  Quantum annealers are commercial devices aiming to solve very hard
computational problems named spin glasses. Just like in metallurgic annealing
one slowly cools a ferrous metal, quantum annealers seek good solutions by
slowly removing the transverse magnetic field at the lowest possible
temperature. The field removal diminishes quantum fluctuations but forces the
system to traverse the critical point that separates the disordered phase (at
large fields) from the spin-glass phase (at small fields). A full understanding
of this phase transition is still missing. A debated, crucial question regards
the closing of the energy gap separating the ground state from the first
excited state. All hopes of achieving an exponential speed-up, as compared to
classical computers, rest on the assumption that the gap will close
algebraically with the number of qspins, but renormalization group calculations
predict that the closing will be instead exponential. Here we solve this debate
through extreme-scale numerical simulations, finding that both parties grasped
parts of the truth. While the closing of the gap at the critical point is
indeed super-algebraic, it remains algebraic if one restricts the symmetry of
possible excitations. Since this symmetry restriction is experimentally
achievable (at least nominally), there is still hope for the Quantum Annealing
paradigm.

Disordered Systems and Neural Networks;Computational Physics;Quantum Physics