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The Quantum Lov\'asz Local Lemma (QLLL) [AKS12] establishes non-constructively that any quantum system constrained by a local Hamiltonian has a zero-energy ground state, if the local Hamiltonian terms overlap only in a certain restricted way.
Problems and results on 3-chromatic hypergraphs and some related questions
Paul Erdős and László Lovász · 1975
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Asymptotic lower bounds for ramsey functions
Joel Spencer · 1977
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An Algorithmic Approach to the Lovász Local Lemma. I
József Beck · 1991
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Coding Theorems of Quantum Information Theory
Andreas Winter · 1999
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The probabilistic method
Noga Alon and Joel H. Spencer · 2000
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Quantum Computation and Quantum Information
M. Nielsen and I. Chuang · 2000
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Elements of Information Theory
Thomas M. Cover and Joy A. Thomas · 2006
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A constructive proof of the Lovász Local Lemma
Robin A. Moser · 2009
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Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation
F. Verstraete, M. M. Wolf, and J. I. Cirac · 2009
Cited alongside, same era.
A constructive proof of the general Lovász Local Lemma
R. A. Moser and G. Tardós · 2010
Cited alongside, same era.
On the complexity of Commuting Local Hamiltonians, and tight conditions for Topological Order in such systems
Dorit Aharonov and Lior Eldar · 2011
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A constructive commutative quantum Lovász Local Lemma, and beyond
Toby S. Cubitt and Martin Schwarz · 2011
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Complexity of commuting hamiltonians on a square lattice of qubits, 2011
A Quantum Lovasz Local Lemma
A. Ambainis, J. Kempe, and O. Sattath · 2012
Later among the works it cites.
Exact Algorithms for Constraint Satisfaction Problems
Robin A. Moser · 2012
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Hamiltonian complexity
Tobias J. Osborne · 2012
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A Constructive Quantum Lovász Local Lemma for Commuting Projectors
Itai Arad and Or Sattath · 2013
Closest in time.
Preparing topological projected entangled pair states on a quantum computer
M. Schwarz, K. Temme, F. Verstraete, D. Perez-Garcia, and T. S. Cubitt · 2013
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Quantum Information Theory
Mark M. Wilde · 2013
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Norbert Schuch · 2011
Cited alongside, same era.