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We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field.
David Sherrington and Scott Kirkpatrick, Solvable model of a spin-glass , Physical review letters 35
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Francisco Barahona, On the computational complexity of Ising spin glass models , Journal of Physics A: Mathematical and General 15
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Lenore Blum, Mike Shub, and Steve Smale, On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines , [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, IEEE, 1988, pp. 387–397
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Peter Gemmell, Richard Lipton, Ronitt Rubinfeld, Madhu Sudan, and Avi Wigderson, Self-testing/correcting for polynomials and for approximate functions , STOC, vol. 91, Citeseer, 1991, pp. 32–42
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Uriel Feige and Carsten Lund, On the hardness of computing the permanent of random matrices , Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, ACM, 1992, pp. 643–654
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Peter Gemmell and Madhu Sudan, Highly resilient correctors for polynomials , Information processing letters 43
1992
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Erich Kaltofen, Polynomial factorization 1987–1991 , Latin American Symposium on Theoretical Informatics, Springer, 1992, pp. 294–313
1992
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Madhu Sudan, Maximum likelihood decoding of Reed Solomon codes , Proceedings of 37th Conference on Foundations of Computer Science, IEEE, 1996, pp. 164–172
1996
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Jin-Yi Cai, Aduri Pavan, and D Sivakumar, On the hardness of permanent , Annual Symposium on Theoretical Aspects of Computer Science, Springer, 1999, pp. 90–99
1999
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Sorin Istrail, Statistical mechanics, three-dimensionality and NP-completeness: I. universality of intracatability for the partition function of the ising model across non-planar surfaces , STOC, 2000, pp. 87–96
2000
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Imre Csiszar and János Körner, Information theory: coding theorems for discrete memoryless systems , Cambridge University Press, 2011
2011
Later among the works it cites.
Lenore Blum, Felipe Cucker, Michael Shub, and Steve Smale, Complexity and real computation , Springer Science & Business Media, 2012
2012
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Dmitry Panchenko, The Sherrington-Kirkpatrick model , Springer Science & Business Media, 2013
2013
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Yury Polyanskiy and Yihong Wu, Lecture notes on information theory , Lecture Notes for ECE563 (UIUC) and 6.441 (MIT) (2016), 2012–2016
2016
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2018
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2005
Cited alongside, same era.
Michel Talagrand, Mean field models for spin glasses: Volume i: Basic examples , vol. 54, Springer Science & Business Media, 2010
2010
Cited alongside, same era.
Scott Aaronson and Alex Arkhipov, The computational complexity of linear optics , Proceedings of the forty-third annual ACM symposium on Theory of computing, ACM, 2011, pp. 333–342
2011
Cited alongside, same era.
2018
Closest in time.