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Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-body Hamiltonian up to an absolute error $\epsilon$.
Computers and Intractability: A Guide to the Theory of NP-Completeness
Michael R. Garey and David S. Johnson · 1979
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Ergodic quantum computing
Dominik Janzing and Pawel Wocjan · 2005
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The Complexity of the Local Hamiltonian Problem
J. Kempe, A. Kitaev, and O. Regev · 2006
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The PCP Theorem by Gap Amplification
Irit Dinur · 2007
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An area law for one-dimensional quantum systems
M B Hastings · 2007
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New construction for a QMA complete three-local Hamiltonian
D. Nagaj and S. Mozes · 2007
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The complexity of quantum spin systems on a two-dimensional square lattice
R. Oliveira and B. Terhal · 2008
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The Complexity of Stoquastic Local Hamiltonian Problems
Sergey Bravyi, David P. Divincenzo, Roberto Oliveira, and Barbara M. Terhal · 2008
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Realizable Hamiltonians for Universal Adiabatic Quantum Computers
J. D. Biamonte and P. J. Love · 2008
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Perturbative gadgets at arbitrary orders
S. P. Jordan and E. Farhi · 2008
Cited alongside, same era.
S. Bravyi, D. DiVincenzo, D. Loss, and B. Terhal · 2008
Cited alongside, same era.
J. D. Biamonte · 2008
Cited alongside, same era.
Nonperturbative Gadget for Topological Quantum Codes
Samuel A. Ocko and Beni Yoshida · 2011
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Schrieffer-Wolff transformation for quantum many-body systems
S. Bravyi, D. DiVincenzo, and D. Loss · 2011
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Universal two-body-hamiltonian quantum computing
Daniel Nagaj · 2012
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Guest Column: The Quantum PCP Conjecture
Dorit Aharonov, Itai Arad, and Thomas Vidick · 2013
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Adiabatic quantum optimization with the wrong Hamiltonian
Kevin C. Young, Robin Blume-Kohout, and Daniel A. Lidar · 2013
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N. Schuch and F. Verstraete · 2009
Cited alongside, same era.
Colloquium
J. Eisert, M. Cramer, and M. B. Plenio · 2010
Cited alongside, same era.
Simplifying quantum double Hamiltonians using perturbative gadgets
Robert Koenig · 2010
Cited alongside, same era.
The 1D Area Law and the Complexity of Quantum States: A Combinatorial Approach
D. Aharonov, I. Arad, Z. Landau, and U. Vazirani · 2011
Cited alongside, same era.
Yudong Cao, Ryan Babbush, Jacob Biamonte, and Sabre Kais · 2014
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Local tests of global entanglement and a counterexample to the generalized area law
Dorit Aharonov, Aram Harrow, Zeph Landau, Daniel Nagaj, Mario Szegedy, and Umesh Vazirani · 2014
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