  Consider the unstructured search of an unknown number l of items in a large
unsorted database of size N. The multi-object quantum search algorithm consists
of two parts. The first part of the algorithm is to generalize Grover's
single-object search algorithm to the multi-object case and the second part is
to solve a counting problem to determine l.
  In this paper, we study the multi-object quantum search algorithm (in
continuous time), but in a more structured way by taking into account the
availability of partial information. The modeling of available partial
information is done simply by the combination of several prescribed, possibly
overlapping, information sets with varying weights to signify the reliability
of each set. The associated statistics is estimated and the algorithm
efficiency and complexity are analyzed.
  Our analysis shows that the search algorithm described here may not be more
efficient than the unstructured (generalized) multi-object Grover search if
there is ``misplaced confidence''. However, if the information sets have a
``basic confidence'' property in the sense that each information set contains
at least one search item, then a quadratic speedup holds on a much smaller data
space, which further expedite the quantum search for the first item.
