First-order transitions and the performance of quantum algorithms in random optimization problems

Details First-order transitions and the performance of quantum algorithms in random optimization problems First-order transitions and the performance of quantum algorithms in random optimization problems

2009-11-17

arxiv.org/abs/0911.3438v2

Phys. Rev. Lett. 104, 207206 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures; final version accepted on Phys.Rev.Lett

Scientific paper

10.1103/PhysRevLett.104.207206

We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase transition. We provide evidence that the gap vanishes exponentially with the system size at the transition. This indicates that the Quantum Adiabatic Algorithm requires a time growing exponentially with system size to find the ground state of this problem.

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