Американский Научный Журнал PHYSICAL–TECHNICAL ASPECTS OF REALIZATION OF QUANTUM COMPUTER (30-35)

This article analyzes the main physical and technical aspects of the implementation of quantum computers. Existing element bases are considered, on the principles of which the work of new generations of computer technology - ultra-modern types of computers. Quantum calculations are carried out in less time than in classical computers, due to the parallel work, and the increase in speed is exponential. This determines the relevance and prospects of research in the field of quantum technologies. Quantum algorithms use the concept of a quantum bit - qubit and quantum superposition. At present, high-precision technologies and methods for producing high-purity materials allow the creation of experimental models of quantum computers. Скачать в формате PDF
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ФИЗИКО -МАТЕМ АТИЧЕСКИЕ НАУКИ

УДК 004.273
PHYSICAL –TECHNICAL A SPECTS OF REALIZATIO N OF QUANTUM COMPUTE R
Babayan M.G.,
Cherkesova L.V.,
Smirnov I.A.,
Razumov P.V.,
Safaryan O.A.,
Porkshyan V.M.
Don State Technical University, Rostov –on –Don

Annotation. This article an alyzes the main physical and technical aspects of the implementation of quantum
computers. Existing element bases are considered, on the principl es of which the work of new generations of
computer technology - ultra -modern types of computers. Quantum calcu lations are carried out in less time than in
classical computers, due to the parallel work, and the increase in speed is exponential. This determ ines the
relevance and prosp ects of research in the field of quantum technologies. Quantum algorithms use the c oncept of
a quantum bit - qubit and quantum superposition. At present, high -precision technologies and methods for
producing high -purity material s allow the creation of expe rimental models of quantum computers.
Keywords: quantum computer, quantum algorithm , qubit, nanoelectronics, multiparticle quantum system,
quantum effects, parallel computing.

Introduction
The acceleration of technological prog ress led
to the transition f rom industrial to postindustrial
information society, in which information plays a
crucial role, and its processing is the key to the
success of the state. A continuous process of
improving methods and technologies is underway,
allowing to create more effi cient and faster software
and hardware tools of smaller sizes, working on
other pr inciples. This approach leads to an increase
in the speed of computational operations with the use
of state -of -the -art technical means, the princi ple of
which is fundamentall y different from classical
computers. These tools include quantum
technologies – c omputers of new generations, in the
process of which quantum effects are applied,
quantum algorithms are implemented in quantum
programming langua ges.
Quantum computations ar e carried out in
incomparably less time, in comparison with classical
computers. T he increase in speed and shorter time for
solving problems is exponential, which makes future
research in the field of quantum technologies
promis ing.
Quantum algorithms cann ot be executed (in such a
short period of time) on classical computers in which th e
basic unit of information is bit. It is necessary to single out
a number of problems that cannot be solved on classical
computers: these are pro blems based on number–theore tic
functions, Abelian groups, factorization of large numbers
(factorization of la rge numbers), discrete logarithms, etc.,
as well as the tasks of processing large amounts of data
and search records in an unstructured and disord ered
database [1].
With the advent of quantum computers, in
industry and manufacturing, growth in productivity and
speed is predicted when performing computational
tasks. Considering the use of quantum algorithms in pharmacology in the production of drugs,
it should be
noted that quantum computers are able to perform
various functions of testing the effects of dru gs at the
molecular level. So, the introduction of quantum
computers promises to make significant changes in
many areas of human life.
Modeling th e behavior of a wide ran ge of
multiparticle quantum systems is one of the applications
of computing quantum al gorithms. This feature allows us
to predict the state of crystals and molecules, which will
provide the opportunity to design nanoelectronic devic es,
the dimensions of which can be several tens of angstroms
[2].
The relevance of quantum technology research is
due to many factors – the problems of modeling
physical processes in nanoelectronics devices and in
multi –qubit quantum devices, the developme nt of
technology for the production of nanometer –scale
processing devices, as well as the problems of
modeling the physical properties of complex organic
systems with a molecular structure.
Ideas and principles underlying the quantum computer
Elemental bas e. In a quantum computer, in
comparison with the classical one, where the basic unit
of information is a bit, a quantum bit (qubit) is used. As
qubits, various quantum two -level systems are used, in
particular [1]:
1. Neutral atoms or ions with two low -lying
vibrational o r hyperfine levels held in power traps
created in vacuum by electric and magnetic fields
durin g laser cooling to micro -kelvin temperatures.
2. Superconducting structures with Josephson
junctions.
3. Separate electron and nuclear spins in a
magnetic field.
4. Quantum dots with two electronic orbital and
spin states.
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5. Certain states of a quantized electromagnetic
field in electrodynamic resonators and photonic
crystals. The qubit and the superposition of its states.
Consider a comparison of a qubit with the classical bit
model, in which a unit of information takes only two
possible values (0 or 1). The qubit has the ability to be
in a superposition of these states.
The element under consideration admits two states,
denoted by rç and sç , but can also be in the state of their
superposition, in other words Ùrç
EÚsç , in the state
where Ù and Ú are any complex numbers that satisfy the
condition Ù 
6
E Ú  6
L s. Each time a qubit’s state is
measured, it randomly changes one of its stat es to: r; or 
s ;. The probabilities with which the transition to these states
is carried out are equal to Ù 
6 and Ú  6.
The main advantage of a quantum computer,
compared with the classical one, is the presence of
entangled (linked) states betwee n qubits. Such a
process is characterized in that for any change in the
state of one of the qubits, all the ot hers also change their
state according to the initially changed state of the first
qubit. This occurs through nonlocal quantum
correlations, chang es in which affect at the same
moment in time, while the distance between qubits does
not affect the process [ 3]. If, prior to measuring the data
output operation, the m – bit quantum register is in the
state [2]:
Í
5
á
Ø 7 - @ 4
Í
5
á
Ø 7 . @ 4

Í ? á Ø 7 - á Ø 7 . å á ,J à ? 5 J à ? 6 å J 4
5
á
, @ 4
çá
?
á Ø 7 - á Ø 7 . å á ,Ð %á (1)

whic h is a superposition of base conditions
 J
à ? 5 çJ à ? 5 çä ää J 4ç ,
w here each J
Ýç
L rç or sç
then if it is impossible to represent i n the form:

T
5ç ä ää T àç (2)
w here T
Ýç
L Ù Ýrç
EÚ Ýsç :F
L sáäääá I ;, state
(1) is linke d.
The set of interconnected qubits of a quantum
computer can be considered as a filled quantum register
(pic.1).


Pic. 1 – Scheme of possible states of the standard register and qubit register

Quantum register (1) is muc h more informative
than classi cal register. It is able to be in all kinds of
combinations of its constituent bits, realizing various
subtle relationships between them [4].
Quan tum Concurrency . The main factor
responsible for quantum parallelism is the presence of
entangled states betwe en qubits [5]. This phenomenon
has no analogue in the work of classical computers. If
a single PC calculates a single output value for a single
in put state, then a quantum computer calculates the
output values for all input states at once. A qubit -based
co mputer on each step of its work converts all the basic
states at once using quantum parallelism.
So, quantum computing is parallel, which allows
to obtain a significant increase in speed and efficiency
of computing [4].
Variants of the execution of quantum
computers Currently, the following directions are being
discussed in changing the state of the element base
of quantum computers [5]:
Quantum c omputer on ion traps. It is proposed to
use ion energy levels as qubits (the ground and excited
states of ions c orrespond to the values of and) trapped by
ion traps that are created in vacuum by a certain
configuration of the electric field during laser cooling of
ions to a temperature of about 20 microkelvin. In the chain
of these traps, the interaction between charged ions occurs
due to the excitation of their collective motion, and the
infrared lasers individually control them. This approach
implements a relatively simple individual control of
individual qubits.
The main disadvantages of this area:
1. The need to u se ultra–low temperatures.
2. Ensuring the stability of the states of ions in the
chain.
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3. Decoherence of quantum states, determined by
the strong in teraction of charged particles with their
environment.
4. The limite d number of qubits is possible (their
value doe s not exceed 40 –50, and in the near future their
number cannot be substantially increased).
As a result, such systems cannot be considered as
ha rdware for a quantum supercomputer , although they
undoubtedly hav e certain prospects as model structures.
Quantum NMR (Nuclear magnetic resonance) is
an organic fluid computer. Quantum computers of this
type are based on the use, as qubits, of the spins of the
atomic nucleus (states rç and sç can correspond to the
direction of the spin of the atomic nucleus - “spi n up” and
“spin down”) belonging to molecules of organic liquids,
indirect scalar interaction between spins, and on the
application nuclear magn etic resonance methods
(hereinafter NMR ) for controlling qubits. At present, the
simplest quantum computers base d on organic liquids
based on NMR methods have been implemented.
The following quantum algorithms were
implemented on them: the Shore factorization algorithm
and the Grover data searc h algorithm, quantum error
correction, quantum Fourier transform, quantum
simulation, quantum teleportation.
Advantages of QC on an organic liquid:
1. The possibility of stable operation at room
temperature.
2. Well –known nuclear magnetic resonance
technologies can be used to control qubits and
measure their states.
3. The physical sys tem of qubits is the
macroscopic volume of weakly interacting liquid
molecules containing atoms with nuclear spins, the
resonant frequency of wh ich is different.
4. The decoherence time of the quantum states
of nuclear spins in an organic liquid is quite larg e up
to several seconds. The main limitations for this area are:

1. The mixed nature of the initial quantum state of
qubits at liquid state tempera tures; solving this problem
requires the development of special qubit management
methods.
2. For liquid quantum NMR computers, today, the
number of qubits cannot exceed two dozen, due to the
exponential decrease in the intensity of the measured
signal with in creasing number of qubits; t he solution to
this problem requires an exponential increase in the
sensitivity of m easuring instruments and equipment.
3. The number of nuclear spins - qubits differing in
the resonant frequency - qubits in an individual molecule
cannot be arbitrarily large.
4. One- qubit and two -qubit quantum operations are
relatively slow.
Thus, even this ver sion of the element base
cannot form the basis for creating a quantum
supercomputer that significantly exceeds the
capabilities of a modern clas sical computer [3].
Semicond uctor quantum NMR computer with
individual access to qubits at low temperatures. In
quantum computers of this type, the role of qubits is
played by the nuclear spins of identical donor atoms in a
semiconductor structure, for the electronic control of
which and the measurement of their states, a structure
must be created from gates of nanometer scale. Given the
achievements of modern nanotechnology, in this option,
you can create a system of many thousands of qubits.
Semiconductor quantum NMR computers (base d on
nuclear magnetic resonance effects, pic. 2), with
individual access to qubits, when operating at low
temperatures, can solve the problem of an exponential
decrease in signal intensity with increasing number of
qubits.


P ic. 2 – IBM's quantum computer announced at CES 2019

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The main problem of this option is the need to
measure th e state of an individual qubit. A number of
methods have been proposed to solve this problem, but
not one of them has yet been implemented. Anoth er
difficulty is assoc iated with the presence of control
gates, the noise voltage at which is a source of
decoh erence. This version of the element base of a
quantum computer, despite the existing difficulties and
unsolved problems, undoubtedly deserves fur ther
development.
Solid –state quantum NMR is computer with
ensemble access to qubits. A quantum computer of thi s
type is more promising than the previous model.
There is an opportunity to significantly simplify the
management of qubits and the measurement of their
states. When using the principles of a quantum
cellular automaton in ensemble versions, it is
possible to greatly simplify the system of control
shutters, or even abandon them altogether. This
would eliminate the significant noise mechanisms of
de coherence of nuclear spins associated with them.
Semiconductor quantum NMR computer us ing
microwave and laser p ulses. A semiconductor quantum
NMR computer, in which microwave and laser pulses
are used to control qubits and measure their states, is an
alter native to the model of semiconductor quantum
NMR - a computer with individual access t o qubits. This
version of the element base makes it easier to solve
problems associated with measuring the states of
individual qubits, but at the same time, the disadvantages
associated with the presence of a gate system remain.
The use of the ensemble ap proach is promising here.
Quantum computers on quantum dots with
electronic orbital and spin states. Computers of this
type have several advantages over quantum NMR
compu ters:
1. The ability to work at significantly higher
temperatures than semiconductor NMR –quantum
computers.
2. Higher clock frequency and magnitude of
the measured signal.
3. The fact that modern nanotechnology allows
us to create quantum structures with an almost
unlimited number of quantum dots.
The main difficulty for such computers is the
relatively fast decoherence of quantum states
associated with the electric charge of an electron and
electric qubit control methods, for the suppression of
which there are no w ell-developed methods. The
solution may be to use for this not optical, but opti cal
ultrafast methods.
Quantum computers at Josephson junctions. In
such quantum computers, the charge states of Cooper
pairs at quantum dots associated with Josephson junction s
are used as qubits. The prospect of this direction lies in the
possibility of creating electronic quantum dev ices with a
high degree of integration on a single crystal, and cumbersome laser or
nuclear magnetic resonance NMR
installations are not required to control qubits.
The superconducting version of the elemental base
of a quant um computer, despite the existi ng
achievements in the implementation of a single qubit,
has a number of difficulties. They are associated with
the need for tight control of the perfection of
manufacturing Josephson tunnel junctions, the
temporal characteri stics of pulsed effects, the us e of
electrical circuits for controlling individual qubits, and
voltage fluctuations, which are the main cause of
decoherence. The system of a la rge number of qubits
associated with the electromagnetic environment is a
comple x nonlinear system in which man y undesirable
nonlinear effects can occur [5].
3. Promising directions in the construction of
quantum computers
Of all the directions in the deve lopment of the
elemental base of quantum computers, the most
attractive from the point of view of creating
supe rcomputers are currently the following:
 semiconductor NMR – quantum computers;
 quantum computers at Josephson junctions;
 quantum computers on qua ntum dots.
These promising areas of designing quantum
computers allow for an arbitrarily large number of
qubits , and for them there are many proven methods
of micro - and nanotechnology for creating
semiconductor and superconducting integrated
circuits.
The most important advantages are solid state
NMR – quantum computers.
Among th em stand out:
 Nuclear spins themse lves are qubits.
 At low temperatures, they are characterized by
a longer relaxation time (and decoherence) compared
to electron spins.
 Nanometer –scale technological structures in
semiconductor quantum NMR computers are not
intended to create qubits, as in the case of
superconducting devices, but to control qubits and
measure their states [6].
Software emulation of the solution of the
equivalence pr oblem of two quantities
Summing up the analysis of possible elemental bases
for the implementation of quantum computers, we will
solve a certain problem in a standard way (on a classical
PC), as well as using a quantum computer emulator.
We formulate the p roblem as follows: let there be
some function that can be a constant, that is, it
constantly returns the value 0 or 1, or balanced, that is,
it returns 0 or 1 in half of its arguments [7]. The solution
to this problem within the framework of the standard
a pproach is performed by a regular loop in the Python
program ming language:
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Now we illustrate the solution to this problem in
the framework of quantum computing. In most cases,
quantum algorithms include:
1. Initialization of the quantum register.
2. A set of u nitary transformations over it. 3.
Measurement of the result.
First, we implement the emulation of elements
com mon to most algorithms (these are the registers of
a quantum computer) and the final measurement of the
result:



A quantum register of n qubits wi ll be described
by an n – dimensional Hilbert space , and will have n
basis states. Based on this space, w e implement a
function to implement the computing part [8]:
Thus, we got a modular emulator of quantum
computing, which, thanks to its modularity, allo ws you
to rebuild software for narrowly targeted tasks.
We can conclude that the solution to this proble m
by the quantum method turned out to be more
voluminous, since emulation always consumes more
computer resources, and if the solution to this problem
was performed on a real quantum computer, we would
get a significant gain in speed and volume [9].
Conclu sion
The state of modern high -precision technologies
and technologies of high –purity materials already now
allow experimentally creating the simplest v ersions of
quantum computers. The creation of multi –qubit
samples is still in the distant future.
To over come the existing difficulties in the
physical implementation of a quantum supercomputer,
it will be necessary to use technological and circuitry
achie vements of modern micro - and nanoelectronics, as
well as mathematical modeling of quantum physical
proces ses, and, in particular, decoherence processes in
multi –qubit quantum systems. The advent of full
–fledged quantum computers will
give a powerful impetu s not only to the development of
computer technology, but also to the technology of
information transfer, the organization of fundamentally
new communication systems, such as the quantum
Internet, information security issues and may turn out to
be the begi nning of the development of n ew, as yet
unknown, fields of science and technology.
The exceptional capabi lities of quantum
supercomputers will undoubtedly contribute to a deeper
understanding of the physical laws of the quantum world.
Technologies that yes terday seemed like science fi ction
can become commonplace for humanity.
Literature
Dushkin R.V. Quantum Computing and
Functional Programming M.: DMK Press, 2014.318 s.
Valiev K.A., Kokin A.A. Quantum computers:
hopes and reality. Izhevsk: RHD, 2014.320 s.
Vakhniy T.V., Guts A.K. Physical foundations
and problems of the technical implementation of a
quantum c omputer // Mathematical Structures and
Modeling. 2011. No.22. S. 38 - 47.
Nielsen M., Chuang I. Quantum computing and
quantum information. Cambridge: Cambridge
University Press, 2010. 704 p.
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Guts A.K. Fundamentals of quantum cybernetics:
Textbook. allowanc e. Omsk: KAN, 2008.204 s.
6. Kitaev A., Shen. Ah, Sluggish M. Classical and
quantum computing. M.: ICMMO, Chero, 1999, 192 p.
Kuznetsov K.K. Simulation of the relationship of
the initiators of high -tech innovations // Engineering
Bulletin of the Don, 2009, No. 1 URL:
ivdon.ru/magazine/archive/n1y2009/250/. Kosyakov M.S. Introduction to distributed
computing. St. Petersburg: NIUITMO, 2014.155 s .
Markov I .L., Saeedi M., Constant – optimized
quantum circuits for modular multiplication and
exponentiation, Quan tum Information and
Computation, 2012, vol. 12, no 5, p. 361 – 394.

БАРИОННАЯ СОСТАВЛЯЮЩ АЯ ЭНТРОПИИ ВСЕЛЕННОЙ И ВТОРОЕ НАЧАЛО
ТЕРМОДИНАМИКИ

Кошман Валентин Семенович
канд. техн. наук, доцент
Пермский государственный аграрно -технологический университет
г. Пермь, Россия


THE BARYON COMPONENT OF THE UNIVERSE ENT ROPY AND THE SECOND LAW OF
THERMODYNAMICS

Valentin Koshman
Cand. tech. sciences, associate Professor,
Perm state Agrarian and Technological University,
Perm , Russia

Аннотация. Рассматриваетс я модель горячей Вселенной, которая расширяется с охлаждением. В
предлагаемой модели Вселенной в качестве параметров её состояния рассматриваются безразмерные
планковские величины, характер зависимости между которыми устанавливается законами физики. С
опор ой на закон излучения Стефана - Больцмана получена формула для фотонной составляющей энтропии
Вселенной. Получены две фо рмулы для энтропии барионного га за Вселенной. В согласие со вторым
законом термодинамики, следуя полученным формулами для составляющих э нтропии Вселенной,
показано, что на планковское мгновение времени материя Вселенной была низкоэнтропийной, а
следователь но, и высокоорганизованной. Прив едены аргументы в пользу возможности ядерного взрыва
на планковский момент времени.
Abstract. We conside r a model of a hot Universe that expands with cooling. In the proposed model of the
universe, dimensionless Planck quantities are considered as paramete rs of Its state. the nature of the dependence
between them is determined by the laws of physi cs. Based on the Stefan - Boltzmann radiation law, a formula for
the photon component of the entropy of the Universe is obtained. Two formulas for the entropy of t he baryon gas
of the Universe are obtained. In accordance with the second law of thermodynami cs, following the formulas
obtained for the components of the entropy of the Universe, it is shown that at the Planck instant of time, the matter
of the Universe w as low-entropic, and therefore highly organized. Arguments are given in favor of the possibil ity
of a nu clear explosion at the Planck time.
Ключевые слова: модель расширяющейся Вселенной, реликтовое излучение, планковские
величины, формула Больцмана, зако н Стефана – Больцмана, энтропия фотонного излучения, энтропия
барионного газа, второе начало термодинамики, первичный ядерный взрыв.
Key words: model of the expanding Universe, relic radiation, Planck values, Boltzmann formula, Stefan –
Boltzmann law, entr opy of photon radiation, entropy of baryon gas, second beginning of thermodynamics, primary
n uclear expl osion.
« Если кто – то скажет вам, что выстраданная вами теория устройства Вселенной противоречит
уравнениям Максвелла, - то можно ответить,
что тем хуж е для уравнений Максвелла. Если окажется, что она не
согласуется с результатами наблюдений, - ну что ж, и экспериментаторы
могут ошибаться. Но если ваша теория окажется в противоречии
со Вторым законом термодинамики, то я не могу оставить вам
никакой н адежды, и вашей теории придется признать
свое полное поражение »
Артур Эддингтон

Предсказан ные теоретически движение звёзд
как бы от центра к периферии и остаточное
фотонное излучение подтверждаются многочисленными наблюдениями с поверхности
Земли и с бо рта космических аппаратов.
Следовательно, в первом приближении мы можем
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