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# 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} }

- Published 2010 in Physical review letters

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.