
Finding Maximum Cliques on the D-Wave Quantum Annealer - Katydid
https://arxiv.org/abs/1801.08649
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jepler
"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.

