  Database search has wide applications and is used as a subroutine in many
important algorithms. We shall consider a database with one target item.
Quantum algorithm finds the target item in a database faster than any classical
algorithm. It frequently occurs in practice that only a portion of information
about the target item is interesting, or we need to find a group of items
sharing some common feature as the target item. This problem is in general
formulated as search for a part of the database [a block] containing the target
item, instead of the item itself. This is partial search. Partial search trades
accuracy for speed, i.e. it works faster than a full search. Partial search
algorithm was discovered by Grover and Radhakrishnan. We shall consider
optimized version of the algorithm and call it GRK. It can be applied
successively [in a sequence]. First the database is partitioned into blocks and
we use GRK to find the target block. Then this target block is partitioned into
sub-blocks and we use GRK again to find the target sub-block. [We can call it
binary quantum search.] Another possibility is to partition the database into
sub-blocks directly and use GRK to find the target sub-block in one time. In
this paper we prove that the latter is faster [makes less queries to the
oracle].
