#### Abstract

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\to \infty $.

- Received 8 October 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.020502

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