First-Order Phase Transition in the Quantum Adiabatic Algorithm

A. P. Young, S. Knysh, and V. N. Smelyanskiy
Phys. Rev. Lett. 104, 020502 – Published 14 January 2010


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.

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  • Received 8 October 2009


©2010 American Physical Society

Authors & Affiliations

A. P. Young

  • Department of Physics, University of California, Santa Cruz, California 95064, USA

S. Knysh

  • ELORET Corporation, NASA Ames Research Center, MS 229, Moffett Field, California A 94035-1000, USA

V. N. Smelyanskiy

  • NASA Ames Research Center, MS 269-3, Moffett Field, California 94035-1000, USA

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Vol. 104, Iss. 2 — 15 January 2010

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