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The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete.
Introduction to Matrix Analysis
R. Bellman · 1970
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Informational complexity and efficient methods for the solution of convex extremal problems
D.B. Yudin and A.S. Nemirovskii · 1977
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Geometric algorithms and combinatorial optimization
M. Grötschel, L. Lovász, and A. Schrijver · 1988
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Matrix analysis
R. Bhatia · 1997
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Quantum computation by adiabatic evolution
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser · 2000
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Quantum computation and quantum information
M.A. Nielsen and I.L. Chuang · 2000
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Quantum NP - a survey
D. Aharonov and T. Naveh · 2002
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Classical and quantum computation
A. Yu. Kitaev, A. H. Shen, and M. N. Vyalyi · 2002
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Private communication, 2004
D. Aharonov · 2004
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Solving convex programs by random walks
D. Bertsimas and S. Vempala · 2004
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Efficient simulation of one-dimensional quantum many-body systems
G. Vidal · 2004
Cited alongside, same era.
The complexity of quantum spin systems on a two-dimensional square lattice
R. Oliveira and B.M. Terhal · 2005
Cited alongside, same era.
The density-matrix renormalization group
U. Schollwöck · 2005
Cited alongside, same era.
Merlin-Arthur games and stoquastic complexity
S. Bravyi, A.J. Bessen, and B.M. Terhal · 2006
Cited alongside, same era.
The complexity of stoquastic local hamiltonian problems
S. Bravyi, D.P. DiVincenzo, R.I. Oliveira, and B.M. Terhal · 2006
Cited alongside, same era.
Compatibility of subsystem states and convex geometry
W. Hall · 2006
Cited alongside, same era.
A new construction for a QMA complete 3-local Hamiltonian
D. Nagaj and S. Mozes · 2006
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The power of quantum systems on a line
D. Aharonov, D. Gottesman, and J. Kempe · 2007
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Realizable Hamiltonians for universal adiabatic quantum computers
J.D. Biamonte and P.J. Love · 2007
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The complexity of quantum systems on a one-dimensional chain
S. Irani · 2007
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A QMA-complete translationally invariant Hamiltonian problem and the complexity of finding ground state energies in physical systems
A. Kay · 2007
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Simulated Annealing for Convex Optimization
A.T. Kalai and S. Vempala · 2006
Cited alongside, same era.
The complexity of the local Hamiltonian problem
J. Kempe, A. Kitaev, and O. Regev · 2006
Cited alongside, same era.
Consistency of local density matrices is QMA-complete
Y.-K. Liu · 2006
Cited alongside, same era.
The Complexity of the Consistency and N-representability Problems for Quantum States
Y.-K. Liu · 2007
Closest in time.
Quantum computational complexity of the N-representability problem: QMA complete
Y.-K. Liu, M. Christandl, and F. Verstraete · 2007
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Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules
D.A. Mazziotti, editor · 2007
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Interacting electrons, density functional theory, and Quantum Merlin Arthur
N. Schuch and F. Verstraete · 2007
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