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Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms.
An optimal Poincaré inequality for convex domains
L. E. Payne and H. F. Weinberger · 1960
Earlier work this paper cites.
Quantum Mechanics
Albert Messiah · 1961
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A lower bound for the smallest value of the Laplacian
Jeff Cheeger · 1970
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λ 1 \lambda_{1} , isoperimetric inequalities for graphs, and superconcentrators
N. Alon and V. D. Milman · 1985
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Some eigenvalue inequalities for a class of Jacobi matrices
Mark S. Ashbaugh and Rafael D. Benguria · 1990
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Geometric bounds for eigenvalues of Markov chains
Persi Diaconis and Daniel Stroock · 1991
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Algorithms for random generation and counting: a Markov chain approach
Alistair Sinclair · 1993
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Quantum annealing: a new method for minimizing multidimensional functions
A. B. Finnila, M. A. Gomez, C. Sebenik, C. Stenson, and J. D. Doll · 1994
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Spectral Graph Theory
Fan R. K. Chung · 1997
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Comparing eigenvalue bounds for Markov chains: when does Poincaré beat Cheeger?
J. Fulman and E. L. Wilmer · 1999
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A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda · 2001
Earlier work this paper cites.
How powerful is adiabatic quantum computation?
Wim van Dam, Michele Mosca, and Umesh Vazirani · 2001
Cited alongside, same era.
Quantum adiabatic evolution algorithms versus simulated annealing
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2002
Cited alongside, same era.
Quantum adiabatic evolution algorithms with different paths
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2002
Cited alongside, same era.
Adiabatic quantum state generation and statistical zero knowledge
Dorit Aharonov and Amnon Ta-Shma · 2003
Cited alongside, same era.
Exponential algorithmic speedup by a quantum walk
Andrew M. Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, and Daniel A. Spielman · 2003
Cited alongside, same era.
Limits of quantum adiabatic optimization
Wim van Dam and Umesh Vazirani · 2003
First order quantum phase transition in adiabatic quantum computation
M. H. S. Amin and V. Choi · 2009
Later among the works it cites.
Complexity of stoquastic frustration-free Hamiltonians
Sergey Bravyi and Barbara Terhal · 2009
Later among the works it cites.
Energy gaps of Hamiltonians from graph Laplacians
Abbas Al-Shimary and Jiannis K. Pachos · 2010
Later among the works it cites.
Anderson localization makes adiabatic quantum optimization fail
Boris Altshuler, Hari Krovi, and Jérémie Roland · 2010
Later among the works it cites.
Quantum adiabatic algorithms, small gaps, and different paths
Edward Farhi, Jeffrey Goldstone, David Gosset, Sam Gutmann, Harvey B. Meyer, and Peter Shor · 2011
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The quantum adiabatic optimization algorithm and local minima
Ben Reichardt · 2004
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Adiabatic quantum computation is equivalent to standard quantum computation
Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev · 2007
Cited alongside, same era.
Bounds for the adiabatic approximation with applications to quantum computation
Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler · 2007
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Effect of local minima on adiabatic quantum optimization
M. H. S. Amin · 2008
Cited alongside, same era.
The complexity of stoquastic local Hamiltonian problems
Sergey Bravyi, David P. DiVincenzo, Roberto Oliveira, and Barbara M. Terhal · 2008
Cited alongside, same era.
Later among the works it cites.
Criticality without frustration for quantum spin-1 chains
Sergey Bravyi, Libor Caha, Ramis Movassagh, Daniel Nagaj, and Peter Shor · 2012
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A note on the switching adiabatic theorem
Alexander Elgart and George A. Hagedorn · 2012
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Quantum speedup by quantum annealing
Daniel Nagaj, Rolando D. Somma, and Maria Kieferova · 2012
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A note on the Poincaré and Cheeger inequalities for simple random walk on a connected graph
John Pike · 2012
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Different strategies for optimization using the quantum adiabatic algorithm
Elizabeth Crosson, Edward Farhi, Cedric Yen-Yu Lin, Han-Hsuan Lin, and Peter Shor · 2014
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Fundamental gap for a class of Schrödinger operators on path and hypercube graphs
Michael Jarret and Stephen P. Jordan · 2014
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