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the mathematical model of quantum computation has appeared in the 1980-th with the works of david deutsch [ 1 ] and others [ 2 - 4 ] . in 1994
peter shor [ 5 ] proposed an effective quantum algorithm for solving the npi - candidate task  factorisation of big composite numbers .
this breakthrough allowed to expect , that any task from np could have an effective solution on a quantum computer .
this hope was weakened after the lov grover s work [ 6 ] in 1996 , which proposed the general quantum algorithm for solving any task from np .
the algorithm was designed to search the particular point in the unsorted database of size n with only @xmath0 oracle queries .
grover has shown that under the considered assumptions the algorithm is optimal , so only quadratic speedup can be achived by the quantum computer compared to the classical one , if we do nt have additional information about the oracle functioning .
this paper describes the improvement of the quantum database search algorithm , exhibiting the exponential speedup over the classical search , by changing some preliminary assumptions about the model of computation .
the reasoning goes as follows . in section 2
we recall the grover s database search algorithm .
section 3 describes the new quantum computation model with von neumann architecture applied , and the new algorithm for the unsorted database search is proposed along with its complexity estimation .
section 4 glues everything together thus serving as a conclusion .
first , let us recall the algorithm proposed by lov grover . let s consider the function f :    @xmath1 @xmath2    which is some decision function over the set of n - bit strings .
@xmath3  is the number of all possible n - bit strings , thus the number of all possible inputs to f. function f is implemented as a black box .
our purpose is to find the n - bit string @xmath4 on which f returns 1 .
grover defines the quantum oracle @xmath5 :    @xmath6    where x is n - bit string , and y is one bit .
on the first n qubits @xmath5 acts as follows :    @xmath7    @xmath5 acts identically on any vector orthogonal to @xmath8 , while changes the sign of @xmath8 itself , thus it can be considered as the reflection of any vector over the hyperplane orthogonal to @xmath8
.    then the vector @xmath9 and operator @xmath10 are introduced as follows :    @xmath11 @xmath12    where h is n - qubit hadamard transform .
operator @xmath10 reflects any vector over the vector @xmath9 .
the grover iteration is    @xmath13    the @xmath14 operator rotates the initial vector @xmath9 towards the desired vector @xmath8 by the angle @xmath15 , where @xmath16 .
the action of the first two grover iterations is shown on the figures [ grov_1 ] and [ grov_2 ] .
[ grov_1 ]     [ grov_2 ]
the von neumann architecture was introduced by john von neumann [ 7 ] in 1945 .
one of its most famous concepts is the idea of representing algorithms as a special type of data , which can be stored in computer memory along with the information they process .
the computer hardware may then become universal and not depending on the solved tasks .
this idea is considered to be very common and natural for the classical computing model .
however , the quantum computing model still distinguish data ( quantum system state ) from a program ( sequence of unitary transforms in the system state space ) .
some of these unitary tranforms have the natural mapping on the system states .
for example , the state @xmath9 defines the transform @xmath17 in the previous section .
if we assume , that the state of one quantum system can be used as a reflection tranform in another quantum system , then we can introduce a much simplier and effective algorithm for the unsorted database search .    following grover
, we will denote :    @xmath18 @xmath6 @xmath19    we still consider the case of searching of the special input @xmath4 among all n - bit strings .
the number of grover s iterations needed to get the result with high probability after measurement is estimated by @xmath20 .
for example , if n equals to 8 ( each input is one byte ) , then the number of grover s iterations must be close to 12 .
let s suppose that we already have performed a half of these 12 iterations in one system , while in another system we ve prepared the initial state @xmath9 ( figure [ new_alg_1 ] ) .
[ new_alg_1 ]   with 6 grover s iterations.,title="fig:",width=336 ]    if the vector @xmath21 can be used as the operator @xmath22 in the left system with the initial state @xmath9 , then we need only one iteration to get close to @xmath4 instead of the remained 6 grover s iterations ( figure [ new_alg_2 ] ) .
[ new_alg_2 ]   applied.,title="fig:",width=336 ]    again , the vector @xmath21 itself can be constructed from the vector @xmath23 with the same process , thus omitting 3 grover s iterations ( figure [ new_alg_3 ] ) . continuously applying this trick we can reduce the number of all grover s iterations to @xmath24 .
each such reflection divides the number of nesessary grover s iterations by 2 .
[ new_alg_3 ]   applied.,title="fig:",width=336 ]    this means that for solving the unsorted database search problem we need to :    1 .
perform one grover s iteration to get vector @xmath25 .
2 .   prepare the state @xmath9 on another system .
apply the vector from the first system as a reflection to the second system .
4 .   repeat @xmath26 times the steps 2 - 3 .
the implementation of @xmath27 operator , which depends on some quantum state @xmath28 and acts on another quantum system is an open question in the scope of this work .
the proposed quantum algorithm allows us to solve the unsorted database search problem exponentialy faster than that described by grover .
however , the assumption of possibility of applying states as operators to other systems does nt correspond to the classical quantum computation model , developed to these days .
note that with the new algorithm we need only one call to the @xmath5 oracle to get the direction .
after that all the remained iterations do not call the oracle directly . to implement the new algorithm
we need only two quantum systems , which will change their roles on each iteration . the `` algorithm '' system ( which is used as an operator ) on the next iteration must prepare the initial state @xmath9 and become a `` data '' system and vice versa .
w.  shor , _ algorithms for quantum computation : discrete logarithms and factoring_.1em plus 0.5em minus 0.4emproceedings of the 35th ieeesymposium on foundations of computer science .
pp . 124  134 .
the new model of quantum computation is proposed , for which an effective algorithm for solving any task in np is described . the work is based on and inspired by the grover s algorithm for solving np - tasks with quadratic speedup compared to the classical computation model . 
 the provided model and algorithm exhibit the exponential speedup over that described by grover . 
 the main idea of the model improvement is employing the von neumann architecture for a quantum computer , allowing program parts to be stored as quantum states along with the processed data .    
 quantum computing , class np , quantum algorithm , grover s algorithm , von neumann architecture