Annealing of Embedded Spin Glasses

We discuss recent results on thermal and quantum annealing of random spin glasses on fully-connected graphs and on fully-connected bipartite graphs. After the description of the embedding of their classical Hamiltonian onto Chimera graphs, we discuss what are the optimal embedding parameters, in relation with the signatures of the quantum phase transitions occurring during the annealing. Finally, we compare numerical simulations and analytical expectations for both the embedded spin glass models with results on the non-embedded models and with runs on D-Wave Machine installed at NASA Ames.