Quantum
computers have a potential for an effective
solution
to problems

which are infeasible on a classical computer.

The actual utilization
of this potential would require much progress
in the development of

suitable hardware as well as of algorithms
which would

exploit the strengths while overcoming the
shortcomings
of quantum

computers, in particular the problem of
decoherence.

This process is likely to provide new insights
into quantum effects,

computational complexity as well as prospects
for new technologies.

Unlike
classical computers in which each bit

is a two state system which can be either in
state 0 or 1, the quantum

bit (or qubit) can be in any superposition of
the two states.

The potential strength of quantum computers is
due to the fact that

computations on an n-bit register are performed
simultaneously on

all 2^{n}
states in the superposition.

However, this potential can be realized only
by using sophisticated

interference schemes to
extract the desired
results.

One of the
most important quantum algorithms found
so far is

Grover's search algorithm.
This algorithm is capable of

finding a marked element in an unsorted list
of size N

in O(N^{1/2})
queries compared to
O(N) queries on a classical computer.

Grover's algorithm requires, though,
a careful preparation of the initial quantum
state.

Recently, we
generalized Grover's algorithm

to apply with an arbitrary initial amplitude

distribution.
We found the recursion equations

which describe the time evolution of the
amplitudes
of the

quantum states and solved them exactly.
Our approach, in which

the time evolution of the amplitudes is analyzed
as a dynamical

system, has already lead to very useful
developments

in the field of quantum algorithms.

It is widely believed that the
speedup provided by quantum algorithms is
related

a quantum property called entanglement.
This is a quantum correlation between the

states of different qubits that has no classical analoge. In order to
quantify this connection

one needs a way to measure the entanglement of a given quantum state.
We have shown

that Grover's search algorithm can be used in order to quantify the
entanglement of quantum

states of multiple qubits.