"We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms" However, if you choose special gr

"We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms" However, if you choose special graphs whose structure happens to be similar to DW ("chimera graphs"), then DW solves them faster and/or better than classic algorithms, which basically means DW simulates itself faster than general software for the Maximum Clique problem software simulates DW. When it comes to larger graphs that must be split to fit in DW, they have an approach that "works", but the part that runs on a classical computer (the splitting) is exponential in runtime with respect to graph size. They also note that doubling the size of the DW in in qubits only gets you the ability to embed a graph √2 times as big. So for real, general graphs of plausible sizes you still don't escape having an exponential-time nonquantum "part" to the process, even if DW manufactures bigger and bigger devices over time. The part where they state that the combination of the subproblems is optimal assuming that the solution to each subproblem is optimal puzzles me, but that may be because I didn't read closely enough. Generally with problems thought to be in NP, you can't recursively subdivide them, then combine the subproblem solutions into an optimal solution; if you could do that in general, you'd have a golden road to a polynomial time solution to the problem. But that's assuming the subdivision is trivial (like, you divide the nodes in your traveling salesman problem into those west of chicago and those not west of chicago). Since they chose an algorithm for splitting the problem which runs in exponential time on a classical computer, they probably have time to choose special subdivisions where this property of combinability holds--but they haven't escaped "we have to run exponentially many steps on a classical computer", which is not a very good result for DW.