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The local Hamiltonian problem consists of estimating the ground-state energy (given by the minimum eigenvalue) of a local quantum Hamiltonian.
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MAX-CUT has a randomized approximation scheme in dense graphs
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Classical and Quantum Computation
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Polynomial time approximation schemes for dense instances of minimum constraint satisfaction
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Is entanglement monogamous?, 2003, arXiv:quant-ph/0307120
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Efficient classical simulation of slightly entangled quantum computations
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Realization of quantum chemistry without wave functions through first-order semidefinite programming
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Quantum fluctuations and rate of convergence towards mean field dynamics, 2007, arXiv:0711.3087
I. Rodnianski and B. Schlein · 2007
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S. Bravyi, D. DiVincenzo, D. Loss, and B. Terhal · 2008
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The quantum moment problem and bounds on entangled multi-prover games
A. Doherty, Y. Liang, B. Toner, and S. Wehner · 2008
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Robustness of quantum Markov chains
B. Ibinson, N. Linden, and A. Winter · 2008
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The complexity of quantum spin systems on a two-dimensional square lattice
R. Oliveira and B. M. Terhal · 2008
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T. Osborne · 2011
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Label cover, hardness of set cover, 2011
M. Salavatipour · 2011
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Complexity of commuting Hamiltonians on a square lattice of qubits
N. Schuch · 2011
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Solving condensed-matter ground-state problems by semidefinite relaxations
T. Barthel and R. Hübener · 2012
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Lower bounds for ground states of condensed matter systems
T. Baumgratz and M. Plenio · 2012
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SDP gaps from pairwise independence
S. Benabbas, K. Georgiou, A. Magen, and M. Tulsiani · 2012
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QMA-complete problems, 2012, arXiv:1212.6312
A. D. Bookatz · 2012
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Convergence of SDP hierarchies for polynomial optimization on the hypersphere, 2012, arXiv:1210.5048
A. C. Doherty and S. Wehner · 2012
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personal communication
S. Gharibian and J. Kempe, 2012 · 2012
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Approximation algorithms for QMA-complete problems
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M. Hastings · 2012
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M. B. Hastings · 2012
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Distinguishing multi-partite states by local measurements, 2012, arXiv:1206.2884
C. Lancien and A. Winter · 2012
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Some applications of hypercontractive inequalities in quantum information theory
A. Montanaro · 2012
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M. Navascues, A. Garcia-Saez, A. Acin, S. Pironio, and M. Plenio · 2012
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Approximating CSPs with global cardinality constraints using SDP hierarchies
P. Raghavendra and N. Tan · 2012
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Guest column: the quantum PCP conjecture
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The church of the symmetric subspace, 2013, arXiv:1308.6595
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Ground states of fermionic lattice Hamiltonians with permutation symmetry
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