  In the SEARCH WITH ADVICE problem, a single entry of interest within a
database of N entries is to be found assuming that an ordering of the entries,
from that with the highest probability of being the entry of interest (as
determined by a so-called advice distribution) to that with the lowest, is
provided. We present a quantum algorithm that, in the presence of significant
levels of quantum noise, solves SEARCH WITH ADVICE for a power law advice
distribution with average-case query complexity O(1) as N tends to infinity.
Since as we also show the best classical algorithms for this problem exhibit
average-case query complexity of order no better than log(N), our quantum
algorithm provides a super-exponential reduction in query complexity.
