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Although strongly regular graphs and the hypercube are not complete, they are"sufficiently complete" such that a randomly walking quantum particleasymptotically searches on them in the same $\Theta(\sqrt{N})$ time as on thecomplete graph, the latter of which is precisely Grover's algorithm. We showthat physically realistic nonlinearities of the form $f(|\psi|^2)\psi$ canspeed up search on sufficiently complete graphs, depending on the nonlinearityand graph. Thus nonlinear (quantum) computation can retain its power even whena degree of noncompleteness is introduced.

Completeness is Unnecessary for Fast Nonlinear Quantum Search