# 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

30 American Scientific Journal № (34) / 20 20

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.

ASJ (2) / 2020

American Scientifi c Journal № ( 34) / 2 0 20 31

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 ? áØ7- áØ 7. å á,Jà ?5 Jà ?6 å J 4

5

á

,@ 4

çá

?

áØ 7- áØ 7. åá,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.

ASJ (2) / 2020

32 American Scientific Journal № (34) / 20 20

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

ASJ (2) / 2020

American Scientifi c Journal № ( 34) / 2 0 20 33

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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34 American Scientific Journal № (34) / 20 20

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

ASJ (2) / 2020

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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American Scientifi c Journal № ( 34) / 2 0 20 31

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 ? áØ7- áØ 7. å á,Jà ?5 Jà ?6 å J 4

5

á

,@ 4

çá

?

áØ 7- áØ 7. åá,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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32 American Scientific Journal № (34) / 20 20

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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American Scientifi c Journal № ( 34) / 2 0 20 33

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

ASJ (2) / 2020