Quantum adiabatic algorithms, small gaps, and different paths

@article{Farhi2011QuantumAA,
  title={Quantum adiabatic algorithms, small gaps, and different paths},
  author={Edward Farhi and Jeffrey Goldstone and David Gosset and Sam Gutmann and Harvey B. Meyer and Peter W. Shor},
  journal={ArXiv},
  year={2011},
  volume={abs/0909.4766}
}
We construct a set of instances of 3SAT which are not solved efficiently using the simplestquantum adiabatic algorithm. These instances are obtained by picking randomclauses all consistent with two disparate planted solutions and then penalizing one ofthem with a single additional clause. We argue that by randomly modifying the beginningHamiltonian, one obtains (with substantial probability) an adiabatic path thatremoves this difficulty. This suggests that the quantum adiabatic algorithm should… 
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