  We show how an algorithm for the problem of inverting a permutation may be
used to design one for the problem of unordered search (with a unique
solution). Since there is a straightforward reduction in the reverse direction,
the problems are essentially equivalent.
  The reduction we present helps us bypass the hybrid argument due to Bennett,
Bernstein, Brassard, and Vazirani (1997) and the quantum adversary method due
to Ambainis (2002) that were earlier used to derive lower bounds on the quantum
query complexity of the problem of inverting permutations. It directly implies
that the quantum query complexity of the problem is asymptotically the same as
that for unordered search, namely in Theta(sqrt(n)).
