computers have a potential for an effective
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.
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.
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
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.