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The quantum analogue of a constraint satisfaction problem is a sum of local Hamiltonians - each local Hamiltonian specifies a local constraint whose violation contributes to the energy of the given quantum state.
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Physical Review A 71
J. Roland and N. Cerf, Noise resistance of adiabatic quantum computation using random matrix theory · 2005
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to appear: http://www. cs. princeton.edu/theory/complexity
S. Arora and B. Barak, Computational Complexity: A Modern Approach
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S. Bravyi, D. DiVincenzo, D. Loss and B. Terhal, Quantum Simulation of Many-Body Hamiltonians Using Perturbation Theory with Bounded-Strength Interactions · 2008
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Physical Review A (Atomic, Molecular, and Optical Physics) 77
S. P. Jordan and E. Farhi, Perturbative gadgets at arbitrary orders · 2008
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D. A. Lidar, Towards Fault Tolerant Adiabatic Quantum Computation · 2008
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Quant. Inf. Comp. 8
R. Oliveira and B. Terhal, The complexity of quantum spin systems on a two-dimensional square lattice · 2008
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