First-order phase transition in the quantum adiabatic algorithm.
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.
Young
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AP
Department of Physics, University of California, Santa Cruz, California 95064, USA.
Knysh
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S
Smelyanskiy
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