  The use of superposition of states in quantum computation, known as quantum
parallelism, has significant advantage in terms of speed over the classical
computation. It can be understood from the early invented quantum algorithms
such as Deutsch's algorithm, Deutsch-Jozsa algorithm and its variation as
Bernstein-Vazirani algorithm, Simon algorithm, Shor's algorithms etc. Quantum
parallelism also significantly speeds up the database search algorithm, which
is important in computer science because it comes as a subroutine in many
important algorithms. Quantum database search of Grover achieves the task of
finding the target element in an unsorted database in a time quadratically
faster than the classical computer. We review the Grover quantum search
algorithms for a singe and multiple target elements in a database. The partial
search algorithm of Grover and Radhakrishnan and its optimization by Korepin,
called GRK algorithm are also discussed.
