Vol.2, No.8, 923-927 (2010) Natural Science
http://dx.doi.org/10.4236/ns.2010.28114
Possible schemes of calculation modeling in a quantum
computer
Vladimir Voronov
Irkutsk State Technical University, Irkutsk, Russia;
Received 21 April 2010; revised 21 May 2010; accepted 26 May 2010.
ABSTRACT
In the present work a possibility of computation
modeling, which should be realized in a real
quantum computer, is discussed. In this con-
nection two models of a device, which work is
determined by the structure and dynamics of
real molecular systems are reported.
Keywords: Quantum Computers; Strong-Correlated
Systems; Entanglement of States
1. INTRODUCTION
The present work deals with a possibility of computation
modeling, which should be realized in a real quantum
computer. In this connection, the models of a device,
which work is determined by the structure and dynamics
of real molecular systems are reported.
Recently [1,2] we have put forward an idea, which re-
alization would allow one to overcome, at least, some
problems related to the creation of quantum computers,
i.e., the idea of molecular Internet. According to this idea,
every molecular system with its own set of degrees of
freedom and (or) states represents a server having mem-
ory of certain volume. This server is used for storage and
transmission of the information. The latter is further
transformed in computational operations during the so-
lution of specific mathematical task. If to assume that
quantum computer has to perform the same operations as
the classical one, the necessary memory volume of such
a server could be achieved by two (at least, in principal)
routes: 1) introduction of maximum amount of atoms
playing the role of q-bits into the molecular system; 2)
combination of separate molecules in a spatially ordered
structure where physical and chemical interactions of
any nature can be realized. These interactions will ensure
the formation of superpositional coherent states needed
for the performance of computational operations. The
above approaches are quite reasonable from the view-
point of the modern theoretical notions on quantum cal-
culation problem. But, in our opinion, the ways of this
problem solution are beyond the frameworks of the
conventional theory. Below we will discuss some gen-
eral concepts, which can pave the road to new ap-
proaches to the problem of quantum computer creation.
2. MODELING PRESENTMENT OF
QUANTUM COMPUTING
According to the Shor theory [3], a certain number of
states remain free in the course pf information input. In
principle, these states can be used for the performance of
parallel calculations. Since a number of such states can
be very large (relative to the corresponding number of
q-bits), the tasks which previously seems insoluble be-
come realistic. As applied to the molecular Internet idea,
one can correlate the states of quantum particles (q-bits)
with real molecular objects with all far-reaching conse-
quences. Thus, keeping the idea of quantum calculations
intact, it is possible to impart it a real content. Really, if
the quantum states aforementioned are still virtual, the
molecular states are manifested themselves in macro-
world by many phenomena which reflect quite ade-
quately these states. Therefore, these states become ex-
perimentally accessible. The problem is in the correla-
tion of these states with the corresponding mathematical
patterns. Hence, the application of these states for the
solution of specific task should involve the usage of the
information, which is already contained in the molecular
structure.
Logic route to the realization of the molecular Internet
idea is in combined application of the spatial molecular
structure and spin values of q-bits constituting this mo-
lecular structure. Really, we have mentioned above that
the problem is in the search for an approach which al-
lows quantum systems (due to the peculiarities of struc-
ture and/or behavior) to be manifested in the macroworld.
Therefore, if one can manage to correlate q-bit spins
with molecular structure this will mean the realization of
such an approach. Thus, the circle is closed, i.e. there is

V. Voronov / Natural Science 2 (2010) 923-927
924
a principal way to the organization of quantum states
detection without any distortion of this state. Experi-
mental realization of the approach becomes predictable:
combined usage of the information on the molecular
system state and spins (q-bits) contained in this system.
Further problems of quantum calculations are the matter
of technique to some degree, though not very simple.
The experimental investigations carried out by the
present time are far from the realization of quantum cal-
culation idea. Indeed, even though the elementary quan-
tum algorithms have been already elaborated using the
NMR method [4-6], the possibility of the creation of real
quantum computers on the basis of this phenomenon is
yet to be proved. The probable application of other
physical methods for this purpose is under discussion. In
this case, the approach based on the preliminary model-
ing the operation scheme, which should be realized in a
quantum computer (followed with its embodiment in
specific electronic schemes), seems to be intriguing. By
the moment there are many essential prerequisites for
such experiments. Really, the preparation of nano-sized
heterostructures enables to obtain a wide range of prop-
erties for different kinds of device applications. In its
turn, the development of physics and technologies of
synthetic nanostructures makes it possible to prepare
them in quite wide variety (see [7] and the references
therein). That is way the above model route to the crea-
tion of quantum calculation processors may be consid-
ered as promising.
All the aforesaid allow one to propose the following
variant to model the real quantum calculation. Prelimi-
nary it is worthwhile to note that according to the current
theoretical notions, to reach the goal one should have
such devises (as the starting universal logic block),
which can perform repeatedly logic operations “NOR”
and “controlled NOR”. In other words, these devises
(logic gates) must possess a property of reversibility.
Among such devices is the Toffoli three-bit gate (see, for
example, [8,9] and the references therein). If to stay fur-
ther within the framework of the model proposed, one
should create the elementary blocks: gates; each of them
must incorporate three q-bits interacting with each other.
At the same time, the environment of each q-bit must be
suitable for the triggering the calculation procedure.
These blocks can be formed by three nano-sized objects
containing an electron with a specific spin state. Next,
one should model the reversibility property of the three
q-bit gate. This can be attained due to the multiple re-
production of the above block from three nanoobjects as
well as the application of special commutating devices
operating, for example, on the basis of femto-second
laser.
This brings up the questions: “To what degree the pro-
posed method for the organization of quantum calcula-
tions is realistic and what are the dimensions of the de-
vise capable of such operations as quantum calcula-
tions?” If one is limited here by the qualitative answers
to the questions arisen it would be reasonable to pay the
attention to the germanium and silicon nanostructures
prepared recently using scanning tunnel microscope [7].
In this case, one can grow the nanoobjects (islands of
approximately 10 nm size at the base and some nm in
height) located in about 50 nm from each other. It is an
easy to evaluate that every square centimeter will con-
tain about 1010 of such islands. Therefore, from the
nanoobjects mentioned one can create (at least, in prin-
ciple) the appropriate number of the gates (by collecting
the islands in groups) to make up the processor, capable
of solving the real tasks.
3. MODELING OF QUANTUM
CORRELATION
Another step of the quantum calculations needs to be
modeled. We mean here the entanglement of states or
quantum correlation of the q-bits system localized in
nano-islands. This is a mandatory step preceding the
calculations [8,9]. Therefore, one can speak about
preparation of the entangled state. To model the above
step, it is proposed to use the self-organization of quan-
tum (molecular) systems. In other words, one should
synthesize the molecules where the entanglement of
states is provided due to the self-organization of atoms.
Such a possibility could be evaluated as follows. Let the
dependence of deviation amplitude ()
f
x on the initial
state
x
is defined by the expression:
() n
f
xaxbx , (1)
where a and b

are constant positive coefficients,
2n. If
x
<< 1, then n bx << ax , therefore
()
f
xax

(2)
Thus, in the case of (2), ()
f
x grows linearly with
growth of
x
. If
x
value is comparable with 1, it
would be impossible to neglect the n bx member, since
for the description of the system behavior one should use
the initial Equation (1). Hence, the growth of function
deviation at the expense of ax member will cause
nonlinear limitation owing to the deduction of n
bx
value. Under several
x
values, the ()
f
x function will
be close again to zero and all starts from the beginning.
The system will automatically regulate itself, as its
properties depend on a current state (in this case―from
x
value). Therefore, it is reasonable to conclude that by
somehow changing the given molecular system, it is

V. Voronov / Natural Science 2 (2010) 923-927
925
possible to achieve (in principle) the necessary values
for the corresponding parameter (or parameters). Obvi-
ously, such changes could be carried out by three ways:
1) the introduction of new atoms to molecular structure;
2) the external action (for example, applying an electro-
magnetic field); 3) the combination of these two ways.
The fundamental problem is to understand what mo-
lecular objects can be suitable for similar manipulations.
Based on the most general ideas, one can assume that
here one should deal with the compounds where charac-
teristic intramolecular interactions will ensure the reali-
zation of the required (from a position of a problem dis-
cussed here) quantum states. These are the compounds
containing atoms with unfilled 3d, 4
f
 and 5
f

shells. In solids, such atoms retain localized magnetic
moments completely or partially. The strong interaction
of electrons of these groups with each other or with col-
lective electrons of outer shells represent a peculiarity
imparting the unique properties to a variety of the com-
pounds containing atoms of transition and rare-earth
elements. The investigations carried out over the last
fifteen – twenty years have shown that for these com-
pounds the diverse physical phenomena are possible.
Among them are phase transitions resulting in the mag-
net-ordered phases and superconductivity, dielectric and
metal states; transitions with appearance and disappear-
ance of the localized magnetic moments. The specified
properties are the consequence of strong interactions of
electronic and magnetic degrees of freedom. The sys-
tems with strong interaction of electrons are referred to
as the strong-correlated systems [10].
Particularly, the functional dependence (1) can follow
to any parameter, which is characteristic for the given
molecular system. It is only necessary that the parameter
would periodically undergo such changes that its limit-
ing values would correspond to those quantum states
which should be used for modeling the process of the
quantum calculations. These states can be realized for
the molecular systems which behavior at the macroworld
level (in laboratory system of coordinates) is connected
with the manifestations of heterogeneity of intra-mo-
lecular processes. Just due to the peculiarities of struc-
ture and dynamics of the molecular system, the nonlin-
earities, which will provide periodicity in change of a
parameter characterizing its behavior, becomes possible.
Apparently, a vivid illustration of the possibility of the
specified process realization is the compounds belonging
to a new class of polynuclear heterospin complexes con-
taining the ligands with non-paired electron [11]. For
example, this is tetranuclear nickel cluster [Ni2(OH)3
(C5H9O2)5(C5H10O2)4(L)]1.5C7H8 (I), where L

is a
nitroxide radical. The compound (I) is a representative of
the aforementioned strongly correlated systems.
According to the data reported in the work [11],
spin-Hamiltonian, describing the exchange magnetic
interactions in these compounds, looks as follows:

 
0121 132421223
222 ,
H
JJSSJSSS SJSSSS 
(3)
where S with the corresponding index is a spin value
of unpaired electrons localized on()Ni II atoms and
nitroxyl groups,
J

is a parameter characterizing in-
teraction between the mentioned groups. Naturally, in
the case of other compounds which differ from com-
pound (I) in structure, the right part of the expression (3)
will look otherwise. However, it is important that by
selecting the appropriate initial compounds one can ob-
tain such heteronuclear complex where the interaction of
groups having unpaired electron spins will provide the
fulfillment of the condition (1).
The question is arisen: “What is nature of quantum
object state allowing the model of entanglement to be
realized?” To answer the question, one should take into
account the following considerations. The description of
quantum states, based on the application of spin-Hamil-
tonian (3) assumes the availability of free (real) quantum
particles, spin carriersS. Meanwhile, the introduction of
unpaired electron into the ligand molecule can lead to
the appearance of states caused by the interaction of spin
S with electrons of the ligand molecule. It is known
that the description of such a collective behavior is often
associated with the use of the quasi-particle concept. For
example, the notions on magnetic polaron or ferron
turned out to be fruitful for the explanation of different
heterogeneous charge and spin states in magnets [12].
We will start from the established fact, i.e. from the lo-
calization of unpaired electron spins in two positions like
in paramagnetic heterospin complexes of elements of the
first transition group bearing stable iminoxyl radicals
[11]. In the case of unpaired electron spins related to the
central ion, with which the ligand molecules are coordi-
nated, it is a common knowledge that the behavior of the
spins mentioned can be unambiguously described ac-
counting for 3d

orbitals of a metal. We will address
therefore to unpaired electrons which are localized on
ligands.
Let us consider a simple case: the presence of un-
paired electron localized on a ligand. Obviously, this
electron will somehow with an electronic subsystem of
the ligand molecules. Indeed, the electronic structure of
a specific ligand molecule was formed in the absence of
unpaired electron. Therefore, the latter should be con-
sidered as a certain excitation. Further on, let us admit
that that owing to peculiarities (in this case, the specifi-
cation is not important) of spatial and electron structure
of the complex and under the conditions of thermody-
namic equilibrium (set by the sample temperature),

V. Voronov / Natural Science 2 (2010) 923-927
926
ferron-like states are realized in ligands. Here it is nec-
essary to explain that full spin of ferron state is formed
by the local spin and electron spin (see [12] and the ref-
erences therein). As to the local spin is concerned, it is
caused by magnetic (in particular, antiferromagnetic)
state of the matrix, where the conductive electron moves.
In other words, there is always specific information on
the state of such a matrix.
Formally, in the case of heterospin complexes dis-
cussed here, a matrix, in which the unpaired electron
with spin 1/2S is inserted, is a ligand molecule and
not solid phase of microsample as it is observed in man-
ganites [12]. The assumption on realization of ferron-
like states should mean that the result of the interaction
of unpaired electron with electron subsystem of the
ligand will be the state with non-compensated electron
spin which differs from the state of free electron. In our
case, the quantum objects employed in the calculations
are electrons. The emergence of ferron states allows one
to distinguish electrons transferred to these states for a
while. For a certain time, an electron is located on d

,
or
f
-orbitals of the central ion (for example, nickel).
Further, due to the specifics of intramolecular spin-spin
interactions the electron is temporarily transferred to
ferron state. In a certain period of time (typical for
ferron), the electron is again located on metal orbitals.
Then the cycle is repeated. Here, once should stress once
again that the ferron state differs from the free electron
state. Really, it is a common knowledge that a peculiar
feature of the objects called quasi-particles is the differ-
ence of their mass from the mass of the corresponding
free particle. So, the mass of polyaron is hundrets times
higher than that of free electron. This feature is also in-
herits in ferrons [12]. As was mentioned above, the full
spin of ferron state also differs from spin of free electron.
Thus, the state of entanglement, needed for operation of
a quantum computer, turns out to be modeled. The pos-
sible route to a large number of quantum objects has
been described above.
One should explain why heterospin complexes can be
considered as possible objects to model quantum calcu-
lations. These are paramagnetic systems containing as
ligands the molecular systems having unpaired electron
or unpaired electrons. The role of d or
f

metal
orbitals here is two-fold. Their population with unpaired
electrons participating in intramolecular spin-spin inter-
actions ensures the validity of the expression (1). Be-
sides, it is just unpaired electron on these orbitals, being
free relative to its magnetic properties, is transferred for
a while to other state needed for modeling the entangle-
ment of quantum particle. By changing the structure and
composition of a paramagnetic compound as well as the
external conditions one can control the entanglement
degree of ferron state and state of a free electron, thus
controlling also the calculation procedure.
4. CONCLUSIONS
In conclusion, one should make the following remarks.
The experimental investigations carried out by the pre-
sent time are still far from practical realization of the
quantum calculations idea. Therefore, while the suitable
objects for realization of quantum computers idea will be
searched, certain intermediate variants could appear. In
such a situation, an approach based on preliminary mod-
eling the operations which should be realized in a real
quantum computer with their subsequent application in
specific electronic schemes, seems to be attractive. For
this purpose the compounds containing the atoms with
vacant 3d

,4
f

and 5
f
shells could be suitable.
We mean here the compounds (for example, heterospin
complexes), which unique properties are caused by
strong interactions of electronic and magnetic degrees of
freedom, i.e. strongly correlated systems. Among these
compounds could be, in particular, heterospin systems,
i.e. the complexes of paramagnetic ions of transition
metals with organic radicals, since spin-spin coupling
between unpaired electron spin of different paramagnetic
centers of the molecule is typical for such objects. The
coupling mentioned can result in phase immiscibility to
afford heterogeneous spin states. In its turn, such states
can be used for modeling the processes characteristic of
quantum computer.
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