Possible schemes of calculation modeling in a quantum computer

doi:10.4236/ns.2010.28114

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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; [email protected]

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 ()

x on the initial

state

is defined by the expression:

() n

xaxbx , (1)

where a and b



are constant positive coefficients,

2n. If

<< 1, then n

bx << ax , therefore

()

xax



(2)

Thus, in the case of (2), ()

x grows linearly with

growth of

. If

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

value. Under several

values, the ()

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

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

 and 5



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 ,

JJSSJSSS SJSSSS 

(3)

where S with the corresponding index is a spin value

of unpaired electrons localized on()Ni II atoms and

nitroxyl groups,



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



-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



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



and 5

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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