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We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian.
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3-local Hamiltonian is QMA-complete
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D. de Falco, D. Tamascelli, Speed and Entropy of an Interacting Continuous Time Quantum Walk, J. Phys. A: Math. Gen. 39 (2006) 5873-5895
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A promise problem: Is the ground state energy of a 3-local Hamiltonian less than some a a , or more than some b b , with ( b − a ) > 1 / p o l y ( L ) (b-a)>1/poly(L)
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A. Mizel, D. A. Lidar and M. Mitchell, Simple Proof of Equivalence Between Adiabatic Quantum Computation and the Circuit Model, Phys. Rev. Lett. 99, 070502 (2008)
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J. D. Biamonte and P. J. Love, Realizable Hamiltonians for Universal Adiabatic Quantum Computers, Physical Review A, 78, 012352 (2008)
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D. Nagaj and D. Reitzner, Quantum Walks on Necklaces, in preparation (2009)
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