We apply classical algorithms for approximately solving constraint satisfaction problems to find bounds on extremal eigenvalues of local Hamiltonians. We consider spin Hamiltonians for which we have an upper bound on the number of terms in which each spin participates, and find extensive bounds for the operator norm and ground-state energy of such Hamiltonians under this constraint. In each case the bound is achieved by a product state which can be found efficiently using a classical algorithm.
 N. Bansal, S. Bravyi, and B. Terhal. Classical approximation schemes for the ground-state energy of quantum and classical Ising spin hamiltonians on planar graphs. Quantum Inf. Comput., 9(8):0701-0720, 2009, arXiv:0705.1115.
 B. Barak, A. Moitra, R. O'Donnell, P. Raghavendra, O. Regev, D. Steurer, L. Trevisan, A. Vijayaraghavan, D. Witmer, and J. Wright. Beating the random assignment on constraint satisfaction problems of bounded degree, 2015, arXiv:1505.03424.
 F. G. S. L. Brandão and A. W. Harrow. Product-state approximations to quantum ground states. Communications in Mathematical Physics, 342(1):47-80, 2006. arXiv:1310.0017.
 I. Dinur, E. Friedgut, G. Kindler, and R. O'Donnell. On the Fourier tails of bounded functions over the discrete cube. Israel Journal of Mathematics, 160:389-412, 2007.
 E. Farhi, J. Goldstone, and S. Gutmann. A quantum approximate optimization algorithm applied to a bounded occurrence constraint problem. Technical Report MIT-CTP/4628, MIT, 2014, arXiv:1412.6062.
 M. Hartmann, G. Mahler, and O. Hess. Gaussian quantum fluctuations in interacting many particle systems. Letters in Mathematical Physics, 68(2):103-112, 2004, arXiv:math-ph/0312045.
 A. Montanaro. Some applications of hypercontractive inequalities in quantum information theory. Journal of Mathematical Physics, 53(12):122206, 2012, arXiv:1208.0161.
 R. O'Donnell. Analysis of Boolean Functions. Cambridge University Press, 2014.
 J. Renes, R. Blume-Kohout, A. J. Scott, and C. Caves. Symmetric informationally complete quantum measurements. J. Math. Phys., 45(6):2171-2180, 2003. quant-ph/0310075.
Crossref's cited-by service has no data on citing works. Unfortunately not all publishers provide suitable citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.