiv.org/abs/2202.00645.
  65. Marc Mézard and Andrea Montanari. Information, Physics, and Computation. Oxford University Press, 2009. URL: https://doi.org/10.1093/acprof:oso/9780198570837.001.0001.
  66. Marc Mézard, Giorgio Parisi, and Miguel Angel Virasoro. Spin Glass Theory and Beyond: An Introduction to the Replica Method and Its Applications, volume 9. World Scientific Publishing Company, 1987. URL: https://doi.org/10.1142/0271.
  67. Marco Mondelli and Ramji Venkataramanan. Approximate message passing with spectral initialization for generalized linear models. In International Conference on Artificial Intelligence and Statistics, pages 397-405. PMLR, 2021. URL: https://arxiv.org/abs/2010.03460.
  68. Andrea Montanari. Optimization of the Sherrington-Kirkpatrick Hamiltonian. SIAM Journal on Computing, 2021. URL: https://arxiv.org/abs/1812.10897.
  69. Andrea Montanari, Yonina C. Eldar, and Gitta Kutyniok. Graphical models concepts in compressed sensing. Compressed Sensing, pages 394-438, 2012. URL: https://arxiv.org/abs/1011.4328.
  70. Dmitry Panchenko. The Parisi ultrametricity conjecture. Annals of Mathematics, pages 383-393, 2013. URL: https://arxiv.org/abs/1112.1003.
  71. Dmitry Panchenko. The Sherrington-Kirkpatrick Model. Springer Science & Business Media, 2013. URL: https://doi.org/10.1007/978-1-4614-6289-7.
  72. Dmitry Panchenko. On the k-sat model with large number of clauses. Random Structures & Algorithms, 52(3):536-542, 2018. URL: https://arxiv.org/abs/1608.06256.
  73. Giorgio Parisi. Infinite number of order parameters for spin-glasses. Phys. Rev. Lett., 43:1754-1756, December 1979. URL: https://doi.org/10.1103/PhysRevLett.43.1754.
  74. John Preskill. Quantum computing in the NISQ era and beyond. Quantum, 2:79, August 2018. URL: https://doi.org/10.22331/q-2018-08-06-79.
  75. Tom Richardson and Ruediger Urbanke. Modern Coding Theory. Cambridge University Press, 2008. URL: https://doi.org/10.1017/CBO9780511791338.
  76. Cynthia Rush, Adam Greig, and Ramji Venkataramanan. Capacity-achieving sparse superposition codes via approximate message passing decoding. IEEE Transactions on Information Theory, 63(3):1476-1500, 2017. URL: https://arxiv.org/abs/1501.05892.
  77. Ciarán Ryan-Anderson. Quantum Algorithms, Architecture, and Error Correction. PhD thesis, The University of New Mexico, 2018. URL: https://arxiv.org/abs/1812.04735.
  78. Juspreet Singh Sandhu and Jonathan Shi. Sum-of-squares & Gaussian processes I: Certification, 2024. URL: https://arxiv.org/abs/2401.14383.
  79. Mark Sellke. Optimizing mean field spin glasses with external field. Electronic Journal of Probability, 29:1-47, 2024. URL: https://arxiv.org/abs/2105.03506.
  80. Subhabrata Sen. Optimization on sparse random hypergraphs and spin glasses. Random Structures & Algorithms, 53(3):504-536, 2018. URL: https://doi.org/10.1002/rsa.20774.
  81. Ruslan Shaydulin and Marco Pistoia. Qaoa with n⋅ p ≥ 200. In 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 1, pages 1074-1077. IEEE, 2023. URL: https://arxiv.org/abs/2303.02064.
  82. David Sherrington and Scott Kirkpatrick. Solvable model of a spin-glass. Physical Review Letters, 35(26):1792, 1975. URL: https://doi.org/10.1103/PhysRevLett.35.1792.
  83. Allan Sly and Nike Sun. The computational hardness of counting in two-spin models on d-regular graphs. In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science, pages 361-369. IEEE, 2012. URL: https://arxiv.org/abs/1203.2602.
  84. Eliran Subag. Following the ground states of full-RSB spherical spin glasses. Communications on Pure and Applied Mathematics, 74(5):1021-1044, 2021. URL: https://arxiv.org/abs/1812.04588.
  85. Michel Talagrand. The Parisi formula. Annals of Mathematics, pages 221-263, 2006. URL: https://www.jstor.org/stable/20159953.
  86. Ewin Tang. Dequantizing algorithms to understand quantum advantage in machine learning. Nature Reviews Physics, 4:692-693, 2022. URL: https://doi.org/10.1038/s42254-022-00511-w.
  87. David J Thouless, Philip W Anderson, and Robert G Palmer. Solution of `solvable model of a spin glass'. Philosophical Magazine, 35(3):593-601, 1977. URL: https://doi.org/10.1080/14786437708235992.
  88. Zhihui Wang, Stuart Hadfield, Zhang Jiang, and Eleanor G. Rieffel. Quantum approximate optimization algorithm for MaxCut: A fermionic view. Phys. Rev. A, 97:022304, February 2018. URL: https://doi.org/10.1103/PhysRevA.97.022304.
  89. Jonathan Wurtz and Peter Love. MaxCut Quantum Approximate Optimization Algorithm performance guarantees for p>1. Physical Review A, 103(4), April 2021. URL: https://doi.org/10.1103/physreva.103.042612.
  90. Lenka Zdeborová and Florent Krzakala. Statistical physics of inference: Thresholds and algorithms. Advances in Physics, 65(5):453-552, 2016. URL: https://arxiv.org/abs/1511.02476.
  91. Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, Peng Hu, Xiao-Yan Yang, Wei-Jun Zhang, Hao Li, Yuxuan Li, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Zhen Wang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan. Quantum computational advantage using photons. Science, 370(6523):1460-1463, 2020. URL: https://doi.org/10.1126/science.abe8770.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact