Fetching the paper…
Reading the bibliography…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods.
R. Richardson, Journal of Mathematical Physics 6
1965
Earlier work this paper cites.
E. H. Lieb, Communications in Mathematical Physics 31
1973
Earlier work this paper cites.
A. Tsvelik, Physical Review Letters 69
1992
Earlier work this paper cites.
V. Bach, E. H. Lieb, and J. P. Solovej, Journal of Statistical Physics 76
1994
Earlier work this paper cites.
M. X. Goemans and D. P. Williamson, Journal of the ACM (JACM) 42
1995
Earlier work this paper cites.
A. Kitaev, A. Shen, M. Vyalyi, and M. Vyalyi, Classical and Quantum Computation , Graduate studies in mathematics (American Mathematical Society, 2002)
2002
Earlier work this paper cites.
B. M. Terhal and D. P. DiVincenzo, Physical Review A 65
2002
Earlier work this paper cites.
M. Horodecki, P. W. Shor, and M. B. Ruskai, Reviews in Mathematical Physics 15
2003
Earlier work this paper cites.
M. B. Ruskai, Reviews in Mathematical Physics 15
2003
Earlier work this paper cites.
J. Kempe, A. Kitaev, and O. Regev, in International Conference on Foundations of Software Technology and Theoretical Computer Science (Springer, 2004) pp. 372–383
2004
Earlier work this paper cites.
M. Charikar and A. Wirth, in Foundations of Computer Science, 2004. Proceedings. 45th Annual IEEE Symposium on (IEEE, 2004) pp. 54–60
2004
Earlier work this paper cites.
J. Dukelsky, S. Pittel, and G. Sierra, Reviews of Modern Physics 76
2004
Cited alongside, same era.
S. Arora, E. Berger, H. Elad, G. Kindler, and M. Safra, in Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on (IEEE, 2005) pp. 206–215
2005
Cited alongside, same era.
S. Bravyi, Quant. Inf. and Comp. 5
2005
Cited alongside, same era.
S. Bravyi, Physical Review A 73
2006
Cited alongside, same era.
A. Nemirovski, Mathematical programming 109
2007
Cited alongside, same era.
D. Tahara and M. Imada, Journal of the Physical Society of Japan 77
2008
Cited alongside, same era.
S. Gharibian and J. Kempe, SIAM Journal on Computing 41
2012
Later among the works it cites.
D. Aharonov, I. Arad, and T. Vidick, ACM SIGACT News 44
2013
Later among the works it cites.
F. G. Brandao and A. W. Harrow, in Proceedings of the 45th annual ACM Symposium on Theory of Computing (ACM, 2013) pp. 871–880
2013
Later among the works it cites.
S. Gharibian, Y. Huang, Z. Landau, S. W. Shin, et al. , Foundations and Trends® in Theoretical Computer Science 10
2015
Later among the works it cites.
L. Eldar and A. W. Harrow, arXiv preprint arXiv:1510.02082 (2015)
2015
Later among the works it cites.
J. Hastad, “Improved bounds for bounded occurrence constraint satisfaction,” (2015)
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. M.-C. So, in Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms (Society for Industrial and Applied Mathematics, 2009) pp. 1201–1209
2009
Cited alongside, same era.
C. Dankert, R. Cleve, J. Emerson, and E. Livine, Physical Review A 80
2009
Cited alongside, same era.
C. V. Kraus and J. I. Cirac, New Journal of Physics 12
2010
Cited alongside, same era.
A. M.-C. So, Mathematical programming 130
2011
Cited alongside, same era.
In particular, Ref. [ 15 ] shows that if an efficient algorithm achieves this approximation ratio then there exists an algorithm which solves any decision problem in N P NP on input size n n using runtime n poly ( l o g ( n ) ) n^{\mathrm{poly}(\mathop{log}\nolimits(n))} . This is believed to be very unlikely
Cited in the paper.
Given a function Eq. ( 1
Cited in the paper.
2015
Later among the works it cites.
T. Cubitt and A. Montanaro, SIAM Journal on Computing 45
2016
Later among the works it cites.
A. W. Harrow and A. Montanaro, Quantum 1
2017
Later among the works it cites.
S. Bravyi and D. Gosset, Communications in Mathematical Physics 356
2017
Later among the works it cites.