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We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line.
Relationship between d-dimensional quantal spin systems and (d+1)-dimensional ising systems
Masuo Suzuki · 1976
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On the computational complexity of Ising spin glass models
F. Barahona · 1982
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Quantum mechanical computers
R. Feynman · 1985
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Spin glasses: Experimental facts, theoretical concepts, and open questions
K. Binder and A. P. Young · 1986
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NP is as easy as detecting unique solutions
L. G. Valiant and V. V. Vazirani · 1986
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Quantum stochastic optimization
B. Apolloni, C. Carvalho, and D. de Falco · 1988
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A numerical implementation of ”quantum annealing”
B. Apolloni, N. Cesa-Bianchi, and D. de Falco · 1990
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Handbook of Theoretical Computer Science
Peter van Emde Boas · 1990
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Density matrix formulation for quantum renormalization groups
S. R. White · 1992
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Density-matrix algorithms for quantum renormalization groups
S. R. White · 1993
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Critical behavior of random transverse-field Ising spin chains
D. S. Fisher · 1995
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On one-dimensional quantum cellular automata
J. Watrous · 1995
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Quantum computation by adiabatic evolution, 2000
E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser · 2000
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A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem
E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda · 2001
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Robustness of adiabatic quantum computation
A. Childs, E. Farhi, and J. Preskill · 2002
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Classical and Quantum Computation
A.Y. Kitaev, A.H. Shen, and M.N. Vyalyi · 2002
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Adiabatic quantum computation is equivalent to standard quantum computation
D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev · 2004
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Universally programmable quantum cellular automaton
D. J. Shepherd, T. Franz, and R. F. Werner · 2006
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The power of quantum systems on a line
Dorit Aharonov, Daniel Gottesman, Sandy Irani, and Julia Kempe · 2007
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The power of quantum systems on a line, 2007
D. Aharonov, D. Gottesman, and J. Kempe · 2007
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Improved gap estimates for simulating quantum circuits by adiabatic evolution
P. Deift, M. B. Ruskai, and W. Spitzer · 2007
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An area law for one dimensional quantum systems, 2007
M. Hastings · 2007
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The complexity of quantum systems on a one-dimensional chain, 2007
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The complexity of quantum spin systems on a two-dimensional square lattice, 2005
R. Oliveira and B. Terhal · 2005
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The density-matrix renormalization group
U. Schollwöck · 2005
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Error-correcting codes for adiabatic quantum computation
S. P. Jordan, E. Farhi, and P. W. Shor · 2006
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The complexity of the Local Hamiltonian problem
J. Kempe, A. Kitaev, and O. Regev · 2006
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Efficient approximation of the dynamics of one-dimensional quantum spin systems
T. Osborne · 2006
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Personal communication
M. Hastings
Cited in the paper.
S. Irani · 2007
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Dominik Janzing, Pawel Wocjan, and Shengyu Zhang · 2007
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Ground state of a class of noncritical one-dimensional quantum spin systems can be approximated efficiently
T. Osborne · 2007
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The computational power of symmetric hamiltonians
Alastair Kay · 2008
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Local Hamiltonians in Quantum Computation
Daniel Nagaj · 2008
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Hamiltonian quantum cellular automata in 1d, 2008
Daniel Nagaj and Pawel Wocjan · 2008
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