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We investigate the occurrence of many-body localization (MBL) on a spin-1/2transverse-field Ising model defined on a Chimera connectivity graph withrandom exchange interactions and longitudinal fields. We observe a transitionfrom an ergodic phase to a non-thermal phase for individual energy eigenstatesinduced by a critical disorder strength for the Ising parameters. Our resultfollows from the analysis of both the mean half-system block entanglement andthe energy level statistics. We identify the critical point associated withthis transition using the maximum variance of the block entanglement over thedisorder ensemble as a function of the disorder strength. The calculated energydensity phase diagram shows the existence of a mobility edge in the energyspectrum. In terms of the energy level statistics, the system changes from theGaussian orthogonal ensemble for weak disorder to a Poisson distribution limitfor strong randomness, which implies localization behavior. We then realize thetime-independent disordered Ising Hamiltonian experimentally using a reverseannealing quench-pause-quench protocol on a D-Wave 2000Q programmable quantumannealer. We characterize the transition from the thermal to the localizedphase through magnetization measurements at the end of the annealing dynamics,and the results are compatible with our theoretical prediction for the criticalpoint. However, the same behavior can be reproduced using a classicalspin-vector Monte Carlo simulation, which suggests that genuine quantumsignatures of the phase transition remain out of reach using this experimentalplatform and protocol.

Localization transition induced by programmable disorder