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 2n
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(N1/2)
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.