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All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition over the history of the computation.
“Quantum mechanical computers”
Richard Feynman · 1985
Earlier work this paper cites.
“Reversible logic and quantum computers”
Asher Peres · 1985
Earlier work this paper cites.
“Asymptotic Theory of Finite Dimensional Normed Spaces” 1200
V.D. Milman and G. Schechtman · 1986
Earlier work this paper cites.
“Determining computational complexity from characteristic’phase transitions”’
R“’emi Monasson et al · 1999
Earlier work this paper cites.
“The Concentration of Measure Phenomenon” 89
M. Ledoux · 2001
Earlier work this paper cites.
“Classical and Quantum Computation”
A.Y. Kitaev, A.H. Shen and M.N. Vyalyi · 2002
Earlier work this paper cites.
“3-Local Hamiltonian is QMA-complete”
J. Kempe and O. Regev · 2003
Earlier work this paper cites.
“Rigorous location of phase transitions in hard optimization problems”
Dimitris Achlioptas, Assaf Naor and Yuval Peres · 2005
Earlier work this paper cites.
“Spectral Gap and Exponential Decay of Correlations”
M.B. Hastings and T. Koma · 2006
Earlier work this paper cites.
“The complexity of the Local Hamiltonian problem”
J. Kempe, A. Kitaev and O. Regev · 2006
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Patrick Hayden and John Preskill · 2007
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Fernando Brandao and Aram Harrow · 2013
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“On the gap of Hamiltonians for the adiabatic simulation of quantum circuits”
Anand Ganti and Rolando Somma · 2013
Later among the works it cites.
“The local Hamiltonian problem on a line with eight states is QMA-complete”, 2013
Sean Hallgren, Daniel Nagaj and Sandeep Narayanaswami · 2013
Later among the works it cites.
“Space-time circuit-to-Hamiltonian construction and its applications”
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Later among the works it cites.
“Local Random Quantum Circuits are Approximate Polynomial-Designs”
Fernando G. S.. Brand“˜ao, Aram. Harrow and Micha Horodecki · 2016
Later among the works it cites.
“Complexity classification of local Hamiltonian problems”
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Richard. Low · 2009
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N. Schuch and F. Verstraete · 2009
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Fernando G. S.. Brand“˜ao and Micha Horodecki · 2013
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