A Quantum Algorithm for the Hamiltonian NAND Tree

@article{Farhi2008AQA,
  title={A Quantum Algorithm for the Hamiltonian NAND Tree},
  author={Edward Farhi and Jeffrey Goldstone and Sam Gutmann},
  journal={Theory of Computing},
  year={2008},
  volume={4},
  pages={169-190}
}
We give a quantum algorithm for the binary NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a running time proportional to √ N. We also show a lower bound of Ω( √ N) for the NAND tree problem in the Hamiltonian oracle model. ACM Classification: F.1.2, F.2.2 AMS Classification: 68Q10, 68Q17 
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