Quantum Transformation of School Informatics

Serhiy O. Semerikov

1,2,3 a

, Svitlana V. Shokaliuk

1 b

, Liudmyla V. Lehka

1 c

Pavlo V. Merzlikin

1 d

and Olena Yu. Tarasova

1 e

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

Kryvyi Rih National University, 11 Vitalii Matusevych Str., Kryvyi Rih, 50027, Ukraine

Institute for Digitalisation of Education of the National Academy of Educational Sciences of Ukraine,

9 M. Berlynskoho Str., Kyiv, 04060, Ukraine

Keywords:

Methods of Teaching Informatics, General Secondary Education, Methods of Teaching Lyceums Students,

Quantum Technologies, Quantum Informatics, Competencies in the Basics of Quantum Informatics.

Abstract:

The study’s objective was to theoretically examine, create, and experimentally test various approaches for in-

structing lyceum students in the fundamentals of quantum informatics. The following was accomplished as a

result of the research assignments: 1) The sources on the issue of teaching quantum informatics in Ukraine and

abroad were examined; 2) The structure and content of the competences in the basics of quantum informatics

for the lyceum students were theoretically grounded and developed (the results of the expert survey and the

European competence framework in the ﬁeld of quantum technologies were taken into consideration); 3) the

structural and functional model for forming the competences in the basics of quantum informatics were devel-

oped; 4) in the optional course of the same name, it was proposed a methodological framework for teaching

the fundamentals of quantum informatics to lyceum students; and 5) it was also experimentally tested to see

how well the developed methodology worked in developing the students’ competency in the fundamentals of

quantum informatics. Further scientiﬁc investigations into the quantum transformation of the school’s infor-

matics are also described.

1 INTRODUCTION

The changes that took place in the methodology of

teaching informatics in schools were caused by the

development of information technology and changes

in society as a result of their inﬂuence (Semerikov

et al., 2021). The latter led to the fact that school

informatics together with foreign language became

available at all levels of school education – from pri-

mary school to vocational training at the lyceum. In-

formatics tools are an integrator for all school sub-

jects, and its methods are the basis for the integra-

tion of natural sciences, mathematics and technol-

ogy. This creates a deep understanding of the ser-

vice, subordinate and second-row role of informatics

in the system of school education. The fundamental-

ization of teaching content informatics, in particular –

https://orcid.org/0000-0003-0789-0272

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

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

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

https://orcid.org/0000-0002-6001-5672

through a quantum transformation of basic knowledge

about information processes and systems, hardware

and software, networks, algorithms and programs will

help to get rid of it.

According to the analytical report of the National

Institute for Strategic Studies (NISS, 2020), Ukraine

is on the sidelines of the development of break-

through technologies, in particular quantum technolo-

gies, which is due, ﬁrstly, due to insufﬁcient state bud-

get ﬁnancing of scientiﬁc research on the whole, and

secondly, due to the signiﬁcant inadequacy of pro-

fessional and qualiﬁcation workforce to market de-

mands. At the same time, European job search sites

have hundreds of job postings for “quantum software

engineer” and “quantum programmer”.

The analysis of the experience of teaching infor-

matics in Ukraine and the resources on the problems

of research allowed us to identify the contradictions:

• between the importance of quantum informat-

ics for increasing competitiveness and successful

self-fulﬁllment of graduates of lyceums in the la-

bor market (in particular, in the ﬁeld of informa-

220

Semerikov, S., Shokaliuk, S., Lehka, L., Merzlikin, P. and Tarasova, O.

Quantum Transformation of School Informatics.

DOI: 10.5220/0012063200003431

In Proceedings of the 2nd Myroslav I. Zhaldak Symposium on Advances in Educational Technology (AET 2021), pages 220-235

ISBN: 978-989-758-662-0

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

tion technology) and the lack of adequate training

materials in Ukrainian language;

• between the importance of practical experience

with quantum computers and the difﬁculty of di-

rect access to them;

• between the need to form competences in the ba-

sis of quantum informatics in the lyceums and un-

development of the appropriate methods.

The need to solve the above-mentioned contradic-

tions led to the deﬁnition of the study’s aim and for-

mulation of its hypothesis. The aim of the study was

to theoretically analyze, develop and experimentally

test the methods of teaching the basics of quantum in-

formatics to lyceums students. It has been suggested

that the formation of competencies on the basics of

quantum informatics to lyceums students at a high

level is possible by changing some components of the

methodological system of teaching computer science:

content and teaching tools.

2 THEORETICAL

FOUNDATIONS OF TEACHING

THE BASICS OF QUANTUM

INFORMATICS TO LYCEUMS

STUDENTS

2.1 Quantum Informatics as a

Perspective Field of Information

Technology Development

In August 2020, consulting company Gartner pub-

lished yet version of its Hype Cycle of advanced tech-

nologies that will have a signiﬁcant impact on soci-

ety and business in the next ﬁve to ten years. Based

on a review of 1,700 advanced technologies, Panetta

(Panetta, 2021) identiﬁes 5 new trends in their devel-

opment:

• Composite architectures;

• Algorithmic trust;

• Beyond silicon;

• Formative artiﬁcial intelligence (AI);

• Digital me.

The Beyond silicon description of the direction

says that Moore’s Law has run out of steam be-

cause it is almost impossible to create transistors

smaller than 1 nm. There are technical difﬁculties

in manufacturing, so there is a chance to develop

non-silicon technologies – carbon-based transistors

and quantum hardware, including quantum comput-

ers (Panetta, 2021).

At the time when classical computers continue to

develop (processors became multicore, co-processors

appeared to solve photo processing tasks, video cod-

ing, etc.) the pace of quantum technologies develop-

ment is gaining momentum and quantum computers

are becoming a reality. Appearance and development

of quantum equipment, in particular quantum com-

puters, has led to a new ﬁeld of informatics – quantum

informatics (Lehka and Shokaliuk, 2018).

One should understand that quantum computers

by no means supersede classical ones, but they are

indispensable for certain types of tasks – modeling

complex chemical reactions to develop drugs and sub-

stances with predetermined properties, modeling of

physical quantum systems inaccessible for conven-

tional calculations, quantum calculations of complex

mathematical tasks, quantum long-distance commu-

nication, etc. The solution of these problems is based

on already known quantum algorithms – algorithms

for function balancing (Deutsch-Jozsa and Bernstein-

Vazirani algorithms), algorithm for determining the

totality of functions (Simon’s algorithm), harmonic

analysis algorithms (the quantum Fourier transform

algorithm), cryptoanalysis algorithms (Grover’s and

Shor’s algorithms), quantum teleportation algorithm –

and new (still experimental) algorithms.

In many countries of the world the development of

quantum technologies is supported by legislation and

ﬁnanced by the government.

Thus, in the U.S., artiﬁcial intelligence and quan-

tum technologies have been identiﬁed as two strate-

gically important ﬁelds for the country’s economic

growth and national security. In 2018, the U.S. gov-

ernment approved legislation for the National Quan-

tum Initiative, which aims to ensure that the U.S.

remains a world leader in quantum informatics and

its technological applications. Funding for National

Quantum Initiative activities for the ﬁrst ﬁve years is

$1.2 billion (NQIA, 2018). Individual commercial re-

search is conducted at the expense of IBM, Microsoft,

Google, Intel and others.

In China, in 2016 the government approved the

National Science and Technology Innovation Plan un-

til 2030 (NSTI, 2016), and in 2017 the construction

of the National Quantum Informatics Laboratory was

launched with initial funding of 7 billion yuan (Chen,

2018). The Chinese tech giant Alibaba is making sig-

niﬁcant investments in its own quantum initiatives, in-

cluding the launch of a quantum calculator service via

a cloud platform (Alibaba, 2018).

Since October 2018, EU countries have launched

project program to support fundamental quantum re-

Quantum Transformation of School Informatics

221

search – “The European Quantum Flagship” (QFlag-

ship), with a minimum duration of 10 years and an ex-

pected budget of 1 billion billion euros (EQF, 2021).

In addition, to protect against cybersecurity threats,

in June 2019, 24 European states participated in the

signing of a declaration on the research, development

and deployment of quantum communication infras-

tructures (EDS, 2019).

The demand for specialists in the ﬁeld of quantum

technologies becomes urgent. The lack of quantum-

literate specialists hinders the development of the in-

dustry. For example, Hilton (Hilton, 2019), vice pres-

ident of D-Wave, argues that it is necessary to increase

the number of quantum-literate workers, invest in the

training of teenagers, identify capable young people,

develop them in the ﬁeld of quantum technologies and

create a talent pool of promising workers with knowl-

edge in the quantum ﬁeld.

2.2 Teaching Experience of Quantum

Informatics and Popularization of

Quantum Technologies in Ukraine

and the World

In Ukraine all educational programs on quantum in-

formatics were initiated only in universities within the

specialty 104 – Physics and Astronomy (Pinkevych

et al., 2018; NUL-bachelor, 2020; NUL-master,

2021), while in the world the training of correspond-

ing specialists is carried out by different specialties

(QTEdu, 2022).

The European Competence Framework for Quan-

tum Technologies, launched in 2021, provides for

training in quantum informatics, starting from pri-

mary school. Such education should be based on con-

ceptual and intuitive understanding of quantum infor-

matics key essences.

Today, both in Ukraine and abroad, mostly pro-

grams of non-formal education on individual topics of

quantum technologies are offered for students of gen-

eral secondary education institutions. Its are online

schools, master classes, summer camps for children,

etc.

Popular science resources about quantum tech-

nologies for Ukrainian students are offered by

Gnatenko (Gnatenko, 2020a,b). With these electronic

materials (after payment) students can get acquainted

with fundamental concepts of quantum mechanics –

quantum entanglement, quantum beat, quantum par-

allelism, quantum sensing, quantum entanglement,

quantum superposition, tunneling, quantum telepor-

tation, as well as examples of basic tasks of quantum

cryptography.

The Richelieu Lyceum, in cooperation with the

Odesa I. I. Mechnykov National University, of-

fers a series of lectures “Nanoelectronics: Science

and Modernity” (including lectures on quantum ef-

fects) (NSM, 2021), and “Quantum Mechanics” (QM,

2021).

Korshunova and Zavadsky (Korshunova and

Zavadsky, 2018) in their textbook on informatic for

5th grade (section “Information processes and sys-

tems”) gives an overview of quantum computers as a

technology of the future, pointing out the rapid devel-

opment of the quantum industry in the next ten years,

the use of quantum computers to solve certain types of

mathematical problems, emphasizing the use of quan-

tum computers together with conventional computers

(Korshunova and Zavadsky, 2018, p. 28-29).

Since August 2020, the White House Ofﬁce of

Science and Technology Policy and the National Sci-

ence Foundation have launched an innovative project,

the Q-12 National Education Partnership, which over

the next ten years will bring together industry and sci-

ence educator leaders for large-scale quantum tech-

nology education, ranging from providing classroom

tools for hands-on experience, developing educational

materials, and supporting students on their way to

professional careers in quantum technologies (Q12,

2023). Leading IT companies – IBM, Microsoft, D-

Wave, Google and others – offer joint courses with

universities, as well as educational resources for in-

formal education, based on the use of a cloud ac-

cess to quantum simulators and quantum comput-

ers, tools for creating and executing quantum circuits

and programs, language-independent and language-

independent development environments, etc. (QC-

IBM, 2021; Google, 2022; QDKit-Microsoft, 2023).

A variety of educational resources on quantum

technologies for primary and secondary school stu-

dents and all those interested are offered on the QT-

Edu community portal (QTEduCSA, 2021). The por-

tal is designed to develop an educational ecosystem

in support of the QFlagship project aimed at pop-

ularizing, informing and educating in the ﬁeld of

quantum technologies. The portal’s collection of re-

sources, structured by education level and target au-

dience, includes educational programs, hyperlinks to

external resources, quantum games, simulators, video

resources, etc., mostly in English, German and Polish

(Ukrainian and Russian resources are not available on

February, 2023).

Experience of European and world practice of

popularization of quantum technologies among high

school students is a good evidence of the possibility

of mastering the basics of quantum technologies, pro-

vided methodical adaptation of educational materials

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

222

to the speciﬁcs of the audience perceiving them.

2.3 The Competencies in the Basics of

Quantum Informatics to Lyceums

Students

The key idea of the competency-based approach is

to provide all interested individuals with a diagnostic

tool to measure the level of preparedness of an indi-

vidual to perform certain activities.

Review of the previous results of the world

projects for the selection and determination of the list

of competences in quantum technologies – World-

Skills International professional competitions (ﬁg-

ure 1 and 2), seminar “Key Concepts for Future Quan-

tum Information Science Learners” (NSF, 2020),

Competence Framework for Quantum Technologies

(ﬁgure 3) – made it possible to identify competen-

cies in the fundamentals of quantum information sci-

ence of lyceum students as a dynamic combination

of knowledge, skills, abilities, ways of thinking, and

attitudes, other personal qualities in the ﬁeld of quan-

tum technologies, which determine the ability of an

individual to successfully carry out further profes-

sional and/or educational activities using such tech-

nologies. Competences in quantum informatics ba-

sics of lyceum students include 8 groups of compe-

tences:

1) physical basics of quantum technologies (basic

concepts of quantum physics, cubic dynamics);

2) mathematical basics of quantum informatics (ba-

sics of linear algebra, mathematics of quantum

physics basics, basics of quantum measurement

statistics);

3) software technology (optical technology, labora-

tory technology, experimental control);

4) hardware for quantum computers and sensors

(spin-based devices, neutral atoms and ions, new

types of cubes, equipment for integration, manip-

ulation and counting of cubes, use of hardware

platforms for quantum computing);

5) quantum computing and modelling (quantum

gates, quantum languages, programming tools

and platforms, basic quantum algorithms, quan-

tum error correction, quantum modelling ele-

ments);

6) quantum sensors and metrology (atomic gauges,

sectors of quantum sensors application);

7) quantum communication (quantum cryptography,

quantum networks, quantum communication in-

frastructure and equipment);

8) practical skills and general competences (basics

of classical programming, application of quantum

technologies, general skills/competences).

Considering that quantum information technology

is an interdisciplinary branch of knowledge, the rele-

vant competencies cannot be deﬁned as part of digital

competencies.

3 METHODICAL FOUNDATIONS

OF TEACHING THE BASICS OF

QUANTUM INFORMATICS TO

LYCEUMS STUDENTS

3.1 Special Hardware and Software

Tools for Teaching the Basics of

Quantum Informatics

For the selection of special hardware and soft-

ware tools for teaching quantum informatics to

lyceums students we analyzed services from Mi-

crosoft, QuTech, Amazon and IBM (Lehka and

Shokaliuk, 2021; Lehka et al., 2022a,b).

The greatest number of criteria is satisﬁed with

IBM Quantum platform, which was turned into the

main instrumental tool for learning the basics of quan-

tum informatics for the course program.

Now IBM provides the greatest opportunities

for free use of quantum computers and simulators

through two services – IBM Quantum Composer and

IBM Quantum Lab.

The ﬁrst service – IBM Quantum Composer – the

simplest tool for working with quantum algorithms in

the form of quantum circuits.

The second service – IBM Quantum Lab – pro-

vides the possibility to implement quantum algo-

rithms in Python programming language using the

Qiskit library.

3.2 Pedagogical Reasonability and

Content of Teaching the Basics of

Quantum Informatics in Secondary

Schools

The model of the educational process (learning)

within a single educational unit, which reﬂects the or-

dering (elementary in time and space, in accordance

with the goals of education and training and taking

into account the reverse pedagogy) of the students

(those who learn) in terms of the content of training

Quantum Transformation of School Informatics

223

Figure 1: Key skills and roles of the 2020s and 2030s for WorldSkills (WS, 2020, p. 120).

and elements of the learning environment of a par-

ticular learning unit, students (those who are taught)

regarding the content of the teaching and elements of

the learning environment for a particular educational

unit is called a normative teaching methods (Bykov,

2008, p. 310).

The real teaching method is based on the norma-

tive one and differs from it. The real teaching meth-

ods take into account the characteristics of the exist-

ing educational environment and mirror the creative

aspect of the educational process participants (e.g.,

speciﬁcity of the educational environment of a par-

ticular educational institution, mastery of the teacher,

additional meaningful elements that he or she uses in

the lessons).

The normative teaching method of a certain edu-

cational unit (in our case – basics of quantum infor-

matics as a single subject, elective, integrated course,

etc.) can be presented in the form of a structural-

functional model – a model graphically depicts func-

tional peculiarities of structural elements of a certain

process (in our case – formation of competences in

quantum informatics basics).

The developed structural-functional model of

competence formation in the basics of quantum in-

formatics (Lehka, 2022, p. 82) includes 4 basic (sys-

tem) blocks – Purpose, Content, Technological and

Productive (ﬁgure 4) – and 3 additional blocks en-

suring the interaction of the model’s basic blocks:

general didactic principles of teaching quantum in-

formatics, hardware and software tools for teaching

quantum informatics and methodological approaches

(competence-based, systemic, integrative, personal

and activity-based).

Let us consider the aim and content blocks of the

model.

The aim block of the model includes components

(factors) that determine the pedagogical feasibility of

the educational unit in the educational process (local

or global). Factors of pedagogical feasibility of im-

plementation of quantum informatics basics in the ed-

ucational process of secondary general education in-

stitutions are:

• rapid development of quantum technologies;

• demand of the society for qualiﬁed quantum sci-

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

224

Figure 2: Forecast of the time of mass demand for skills from quantum technologies for WorldSkills (WS, 2020, p. 121).

entists;

• quantum computerization (availability of quan-

tum computers and other quantum equipment);

• free access to quantum computers;

• world experience in “quantum transformation” of

the school informatics;

• pre-professional training in quantum informatics.

To substantiate the feasibility of introducing the

basics of quantum informatics into educational pro-

grams of secondary general education institutions, To

ﬁnd out the state of awareness of teachers in the ﬁeld

of quantum technologies and readiness to teach an

elective course (or a course of their choice) to lyceum

students we have studied the opinion (conducted an

interview) of teachers of informatics in secondary

general education institutions. The survey involved

26 IT teachers who teach chemistry, labor and tech-

nology, and mathematics at the same time.

100% of respondents supported the opinion

that secondary education should provide up-to-date

knowledge and take into account the modern achieve-

ments of the industry when studying the disciplines.

All survey participants indicated that they use moder-

ate technologies when teaching their subject (65.4% –

always, 34.6% – only during distance learning).

96.2% of respondents agree that the educational

material (in particular, quantum informatics) should

be adapted according to the age of the students.

96.2% of the respondents indicated that they

would be pleased with the introduction of new sec-

tions and topics to the discipline curriculum, espe-

cially if sufﬁcient methodological support is avail-

able.

The responses of the respondents indicate that

88.5% would like to take the course “Fundamentals

of Quantum Informatics”, and 38.5% of them noted

that they have encountered a lot of publications on

this topic and were interested in it.

Quantum Transformation of School Informatics

225

Figure 3: General structure of Competence Framework for Quantum Technologies (Greinert and M

uller, 2021).

61.6% of respondents responded positively to the

question “Would you offer the course “Fundamentals

of Quantum Informatics” for students at your school?

23.1% refused because, in their opinion, this course

would not meet the proﬁle of the educational institu-

tion where they work. Only 3.8% said no.

The survey indicates that teachers follow new

trends in the ﬁeld and are ready to teach modern and

relevant courses in their institutions. As for the im-

plementation of the basics of quantum informatics for

lyceum students, the teachers expressed their support

for such implementation due to the presence of a cor-

responding course for teachers and methodological

support.

The content block of the model of competence for-

mation in the basics of quantum informatics as a cor-

responding normative teaching methodology reﬂects

the main content of competence formation in the ba-

sics of quantum informatics.

The content block of the model depicts the main

content of the competence formation in the funda-

mentals of quantum informatics:

• European framework of competences for quantum

technologies (see section 2.3);

• State educational standards;

• content of informatics curriculum;

• expert selection.

Analysis of the development of methodologi-

cal systems of teaching informatics (from 1985 and

up to now, with the consolidation of four stages)

showed that content of teaching school informatics

expanded from algorithms and programming through

the knowledge of information and information and

communication technologies to informatics as a basis

for STEM integration.

In order to clarify the content and recommenda-

tions for teaching the basics of quantum informatics

to lyceums students, to determine the importance of

the European framework of competencies for quan-

tum technologies, an interview was conducted among

those who are interested in the ﬁeld of quantum tech-

nologies. 36 respondents took part in the survey, some

of them combining several positions, such as univer-

sity teacher and researcher or university teacher and

school teacher.

The analysis of the evaluation results (taking into

account the competence level of the participant of

the expert survey – “have a basic idea” (1), “know

with some components” (2), “deeply know with some

components” (3), “expert” (4)) has allowed to specify

the content of teaching the basics of quantum infor-

matics of the lyceum students and the system of cor-

responding competences (which included, ﬁrst of all,

those components (knowledge and skills), calculated

parameters of which exceeded the speciﬁed threshold

value).

The ﬁrst group of competencies “Competencies

in the physical foundations of quantum technologies”

includes:

• knowledge of the basic understanding of quantum

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

226

Competency

-based, systemic, integrative, personal and activity

-based methodological approaches

Hardware, general and special software tools

for teaching quantum informatics

General didactic principles of teaching

quantum informatics

The aim: formation competences in the basics of quantum

informatics for lyceum students

The

aim block

The content block

The technology block

The result block

Rapid development of

quantum technologies

Society's need for qualified

specialists in the

quantum

field

Availability of quantum

computers and other

quantum equipment and

free cloud access to

quantum computers

World experience of

"quantum transformation"

of school

informatics

Quantum computerization

Pre-professional training in

computer science

The competence system in the basics of quantum informatics

for lyceum students

European

Competence

Framework for

Quantum

Technologies

State standard of

basic and complete

general education

Content of computer

science

education

Experts' choice

The means of forming

competencies in the basics of

quantum informatics of lyceum

students

The methods of teaching

computer science of

lyceum students

The forms of organizing

lyceum students' training

The means of assessing

learning progress

The means of diagnosing

the formation of competences

in the basics of quantum

informatics of lyceum students

The criteria of assessment, indicators,

levels of competence in the basics of

quantum informatics for lyceum

students

Figure 4: Structural-functional model of competence formation in the basics of quantum informatics.

Quantum Transformation of School Informatics

227

physics;

• skill to determine whether qubits are in binded

states;

• skill to represent qubits on a Bloch sphere.

The second group of competencies “Competen-

cies in mathematical foundations of quantum infor-

matics” includes:

• knowledge of the fundamentals of the theory of

complex numbers;

• knowledge of linear algebra fundamentals;

• knowledge of quantum physics mathematical fun-

damentals;

• knowledge of statistical nature of quantum mea-

surements;

• skill to design vectors (matrix-columns, matrix-

rows) of Dirac notation;

• skill to operate with standard bases;

• skill to arrange a vector in a selected basis;

• skill of giving examples of unitary matrices and

performing operations with them.

The third group of competencies “Competencies

in support technologies” includes:

• knowledge of optical technologies;

• knowledge of laboratory technologies;

• knowledge of experimental control;

• skill to separate photon sources.

The fourth group of competences “Competences

in hardware of quantum computers and sensors” in-

cludes:

• knowledge of the structure of spin-based devices

(in particular, quantum dots);

• knowledge of hardware platforms for quantum

computing, methods of their integration with stan-

dard equipment;

• skill to describe types of quantum structures of

quantum computers and explain their general

principles of operation;

• skill to arrange remote access to quantum comput-

ers;

• skill to perform quantum programs on quantum

computers.

The ﬁfth group of competences “Competences in

quantum calculations and modelling” includes:

• knowledge of quantum gates (single-, double- and

multi-qubits);

• knowledge of quantum programming languages,

tools for development of quantum software and

platforms (including graphical ones);

• knowledge of basic quantum algorithms (Shore,

Grover, quantum optimization, quantum phase

evaluation, quantum linear algebra, etc.);

• skill to record quantum gates by means of unitary

matrices;

• skill to separate and use single-cube gates (Pauli

transubstantiation, Adamar gate, phase tensions);

• skill to perform operations using multi-qubit gates

(CNOT, Toffoli and Fredkin gates);

• skill to use quantum gates for writing quantum al-

gorithms;

• skill to use quantum programming languages and

tools;

• skill to implement quantum algorithms (Shore,

Grover etc.);

• skill to work with quantum simulators.

The sixth group of competencies “Competencies

in quantum sensors and metrology” includes the fol-

lowing:

• knowledge of the quantum sensors applications;

• skill to guide examples of quantum sensors appli-

cation in various ﬁelds.

The seventh group of competencies “Competen-

cies in quantum communication” includes:

• knowledge of quantum cryptography (quantum

key distribution, secure authentication, digital sig-

natures, use halls);

• knowledge of quantum networks (quantum inter-

net, sensor and dinode networks);

• knowledge of quantum communications infras-

tructure and equipment (ﬁber optic systems, wire-

less links, satellite systems; quantum random

number generators; quantum memory, interfaces,

switches; repeaters, terminal nodes);

• skill to describe the operating principles and struc-

ture of quantum network equipment;

• skill to give examples of application of quantum

cryptography in various ﬁelds.

The eighth group of competences “Practical skills

and general competences” includes

• knowledge of classical (non-quantum) program-

ming basics: programming languages, algo-

rithms, complexity classes, cryptography;

• knowledge of quantum technologies application;

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

228

• skill to implement algorithms of basic complexity

classes (in particular, cryptographic algorithms)

using programming languages;

• skill to give examples of using quantum algo-

rithms to achieve quantum advantages.

3.3 Teaching Methodology the Basics of

Quantum Informatics to Lyceums

Students

Experimental realization of the structural-functional

model of forming competences on quantum informat-

ics basics is carried out within the optional course

“The Basics of Quantum Informatics” for students of

10 (11) grades. The course content is represented

by three subject content lines – “Physical and mathe-

matical foundations of quantum informatics”, “Quan-

tum computing, algorithms and programming” and

“Quantum telecommunication technologies”.

Content line “Physical and mathematical foun-

dations of quantum informatics” reveals fundamen-

tal physical and mathematical aspects of quantum

technique functioning, demonstrates physical realiza-

tion of microscience phenomena described mathemat-

ically.

The conceptual apparatus of the content line

“Physical and mathematical foundations of quantum

informatics” – quantum physics, quantum, photon,

superposition principle, quantum entanglement, tun-

neling, singularity principle, quantum teleportation,

chiral function, interference, diffraction coherence,

decoherence, quantum computer, qubit (quantum bit),

bracket notation, complex numbers, Bloch sphere.

Here are formulations of concepts, which should

be mastered by students in classes on fundamentals of

quantum informatics:

• Quantum physics (quantum mechanics) is a sci-

ence that studies laws of microcosm and describes

phenomena at microparticle level (molecules,

atoms, electrons, photons, etc.).

• A quantum is an indivisible microparticle, a por-

tion of some quantity (energy, light, etc.).

• Photon (quantum of light) is the elementary parti-

cle of which light consists.

• The principle of superposition consists in the abil-

ity of a microparticle to be in different states of the

same set of characteristics at the same time.

• Quantum entanglement – microcosm phe-

nomenon meaning dependence of microparticles

on each other regardless of distance between

them.

• Tunneling – ability of microparticles to pass

through a barrier. A microparticle can undercut

a barrier, “overcome” it or pass through it.

• The singularity principle was formulated by W.

Heisenberg and consists in the fact that it is im-

possible to measure simultaneously coordinates

and momentum of a microparticle with a certain

accuracy.

• Quantum teleportation is an ultra-fast (on aver-

age) transfer of states from one microparticle to

another. Quantum teleportation is not transporta-

tion or any other physical movement of a mi-

croparticle from one place to another.

• Quantum function (state vector) is a quantity,

which completely describes a state of a micropar-

ticle or quantum system as a whole. Quantum

function determines not physical parameters, but

approximate law of microparticle state distribu-

tion.

• Wave interference is a phenomenon that occurs

when two waves arising in the same medium

come in contact with each other.

• Diffraction – the ability of waves to ignore imper-

fections.

• Coherence – coherence of several colival or chiral

processes in time, which occurs when they over-

lap each other.

• Decoherence – incoherence of several colival or

chiral processes in time, which is found when they

are added to each other.

• Quantum computer – computing device, using

quantum superposition and quantum multiplicity

phenomena to transmit and process data.

• Qubit (quantum bit) is the most important element

for data storage in quantum computers. A qubit is

a quantum object with two basic structures, for ex-

ample: electron spin, photon, neutral atom or ion.

Mathematical model of a qubit state is a single

two-dimensional vector.

The competence in the basics of linear algebra in-

cludes understanding not only the concept of vectors

but also matrices, as well as the basic operations over

matrices (addition, matrix multiplication by number,

usual matrix multiplication, tensor matrix multiplica-

tion).

At this stage, students must understand that a vec-

tor can be represented algebraically – in the form of

a linear (vertical or horizontal) table of numbers or

geometrically – in the form of a tensed frame. Vec-

tor column, which represents the state of the cube, is

a certain table of numbers with one column and two

Quantum Transformation of School Informatics

229

rows. Further, it is worth explaining that there can be

several columns and rows of numbers. Such a table

of numbers arranged in rows and columns is a matrix.

The number of rows and columns determines the ma-

trix size. Vector columns or vector rows are separate

(partial) kinds of matrices.

The next step will be to familiarize students with

the actions on matrices. We draw students’ atten-

tion to the fact that matrix multiplication by a number

(scalar) is carried out by multiplying each element of

the matrix by the required number (scalar). Demon-

stration of the application of vector multiplication by

a number and matrix multiplication by a number.

Explanation of the operation of conventional

matrix-to-matrix multiplication begins with matrix-

to-vector multiplication, emphasizing that multiplica-

tion can be applied only to matrices in which the num-

ber of columns of the ﬁrst matrix and the rows of the

second matrix are identical. The result of multipli-

cation is a dimension matrix equal to the number of

rows of the ﬁrst matrix and the number of columns

of the second matrix. The elements of the result ma-

trix are the sum of pairwise additions of the elements

of the row of the ﬁrst matrix to the elements of the

corresponding column of the second matrix. To mul-

tiply a matrix by a vector, each matrix row should be

elementally multiplied by the value of the vector.

In the case of a matrix with three (or more) rows

and columns, the multiplication technique is analo-

gous.

It is advisable to offer students examples of square

matrices and vectors whose elements are exclusively

zeros and ones, both for manual (written) execution

and using the capabilities of a table processor (and/

or a universal computer mathematics system or pro-

gramming language) for self-multiplication.

Then students should explain that quantum com-

puting theory uses tensor multiplication of vectors

(matrices), which is used to multiply vectors (matri-

ces) of sufﬁcient size. Students must learn that for

tensor multiplication two steps are necessary:

1) scalar multiplication of each element of the ﬁrst

matrix by another matrix;

2) to combine the obtained matrices according to the

output positions of these elements.

At ﬁrst, students can ﬁnd examples of tensor mul-

tiplication of vectors. As a practical task, students

may be presented with the task of realizing ten-

sor multiplication with the help of a table processor

(or/and a universal system of computer mathematics

or programming language) for two and three vectors.

The following is an application of tensor multiplica-

tion of matrices.

Formation of competence in mathematical foun-

dations of quantum informatics is based on knowl-

edge of statistical nature of quantum measurements.

Microparticle structures described by the Quantum

function have a statistical, i.e., luminescent, nature:

the square of the absolute value (module) of the

Quantum function indicates the luminescence value

of those quantities, on which the Quantum function is

dependent.

Before starting to get acquainted with quantum

gates (actions that can be performed over cubes), it

is necessary to consider the notion of unitary ma-

trix (a special numerical square matrix, elements of

which are real or complex numbers, and the result of

their multiplication by the Hermite-conjugate matrix

is equal to the unity of matrix E), explaining the terms

used in the formula. Namely, the square matrix (ma-

trix in which the number of rows is equal to the num-

ber of columns), the Hermite-conjugate matrix (the

A+ matrix obtained from the A matrix by transposi-

tion and replacement of each element with a complex-

conjugate one), singular matrix (diagonal matrix, di-

agonal elements of which are equal to one), diagonal

matrix (square matrix, posterior diagonal elements of

which are equal to zero). The notion of unitary ma-

trix is suitable to show on two examples – in the ﬁrst

application, we will use matrix with real-integer ele-

ments, and in the second – matrix with complex nu-

merical elements.

Methods of teaching the content line “Physical

and mathematical foundations of quantum informat-

ics” can be revised, expanded with additional expla-

nations, or shortened, taking into account the training

of scientists in mathematics and physics.

Within the framework of the content line “Quan-

tum computing, algorithmization and programming”

the competences in hardware of quantum comput-

ers and sensors, quantum metrology, competences in

quantum computing and modeling are formed and/or

developed, ﬁrst of all, Formation of knowledge and

skills to distinguish and use quantum single- and

large-cube gates for recording quantum algorithms,

use platforms for implementation of quantum algo-

rithms in the form of schemes and programs on quan-

tum simulators and real quantum equipment.

It is advisable to start studying this content line by

looking at the structure of a quantum computer and

then move to the issue of providing special conditions

for their functioning:

• temperature control (close to absolute zero);

• insulation against magnetic, electric and thermal

ﬂuctuations, vibrations;

• air dissipation lower than the atmospheric pres-

sure by billions of times.

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

230

Further it is advisable to acquaint students with

hardware platforms for quantum computing, ways

to integrate them with the classical equipment us-

ing quantum simulators and computers of IBM, Mi-

crosoft, Google, Intel, QuTech and others.

We suggest that competence development in re-

mote access to quantum computers should be based

on the IBM Quantum platform, focusing on the

speciﬁcs of selecting a simulator or quantum com-

puter in graphical (IBM Quantum Composer) and

software (IBM Quantum Lab) modes.

The skill to perform quantum programs on quan-

tum computers should be formed starting with sim-

ple tasks on using quantum gates to change the

state of a quantum system. And then proceed to

implementation of quantum algorithms (Bernstein-

Vazirani, Deutsch-Jozsa, Grover, Shore).

When introducing the concept of “quantum gates”

(basic logical elements/operations for a quantum

computer), it is important to pay attention of students,

that the understanding of quantum gates is similar to

the understanding of gates (logical elements, opera-

tions) of a classical computer, and therefore it is nec-

essary to use the previous knowledge about logical

operations.

Students must learn that the same logical opera-

tions are performed on qubits in order to change their

state as on classic bits. It is necessary to consider

mathematical representation of each gate (in the form

of unitary matrix) and their graphical representation

and result of quantum scheme application at the same

time.

The interface of the IBM Quantum Composer

chromatically oriented service should be considered

in a mandatory order, focusing on the instrumental

panel of quantum operations, peculiarities of color

categorization of gates by type, adding, setting up

and disconnecting of quantum gates in the Quantum

Scheme Editor area, reviewing changes in the state of

qubits.

One should start from one-qubit quantum gates

as the simplest, and then go to two- and three-qubit

gates. At this stage, students’ attention is necessarily

focused on the result, which is reﬂected in the form

of the state vector. It is necessary to explain that the

received record of the state of qubits in the twofold

code is read from right to left. In our application, the

result obtained is 01: the zero qubit has a value of 1

and the ﬁrst one is 0. If there is time, we can ask the

students to use a few more cubes on the diagram one

after another to observe the display of the results.

After familiarization with basic operations on

qubits you can move on to introduction of quantum

algorithms, starting with quantum teleportation algo-

rithm. First students are offered a verbal description

of the algorithm, then a graphical quantum circuit,

and after that a software implementation of the algo-

rithm.

Let us give a verbal description of the quantum

teleportation algorithm, which is described graph-

ically using the IBM Quantum Composer service,

shown in ﬁgure 5:

1) by means of the operation NOT we transfer the

zero qubit to state 1, and we leave the ﬁrst and

second qubits in the primary zero state. It should

be noted that this operation is mandatory for this

example, only to avoid transferring the zero value

of the qubit. Indeed, the zero qubit

2) we put the ﬁrst qubit into superposition by the gate

3) we rotate the ﬁrst and second qubits with the

CNOT gates (the ﬁrst one is control and the sec-

ond one is purpose. If the control (ﬁrst) qubit is in

state 1, the main (second) qubit is inverted by the

CNOT gate);

4) we will similarly loop the zero and ﬁrst qubits;

5) convert the zero qubit to superposition (using gate

H);

6) measurement of the zero and the ﬁrst qubits (Mea-

surement operation). The measurement results are

stored in two classic bits, which are transmitted by

the usual (classic, non-quantum) way of commu-

nication (channel, protocol);

7) on the side where the zero qubit status is transmit-

ted, there is another qubit to which CX and CZ

gates are used (either CX or CZ in turn does not

matter which will be the ﬁrst), as a result we get

the value of zero qubit in the other qubit;

8) we measure the value of the other qubit.

After creating the algorithm for quantum telepor-

tation in IBM Quantum Composer, students should be

given the task of running this scheme with the help

of a simulator or a quantum computer and analyze

the results. At this point, it is appropriate to encour-

age students to focus on automatically generated code

in a programming language (e.g., Python). Students

should conclude that the resulting code is fully con-

sistent with the structure of the reverse language pro-

gram. It would be useful to make an analogy between

the graphical representation of the gates and their

equivalent – the corresponding command (method) in

programming language and open this scheme with au-

tomatically generated code in IBM Quantum Lab.

After acquiring knowledge about the basic quan-

tum gates, creating a quantum teleportation circuit,

Quantum Transformation of School Informatics

231

Figure 5: Quantum teleportation algorithm in IBM Quantum Composer

the students are ready to proceed to the next stage

of learning the basics of quantum informatics – to

implement quantum algorithms in programming lan-

guage, within the framework of which the forma-

tion of knowledge and skills to distinguish and use

quantum one-, two- and three-cube gates for the im-

plementation of quantum algorithms in programming

language (Python), use online programming services,

which support Python work with Qiskit module, for

the implementation of quantum algorithms on quan-

tum simulators and real quantum equipment.

The basic foundation for the teaching methodol-

ogy of this section is the knowledge of the basics of

classical (non-quantum) programming and the ability

to implement basic classical algorithms in program-

ming language.

This is a dedicated platform for working with

quantum algorithms (IBM Quantum) that provides

their implementation in Python language. Therefore,

it is methodologically appropriate to repeat the basics

of structural programming in Python.

Despite the lack of experience of students in the

implementation of Python programs with the help of

Jupyter Notebook, it is obvious, that before starting to

implement quantum algorithms using the IBM Quan-

tum Lab server it is necessary to familiarize students

with the peculiarities of their writing and launching,

for example, using the online service Google Colab

(https://colab.research.google.com/).

After implementing and launching the application

programs by means of the online service Google Co-

lab, it is advisable for the students to propose the au-

tomatically generated code for the implementation of

the quantum teleportation algorithm in IBM Quantum

Lab. It is necessary to ask the students: What is sim-

ilar in the interface of Google Colab and IBM Quan-

tum Lab online services? We make a joint conclusion

about the uniqueness of these environments and pro-

ceed to consider the features of the connection to the

quantum simulators and computers in IBM Quantum

AET 2021 - Myroslav I. Zhaldak Symposium on Advances in Educational Technology

232

Lab on the requested code fragments.

It should be noted that after completing the con-

tent line “Quantum calculations, algorithmization and

programming” students will be able not only to learn

about the most popular algorithms of quantum pro-

gramming and try to learn how to implement them on

real quantum equipment, but also to improve compe-

tence in the basics of programming in Python.

Within the framework of the content line “Quan-

tum telecommunication technologies” the formation

of competencies in security technologies (optical

technologies, laboratory and experimental control

technologies, photon sources) and quantum commu-

nication technologies (quantum cryptography, quan-

tum networks, quantum communication infrastruc-

ture and equipment).

Formation of competences from the enabling tech-

nologies can be carried out in the form of short self-

prepared student reports on the topics suggested by

the teacher, or in the form of watching short popular

science stories that reﬂect the current state of devel-

opment of the ﬁeld.

It is important for students to know about the

limitation of quantum communications. The teacher

states that the main limitations of quantum cryptog-

raphy are the speed of key distribution and the dis-

tance between the transmitter and the receiver. This

problem is trying to be solved by modern physicists

who have proposed new protocols, new optical cir-

cuits, new methods of quantum-state measurements.

It is also necessary to tell the students that an im-

portant task of quantum communication channel qual-

ity is to reduce the number of errors (the critical error

rate is 11%). Students should know that the greater

the distance over which a quantum key is transmitted,

the greater the attenuation of the signal in the ﬁber

optic lines, while the noise remains. Because of this,

it is not possible to transmit information for hundreds

of kilometers in real ﬁber optic lines.

It will be useful to remember the previously dis-

cussed phenomenon of decoherence (disintegration of

quantum state due to interaction of quantum system

with ambient environment). The teacher can describe

that photons after transmission through many kilome-

ters of real ﬁber optic lines in most cases cease to

be quantum entangled (connected) and transform into

usual, not interconnected, quanta of light. Therefore,

in order to produce efﬁcient ﬁber optic line it is nec-

essary to ensure preservation of quantum entangle-

ment when the signal is weakened and when it passes

through an ampliﬁer. Fibre optic cables laid at the

bottom of the oceans contain a number of special am-

pliﬁers based on optical warehouse of rare-earth ele-

ment houses, and these ampliﬁers make high quality

transmission of information possible.

It is worthwhile to ﬁnd some examples of quantum

cryptography application spheres that would motivate

further study. It is worthwhile to make an example

that today world’s bank data centers have encryptors

that use symmetric keys. They are additionally com-

plemented by quantum distribution systems for keys,

which are changed not monthly (in the classical ap-

proach), but every second. On the one hand, this

mechanism is not good for the disposable notebook,

but on the other hand, it gives tremendous advantage.

You can ask students to use any search engine to

ﬁnd information about the use of quantum technolo-

gies in the ﬁeld of ﬁnance, for example, for the last

six months. If a sufﬁcient number of students work,

the task can be reﬁned by geographical location (on

certain continents, in certain countries, etc.).

It will be interesting for students to learn that

quantum cryptography can also be used for dis-

tributed data storage. It is possible to distribute in-

formation in several data centers and constantly move

it by means of quantum-secured channels. Thus, even

if someone gains access to some of these data centers,

he or she does not receive all of the necessary infor-

mation. This will also work if some of the data centers

are disconnected: a light user will be able, by authen-

ticating to the network of data centers, to restore all

relevant information.

We also inform the students that quantum keys

will be useful for securing authentication tasks,

which, in essence, is a check “friend-or-foe”. In this

case, the combination of hash function technologies

and a one-time notepad allows you to check if, for

example, the data for the online speech system came

from the control center or from someone else. This

is very important, because in ﬁve or seven years the

work of quantum computer is a reality. At the same

time on the streets will appear a large number of

driverless cars, which are not just a few, but will be

millions. And all of them will need to receive control

signals and update the ﬁrmware in a trusted manner,

not interacting with people for thousands of years.

This means that they will have to receive quantum

keys and use them afterwards in the process of ﬂight.

Prospects of quantum cryptography can be de-

scribed by the application of China, which has already

established a national quantum network that connects

Beijing, Shanghai, Hefei and Jinan.

The main technological problem nowadays is

whether the humanity will be able to produce a high-

quality quantum repeater in the nearest ten years?

This question can be discussed by the scientists by

dividing them into supporters and opponents of this

idea.

Quantum Transformation of School Informatics

233

4 EXPERIMENTAL TESTING OF

METHODS FOR TEACHING

THE BASICS OF QUANTUM

INFORMATICS TO LYCEUMS

STUDENTS

Forty-ﬁve students from three schools in the city of

Kryvyi Rih (Ukraine) took part in the experiment. In

order to evaluate the level of competence in the fun-

damentals of quantum informatics the entrance exam-

ination and post-assessment test were conducted.

Positive dynamics of changes in the level of com-

petence was noted in each group of competencies,

which conﬁrmed the study hypothesis.

As a result of the experiment the ways of intro-

duction of quantum informatics basics into the educa-

tional process of lyceums were determined:

1. choice module “The Basics of Quantum Informat-

ics” (17 hours);

2. cross-curricular study of quantum informatics

basics in physics, mathematics and informatics

courses (17 hours);

3. integrated course “The Basics of Quantum Infor-

matics” (35 hours).

Regardless of the choice of experimental model of

propaedeutic study of quantum informatics, the main

goal of its implementation is to develop the compo-

nents of computer literacy and information culture

through the acquisition of basic theoretical knowledge

and practical skills to manage quantum computers as

a new generation of computers.

5 CONCLUSIONS

Quantum transformation of school informatics course

should be carried out due to the perspective of

quantum technologies and the demand for quantum-

literate specialists.

The competences of quantum informatics basics

of lyceums students is a natural integration of some

interdisciplinary physical and mathematical compe-

tences and new subject-speciﬁc informatics compe-

tences.

The normative methods of teaching the basics

of quantum informatics to lyceum students is the

structural-functional model of forming the corre-

sponding competences.

Teaching the basics of quantum informatics to 10

(11) grades on the IBM Quantum platform can be car-

ried out with the author’s optional course materials.

This study does not cover all aspects of the prob-

lem of quantum transformation of informatics educa-

tion. Subsequent scientiﬁc searches for its solution

are appropriate in the following directions: 1) devel-

opment of partial methods of competence formation

in the ﬁeld of quantum technologies in accordance

with the European framework; 2) integrated teaching

of quantum physics and informatics to students of sci-

entiﬁc lyceums; 3) use of immersive medium for de-

velopment of virtual manipulatives of quantum tech-

nologies; 4) teaching method development of the ba-

sics of quantum technologies to professional schools

students.

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