First order phase transition in the Quantum Adiabatic Algorithm

Details First order phase transition in the Quantum Adiabatic Algorithm First order phase transition in the Quantum Adiabatic Algorithm

2009-10-07

arxiv.org/abs/0910.1378v2

Phys. Rev. Lett. 104, 020502 (2010)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures. Replaced with published version; two figures slightly changed and some small changes to the text

Scientific paper

10.1103/PhysRevLett.104.020502

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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