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Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits.
The uncertainty principle
H. P. Robertson · 1929
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Optimal assignments of numbers to vertices
L. H. Harper · 1964
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Ramanujan graphs
A. Lubotzky, R. Phillips, and P. Sarnak · 1988
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Existence and explicit constructions of q + 1 regular ramanujan graphs for every prime power q
M. Morgenstern · 1994
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Laplacian eigenvalues and distances between subsets of a manifold
J. Friedman and J.-P. Tillich · 2000
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ℤ 2 \mathbb{Z}_{2} -systolic freedom and quantum codes
M. Freedman, D. Meyer, and F. Luo · 2002
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Violation of local uncertainty relations as a signature of entanglement
H. F. Hofmann and S. Takeuchi · 2003
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Improved simulation of stabilizer circuits
S. Aaronson and D. Gottesman · 2004
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Commutative version of the local Hamiltonian problem and common eigenspace problem
S. Bravyi and M. Vyalyi · 2005
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Lieb-Robinson bounds and the generation of correlations and topological quantum order
S. Bravyi, M. Hastings, and F. Verstraete · 2006
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Lieb-robinson bounds and the generation of correlations and topological quantum order
S. Bravyi, M. B. Hastings, and F. Verstraete · 2006
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Expander graphs and their applications
S. Hoory, N. Linial, and A. Wigderson · 2006
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Homological connectivity of random 2-complexes
N. Linial and R. Meshulam · 2006
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Efficient approximation of the dynamics of one-dimensional quantum spin systems
T. J. Osborne · 2006
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The pcp theorem by gap amplification
I. Dinur · 2007
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The detectability lemma and quantum gap amplification
D. Aharonov, I. Arad, Z. Landau, and U. Vazirani · 2009
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Homological connectivity of random k k -dimensional complexes
R. Meshulam and N. Wallach · 2009
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Quantum LDPC codes with positive rate and minimum distance proportional to n 1 / 2 n^{1/2}
J.-P. Tillich and G. Zémor · 2009
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X. Chen, Z.-C. Gu, and X.-G. Wen · 2010
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Short locally testable codes and proofs: A survey in two parts
O. Goldreich · 2010
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An area law and sub-exponential algorithm for 1D systems
I. Arad, A. Kitaev, Z. Landau, and U. Vazirani · 2013
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Product-state approximations to quantum ground states
F. G. S. L. Brandão and A. W. Harrow · 2013
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On the classification of short-range entangled states, 2013
A. Kitaev · 2013
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Homological product codes
S. Bravyi and M. B. Hastings · 2014
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M. H. Freedman and M. B. Hastings · 2014
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Singularities, expanders and topology of maps. part 2: from combinatorics to topology via algebraic isoperimetry
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M. B. Hastings · 2010
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D. Aharonov and L. Eldar · 2011
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F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki · 2012
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J. Chen, Z. Ji, B. Zeng, and D. L. Zhou · 2012
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J. Haah · 2014
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On the informational completeness of local observables, 2014, arXiv:1405.0137
I. H. Kim · 2014
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Renormalization group constructions of topological quantum liquids and beyond, 2014, arXiv:1407.8203
B. Swingle and J. McGreevy · 2014
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The commuting local Hamiltonian problem on locally expanding graphs is approximable in NP
D. Aharonov and L. Eldar · 2015
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Quantum locally testable codes
D. Aharonov and L. Eldar · 2015
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Local Hamiltonians with approximation-robust entanglement, 2015, arXiv:1503.02269
L. Eldar · 2015
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Quantum error correction for quantum memories
B. M. Terhal · 2015
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Bounded degree cosystolic expanders of every dimension
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Isoperimetric inequalities for Ramanujan complexes and topological expanders
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