The quantum transition of the two-dimensional Ising spin glass

Abstract

Quantum annealers are commercial devices that aim to solve very hard computational problems(1), typically those involving spin glasses(2,3). Just as in metallurgic annealing, in which a ferrous metal is slowly cooled(4), quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. Removing the field diminishes the 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, compared to classical computers, rest on the assumption that the gap will close algebraically with the number of spins(5-9). However, renormalization group calculations predict instead that there is an infinite-randomness fixed point(10). Here we solve this debate through extreme-scale numerical simulations, finding that both parties have grasped parts of the truth. Although the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. As this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the quantum annealing paradigm(11-13).