Prospects of Quantum Informatics and the Study of Its Basics in the

School Course

Liudmyla V. Lehka

1 a

, Andrii O. Bielinskyi

1 b

, Svitlana V. Shokaliuk

1 c

, Vladimir N. Soloviev

1 d

Pavlo V. Merzlykin

1 e

and Yelyzaveta Yu. Bohunenko

Kryvyi Rih State Pedagogical University, 54 Gagarin Ave., Kryvyi Rih, 50086, Ukraine

Keywords:

Quantum Calculations, Quantum Computer, Quantum Circuit, Quantum Algorithm, IBM Quantum Experi-

ence, Python, Jupyter Notebook.

Abstract:

The purpose of this study is to review the main points of the experimental content of the basics of quantum

computer science adapted for lyceum students, based on the prospects of the quantum approach to information

processing for ultra-fast calculations in modeling objects of complex dynamical systems. In addition, software

tools and Internet services are offered to organize effective training.

1 INTRODUCTION

According to experts, the modern IT market is in

the initial state of another technological breakthrough

due to integration (interpenetration, convergence) of

1) nanotechnologies (the ability to control matter at

the atomic level), 2) biotechnologies (the ability to

manipulate genes and genetic information), 3) infor-

mation technologies (the use of communication and

communication tools) and 4) cognitive technologies

(the study of the fundamental essence of thought pro-

cesses and their mechanisms) (Sigov et al., 2019).

The capabilities of modern supercomputers

(“computers of classical architecture”, “classical

computer”) are no longer enough for efﬁcient pro-

cessing of large amounts of data during modeling of

nanoobjects, biogenetic systems, cognitive processes,

and other phenomena. It is felt that the development

of transistor computers has almost reached its limit

and that Moore’s Law, which consists in doubling the

computer power every one and a half to two years,

will soon cease to hold since the size of transistors

will stop decreasing every 18 months (Rotman, 2020;

Fog, 2015; Al-Kilani and Umkeeva, 2016). A quan-

tum approach has a signiﬁcant potential for data pro-

https://orcid.org/0000-0001-5768-5475

https://orcid.org/0000-0002-2821-2895

https://orcid.org/0000-0003-3774-1729

https://orcid.org/0000-0002-4945-202X

https://orcid.org/0000-0002-0752-411X

cessing (information), for increasing the productivity

of cumbersome and secure calculations, for reliable

storage of their results in scientiﬁc ﬁelds, in logistics,

safe trade, and ﬁnance, i.e. new computer science –

quantum information science, or quantum informat-

ics.

Quantum informatics (as a new branch of science,

the subject of which is the theory and practice of

using quantum objects for transmission and proces-

sion of quantum information), in addition to quan-

tum information theory and quantum algorithms, in-

cludes physics and mathematics of quantum comput-

ers, problems of decoherence description, measure-

ment problems, issues of quantum cryptography, sim-

ulation modeling of quantum systems, quantum intel-

ligence, etc.

Leading IT companies, in particular, IBM (since

2016), Intel (since 2017), and Microsoft offer free ac-

cess to experimental models of next-generation com-

puters as an Internet service (IBM, 2021; Microsoft,

2021; Amazon, 2021) to all interested parties. How-

ever, school computer science course, which is up-

dated every 3–5 years, does not address at all either

the general principles of functioning of quantum com-

puters and the peculiarities of their management or

the fundamental principles of quantum computer sci-

ence.

Taking into account the prospects of quantum

modeling of complex systems of various nature,

particularly cryptographic, chemical, and economic

(Ackerman, 2021; YouTube, 2020, 2019), we con-

Lehka, L., Bielinskyi, A., Shokaliuk, S., Soloviev, V., Merzlykin, P. and Bohunenko, Y.

Prospects of Quantum Informatics and the Study of Its Basics in the School Course.

DOI: 10.5220/0010922900003364

In Proceedings of the 1st Symposium on Advances in Educational Technology (AET 2020) - Volume 1, pages 233-240

ISBN: 978-989-758-558-6

233

sider it appropriate and possible to generalize, sys-

tematize, and adapt the basics of quantum informatics

for mastering it by lyceum students.

2 RESULTS AND DISCUSSION

The study of the basics of quantum informatics

and programming is proposed to be organized either

within the framework of a new (experimental) sample

module of the same name – “Fundamentals of Quan-

tum Informatics and Programming” – a standard-level

program for pupils of 10-11th grades, or, in an ex-

tended version, within the framework of the same

elective course, the amount of study hours is 17 and

35, respectively.

The purpose of teaching the sample module (elec-

tive course) “Fundamentals of Quantum Informatics

and Programming” (table 1) there should be the devel-

opment of the components of computer literacy and

information culture of lyceum students through the

acquisition of basic theoretical knowledge and practi-

cal skills to manage quantum computers as new gen-

eration computers.

To achieve this goal (according to the content pre-

sented in table 1), it is planned to solve the following

tasks:

• to form the concepts of “quantum computer”,

“qubit”, “quantum superposition”, “quantum

logic gate”, “quantum algorithm”, “quantum cir-

cuit”, “quantum entanglement”, “quantum pro-

gramming language”, etc.;

• to acquaint with the history of formation, the cur-

rent state, and development prospects of quantum

informatics;

• to introduce physical and mathematical founda-

tions of quantum computing;

• to study the potential and determine the advan-

tages of quantum computers for solving individual

applied problems, modeling problems of complex

systems of various nature, etc.;

• teach the pupils to implement basic quantum algo-

rithms in special and universal environments with

remote and local access.

The expected results of mastering the educational

material of the ﬁrst three lessons – “Digital technolo-

gies: history of formation, current state, development

prospects”, “Basics of classical computer arithmetic”,

and “Basics of classical computer logic” are as fol-

lows:

• student explains the concepts of digital technolo-

gies, classical computers, processor and mem-

ory of a classic computer; number system, num-

ber system alphabet, basis of the positional num-

ber system; binary message code, length of bi-

nary message code, units of measurement for the

length of binary message code;

• student knows the quantum computer deﬁnition,

general principles of its structure and functioning,

and the peculiarities of its using;

• student understands the typical architecture of a

classic computer and the general principles of its

operation;

• student names the units of measurement of the

length of the binary message code (bits, bytes,

kilobytes, megabytes, gigabytes, terabytes);

• student describes the general principles of opera-

tion of the processor and internal storage devices;

• student is able to convert natural numbers from

decimal to binary and vice versa; determine the

length of the binary message code; arithmetic ad-

dition and multiplication of binary numbers; log-

ical operations not, and, or, xor over binary num-

bers;

• student is aware of the role of existing (classical)

digital technologies and the signiﬁcance of their

development prospects.

In particular, a quantum computer should be un-

derstood as a computing device which CPU is based

on the logic of quantum mechanics. Such a com-

puter is fundamentally different from a classical com-

puter (a computer of the von Neumann architecture)

and uses for calculations not classical algorithms of

the macrocosm, but algorithms of phenomena of the

microcosm of quantum nature, based on quantum

parallelism and quantum entanglement (connectivity)

(Bernhardt, 2019).

The expected results of mastering the learning ma-

terial of the next three lessons of the module – “Com-

plex numbers fundamentals”, “Working with objects

of linear algebra: vectors”, and “Working with objects

of linear algebra: matrices” should be as follows: stu-

dent

• student explains the concept of a complex num-

ber; vector, row vector (bra vector), column vec-

tor (ket vector), orthonormal basis, standard ba-

sis, linear combination (superposition) of vectors;

matrix, square matrix, unit matrix, orthogonal ma-

trix, unitary matrix;

• student knows about the Euclidean and Hilbert

spaces;

• student is able to determine the real and imagi-

nary part of a complex number written in alge-

AET 2020 - Symposium on Advances in Educational Technology

234

Table 1: “Fundamentals of Quantum Informatics and Programming”: draft content of the sample module (17 hours).

No Topics

1 Digital technologies: history of formation, current state, prospects of development

2 Basics of classical computer arithmetic

3 Basics of classical computer logic

4 Complex numbers fundamentals

5 Working with linear algebra objects: vectors

6 Working with linear algebra objects: matrices

7 Key concepts of quantum computing

8 Quantum circuits and their design environments

9 Quantum NOT gate

10 Hadamard quantum gate

11 Quantum CNOT gate

12 Quantum Toffoli and Fredkin gates

13 Basic quantum algorithms and peculiarities of their implementation using a programming language

14 Quantum teleportation algorithm

15 Deutsch–Jozsa algorithm

16 Shor’s algorithm

17 Grover’s algorithm

braic form; perform operations on vectors (addi-

tion, scalar, and tensor multiplication, determina-

tion of coordinates in a new basis) and matrices

(transposition, multiplication by a number, matrix

multiplication, inversion);

• student understands the role of vector-matrix ap-

paratus in quantum informatics.

After propaedeutics of the basics of quantum pro-

gramming, it is the turn of the ﬁrst main section –

“Fundamentals of quantum computing using algo-

rithms implemented in circuits”. For 6 lessons stu-

dents should get the following abilities:

• explain the concept of a qubit, spin, qubit state,

quantum superposition, qubit measurement, qubit

entanglement, quantum algorithm, quantum cir-

cuit quantum gate, purpose and content of basic

quantum gates (NOT, Hadamard, CNOT, Toffoli,

Fredkin);

• distinguish between reversible and irreversible

operations;

• establish a correspondence between the matrix

operator and the quantum gate designation in

quantum circuits;

• be able to build basic quantum circuits in a special

environment, use the necessary quantum gates

and interpret the obtained results.

In the ﬁrst lesson of the section, students should

learn that the basis of quantum computing is a qubit

(quantum bit). To explain the concept of “qubit”, it

is necessary to use the method of analogy (with the

classical bit) and the ideas of quantum mechanics.

The teacher states that quantum particles have cer-

tain characteristics that can be used to describe their

behavior and that can be determined in practice (and

therefore implemented in quantum computers). In

particular, photons have a polarization, which is de-

termined by the behavior of the vector of their elec-

tric ﬁeld; some microparticles have their own mag-

netic moment (spin), the projections of which on the

direction of the outer magnetic layer are found exper-

imentally (Bernhardt, 2019). The teacher recalls that

the concept of bit is used in traditional calculations.

It is based on the fact that technically only two states

can be realized: 0 and 1 – for example, the current

ﬂows or does not ﬂow (that is, there is a charge or

there is no charge) (ﬁgure 1).

Figure 1: Qubit representation.

Talking about qubits, the teacher focuses students’

attention on the fact that a qubit may have not only

two states (for example, the spin of a quantum parti-

cle is located in the direction of the external ﬁeld – 0

or against – 1), but also their superposition, due to the

quantum nature of the phenomena of a microcosm.

The superposition of the qubit states is represented

graphically as a coordinate grid on a sphere, where

Prospects of Quantum Informatics and the Study of Its Basics in the School Course

235

each node corresponds to a certain state (see the cen-

tral part of ﬁgure 1).

If the base states of the qubit are denoted as

(ket vector with coordinates (1, 0), which describes

the spin direction of the quantum particle against the

external ﬁeld) and

(ket vector with coordinates

(0, 1), which describes the spin direction of a quan-

tum particle along an external ﬁeld), then any other

state from the set of possible states will be determined

by the relation (linear combination, superposition):

+ β

where α and β are complex numbers that satisfy the

relation

= 1;

and

represent prob-

ability amplitudes of transition to the states

and

Qubits can be connected (entangled) with each

other. This means that a connection can be estab-

lished between them, as a result of which each time

changing the state of one of several qubits, the rest

change in accordance with it, and the set of entan-

gled qubits is interpreted as a ﬁlled quantum regis-

ter. Like a single qubit, the quantum register is much

more complex than the classical bit register. It is able

not only to be in all possible combinations of its con-

stituent bits but also to implement subtle relationships

between them, which signiﬁcantly increases the com-

putational power of systems based on qubits.

In the state of entanglement and superposition,

qubits represent a quantum register. During calcula-

tions in the quantum register, the amplitudes of qubits

(

and

) are arranged in such a way that pos-

itive values of the amplitude of one qubit neutralize

the negative amplitudes of another qubit, and com-

putational errors are canceled (positive amplitudes of

qubits, on the contrary, amplify each other). This

is how the scenario of getting the correct answer is

formed.

Explaining the differences in the principles of

classical and quantum computers, teachers turn to the

problem of ﬁnding a way out of the maze, using the

example of which they illustrate and convince that the

classical computer consistently goes through all ways,

hitting a dead end once at once, but the quantum com-

puter can check all possible variants at once (Sigov

et al., 2019). Next, teachers focus attention and inter-

est, especially of bright and inquisitive students, on

the fact that the main engineering complexity of the

implementation of quantum processor registers is to

maintain the state of superposition and entanglement

of qubits during calculations (measurements) – coher-

ence time.

The calculations in a quantum computer are per-

formed using quantum algorithms. It is proposed to

be understood as an algorithm containing a ﬁnite se-

quence of unitary (reversible) operations/gates with

an indication of the qubits on which they need to be

performed. The correctness of the calculation result

using the corresponding quantum algorithm is deter-

mined with a certain probability. To increase the prob-

ability of getting a correct outcome in quantum algo-

rithms, the multiplicity of operations is especially in-

creased, which are selected in such a way that incor-

rect results are mutually destroyed with a high proba-

bility, and the probability of a correct result increases.

The last section – “Basic quantum algorithms and

their implementation on circuits and using a program-

ming language” – is the second main section of the

sample module, because the expected results of mas-

tering it that the student:

• knows the particularities of the implementation of

quantum algorithms in an environment with re-

mote access and a local one; the basics of the

syntax of quantum algorithm implementation by

a general-purpose programming language;

• understands the basic concepts of quantum algo-

rithms;

• explains the step-by-step structure of basic quan-

tum algorithms;

• uses the capabilities of remote and/or local access

environment to implement quantum algorithms in

the form of circuits and programs;

• implements and executes basic quantum algo-

rithms in a special environment using a general-

purpose programming language and the graphical

editor;

• is aware of the effectiveness of quantum comput-

ing in comparison with classical ones;

• evaluates the compliance of the results of the pro-

gram with the task at hand;

• follows the rules for writing readable code and

comments to it, explains the code to others;

• checks, hypothesizes, critically evaluates, identi-

ﬁes the shortcomings of the implemented algo-

rithms.

Problems that can be solved with the help of quan-

tum computers can also be solved on the computa-

tional basis of classical computers. However, the ad-

vantage of quantum computers, or more precisely,

quantum algorithms (Zahorodko et al., 2021), is to re-

duce the time spent on solving the problem by par-

allelizing operations through the generation of en-

tangled quantum states and their further use. Such

cases are called quantum acceleration. The applica-

tion of quantum acceleration is the most advantageous

AET 2020 - Symposium on Advances in Educational Technology

236

when solving problems of modeling complex dynam-

ical systems, mathematical search problems, in a par-

ticular search.

The main advantages of quantum computers and

algorithms in comparison with classical ones are the

effective solution of quantum cryptography problems

and problems of simulation modeling of quantum sys-

tems.

To master the training material of the mod-

ule/course, in particular, to acquire practical skills in

the ﬁeld of quantum computing, students are offered

to work with universal and special software and Inter-

net services:

1) for building the quantum circuit using drag-and-

drop technology in remote mode – Circuit Com-

poser from IBM Quantum Experience Lab (ﬁg-

ure 2, (IBM, 2021));

2) to master the mathematical foundations of quan-

tum calculations and the implementation of basic

quantum algorithms in the local mode of Ana-

conda Navigator environment – the manager of

packages and programming environments (ﬁg-

ure 3);

3) for studying the mathematical foundations of

quantum calculations and the implementation of

basic quantum algorithms remotely using Collab-

orative Calculation and Data Science cloud-based

educational and scientiﬁc natural information en-

vironment (CoCalc).

CoCalc (ﬁgure 4, (CoCalc, 2021)) is an entire

computer lab in the cloud where:

• each student works 100% online – in their own,

isolated workspace;

• you can follow the progress of each student in

real-time;

• at any time you can jump into a ﬁle of a student,

right where they are working;

• you can use TimeTravel to see each step a student

took to get a solution;

• integrated chat rooms allow you to guide students

directly where they work or discuss collected ﬁles

with your teaching assistants;

• the project’s activity log records exactly when and

by whom a ﬁle was accessed.

The author’s team is developing a set of educa-

tional and methodical materials, which includes:

• educational and methodical manual;

• collection of educational presentations;

• collection of educational video podcasts;

• electronic workbook;

• bank of test tasks.

After ﬁnishing the development of a set of educa-

tional materials adapted for students, it will be possi-

ble to move on to a large-scale experiment on study-

ing the basics of quantum informatics and program-

ming by the lyceum students.

A survey was conducted among computer science

teachers of general secondary education institutions

to study the expediency and readiness of teachers to

teach the course “Fundamentals of Quantum Infor-

matics and Programming” for lyceum students. 26

teachers of Computer Science, Chemistry, Technol-

ogy, and Mathematics took part in the survey, the vast

majority of them live in a city of regional subordina-

tion. The age of teachers who answered the questions

was as follows: 7.7% – 25–35 years; 30.8% – 25–

35 years, 42.3% – 35–45 years, 15% – 45–55 years;

3.8% – over 55 years.

100% of respondents supported the statement

that secondary education should provide up-to-date

knowledge and take into account modern achieve-

ments of the industry when studying the discipline.

All respondents indicated that they use cloud tech-

nologies when teaching their subject (65.4% – al-

ways, 34.6% – during distance learning).

Only one survey participant disagreed with the

fact that the training material can and should be

adapted according to age.

96.2% of teachers indicated that they are happy to

accept the introduction of new sections and topics in

the curriculum of the discipline, especially if there is

sufﬁcient and high-quality methodological support.

Responses from respondent teachers indicate that

88.5% of those who took part in the survey expressed

the opinion that they would like to personally take the

course “Fundamentals of Quantum Informatics and

Programming”, and 38.5% of them said that they had

met many publications on this topic and were inter-

ested. 61.6% of teachers said that you would offer

a course “Fundamentals of Quantum Informatics and

Programming” for applicants for education in your

institution. 23.1% refused because, in their opinion,

this course would not correspond to the proﬁle of the

educational institution where they work. Only 3.8%

answered “no”. The survey shows that teachers fol-

low new trends in the development of the industry and

are ready to teach students in their institution modern

and relevant courses. Regarding the study of “Funda-

mentals of Quantum Informatics and Programming”

in lyceums, the interviewed teachers expressed their

support for the implementation of this course if there

is an appropriate course for teachers and methodolog-

ical support.

Prospects of Quantum Informatics and the Study of Its Basics in the School Course

237

Figure 2: Page with quantum circuit composer from IBM Quantum Experience.

Figure 3: Jupyter notebook page in local access.

AET 2020 - Symposium on Advances in Educational Technology

238

Figure 4: Jupyter notebook page in the CoCalc cloud environment.

3 CONCLUSIONS

1. The new branch of computer science – quantum

computer science – has signiﬁcant potential for in-

creasing the productivity of cumbersome and se-

cure computing, for reliable storage of their re-

sults in scientiﬁc ﬁelds, in the spheres of logistics,

safe trade, and ﬁnance.

2. It is proposed to start studying the basics quantum

computer science and programming in the school

computer science course (obligatory-selective for

students of grades 10-11) within the framework of

a new (experimental) module (17 hours) accord-

ing to the lyceum curriculum of the standard level

or an elective course (35 hours) of the proﬁle level

curriculum.

3. For effective studying of the training material, stu-

dents are offered to work with universal and spe-

cial software and Internet-services – IBM Quan-

tum Experience, Jupyter Notebook using Python

programming language (in remote or local ac-

cess).

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