First-order phase transition in the quantum adiabatic algorithm.

@article{Young2010FirstorderPT,
  title={First-order phase transition in the quantum adiabatic algorithm.},
  author={A. P. Young and Sergey Knysh and Vadim N. Smelyanskiy},
  journal={Physical review letters},
  year={2010},
  volume={104 2},
  pages={020502}
}
We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem for sizes up to N=256 using quantum Monte Carlo simulations incorporating parallel tempering. At large N, we find that some instances have a discontinuous (first-order) quantum phase transition during the evolution of the QAA. This fraction increases with increasing N and may tend to 1 for N-->infinity. 
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@BULLET Making costs and transverse fields random doesn't help so far, but needs to be studied in more detail (c.w. talk by Farhi)

  • @BULLET Making costs and transverse fields random…

@BULLET This is expected to lead to an exponentially small gap, and hence an exponential complexity

  • @BULLET This is expected to lead to an…

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