Quantum coherence, together with the superposition principle, gives rise to the parallelism concept for which processing a single state is like acting simultaneously on all states that participate in the superposition [1,2]. It is also known that a key role in speeding up quantum algorithms is played by multi-particle entanglement [
In addition, quantum superposition of coherence qubits has the advantage of maintaining enormous databases by a single state. It is shown that this superposition of qubits can be applied to an efficient database-finding algorithm and in particular the Grover algorithm that defines a possibility for an efficient search engine [5-7]. The advantage of using quantum memory is shown in [8-10] with the definition of a model for which binary pat- terns of n-bits are stored in the quantum superposition of the appropriate subset of the computational basis of n-qbits.
The grover algorithm divides the Hilbert space into two segments: the requested query (denoted by the state
)
and all the other records
. The initial state is a maximal unsorted state 
while the Grover Oracle is a unitary transformation (logical gate)
that rotates the unsorted state until after a relatively small number of iteration
. The probability of detecting the requested query is almost one. Then, a measurement terminates a successful search.
The selection of the 2-D basis 
and 
yields that each search has to be associated with an exclusive 2-D representation such that preparing the appropriate representation corresponds with a primary knowledge about the searched state. In that sense, the Grover algorithm is not a pure search algorithm. Actually, it’s more likely an “inverting a function” meaning that if we have a function 
that can be evaluated on a quantum computer, this algorithm allows us to calculate 
when given 
[
and 
as vectors, the algorithm corresponds with rotating the 
state with respect to the 
state. This is an equivalent way to represent the constrain of a primary knowledge concerning the searched state 
[
(the subscript 
stand for the observer which determines the searched item) but unlike the register state (which belongs to what we refer to a r-space) that is occupied with the unsorted state, this o-space represents the observer search selection of a definite single record state, say,
. Thus, eventually, the searched item is well defined but only among the observer parallel space and definitely not to the other search component. We will present a scheme which shows that by correlating the observer state with the unsorted state, the later will be represented in the appropriate 2D representation. Once the unsorted state is prepared, we introduce a rapid search algorithm.
where each state presents a possible query. The measurement output is associated with the projective operator:
.
. We can present the 2D-projective-operator:
is the input state then the result will be the
, that is
, will yields the string
:
such that:
, then we obtain
state it activates the link operator 
to present or link to the relevant site. For other cases the observer receive the text massage “Record not found”.
unsorted records state:
.
-records basis into a 2-D space, spanned by the states
—the state under the search and the state
—a superposition of all the other states. Consequently each search is associated with an exclusive 2-D representation such that preparing the appropriate representation corresponds with a primary knowledge about the searched state. In that sense the Grover algorithm is not a pure search algorithm. Actually it more accurate to describe the Grover algorithm as “inverting a function” meaning that if we have a function y = f(x) that can be evaluated on a quantum computer, this algorithm allows us to calculate x when given y [
and 
as vectors, the algorithm corresponds with rotating the 
state with respect to the 
state. This is an equivalent way to represent the constrain of a primary knowledge concerning the searched state 
as nicely described in ref. [
in the plane that contains the unsorted state vector 
and the target state
, where 
depends on the angle between 
and
. So the Grover steps are not almost Target-blind. Far from it.”
(the subscript 
stand for the observer which determine the searched item) but unlike the rspace, this o-space represents the observer search selection of a definite single record state
. Thus, eventually, the searched item is well know but only in the observer parallel space and definitely not by the other search component.
-record, the observer defines the state
. The searching machine first step is to correlate between the observer state 
with the processor unsorted state 
yielding:
being the unsorted state of Equation (7).
-selection can be followed by the r-space such that the unsorted state 
will be represented by the 
- basis?
is the operator that operates within the 
-space and can be coupled to any observer selection
. Clearly there are 
operators of the kind. The global processor task is to associate each operator with its compatible 
-state. This operation is activated by the following 
-operator:
and after the states are correlated as shown in Equation (8), the processor operation provides us with the output:
-representation only. We note that 
can be regarded as an “eigenoperator” [13,14].
on the unsorted state 
(see Equation (9)) and considering this operation by means of conducting a macroscopic measurement, we will probably obtain a 
output and consequently the remaining state will be the 
-state. Therefore in order to improve the odds of detecting the required 
associated data, we apply the Pauli gate that switches between the 
-states while leaving the “eigensymbols” unchanged.
to possess the required eigensymbol data
with the high probability
. Thusnot only we defined a pure searching algorithm by defining the observer query separately from the search engine, we also introduced a very rapid algorithm which composed mainly of two steps: The Pauli gate and a macroscopic measurement.