First-order transitions and the performance of quantum algorithms in random optimization problems.
We present a study of the phase diagram of a random optimization problem in the 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.
Jörg
Thomas
T
LPTENS, CNRS UMR 8549, associée à l'UPMC Paris 06, 24 Rue Lhomond, 75005 Paris, France.
Krzakala
Florent
F
Semerjian
Guilhem
G
Zamponi
Francesco
F