Quantum Computing As a Topic in Computer Science Education

Full text

antum Computing As a Topic in Computer Science Education
Stefan Seegerer
stefan.seegerer@fu-berlin.de
Computing Education Research
Group – Freie Universität Berlin
Berlin, Germany
Tilman Michaeli
tilman.michaeli@fu-berlin.de
Computing Education Research
Group – Freie Universität Berlin
Berlin, Germany
Ralf Romeike
ralf.romeike@fu-berlin.de
Computing Education Research
Group – Freie Universität Berlin
Berlin, Germany
ABSTRACT
Quantum technologies are currently among the most promising
technological developments, with quantum computing, in particu-
lar, playing a crucial role. This is accompanied by promising oppor-
tunities, but also new challenges for our society. However, quantum
computing as a subject of computer science education is still at the
very beginning. This paper aims to discuss quantum computing as
a topic in computer science education and to make a rst approach
to central terms and ideas as well as their explanatory approaches.
With the help of an explorative focus group interview with ex-
perts, ve core ideas of quantum computer science are identied
in this study. A literature review is then used to identify, catego-
rize, and contrast dierent explanatory approaches for these ideas.
The results thus contribute to making quantum computer science
accessible for computing education and raise further questions for
the computing education research community.
CCS CONCEPTS
•Social and professional topics →K-12 education.
KEYWORDS
quantum computing, quantum information science, focus group
interview, core ideas, quantum computer science
ACM Reference Format:
Stefan Seegerer, Tilman Michaeli, and Ralf Romeike. 2021. Quantum Com-
puting As a Topic in Computer Science Education. In Woodstock ’18: ACM
Symposium on Neural Gaze Detection, June 03–05, 2018, Woodstock, NY . ACM,
New York, NY, USA, 6 pages. https://doi.org/10.1145/1122445.1122456
1 INTRODUCTION
With the digital transformation, computer technologies have found
their way into almost all areas of life and people are encountering
them in the form of increasingly numerous information technology
innovations such as embedded ubiquitous systems, big data, or
articial intelligence. A major driving force of these advancements
is computer science. Computer science education aims at making
the corresponding fundamentals, applications, and implications
of these technologies accessible and comprehensible to any target
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©2021 Association for Computing Machinery.
ACM ISBN 978-1-4503-XXXX-X/18/06.. . $15.00
https://doi.org/10.1145/1122445.1122456
audience. Therefore, there is a consensus in computer science ed-
ucation research that teaching should emphasize concepts, ideas
and principles that are fundamental to the subject and relevant
in the long term, rather than short-term devices and technologies
[2, 8, 30].
Quantum technologies are a rapidly emerging innovation at the
intersection between physics, mathematics, and computer science.
In the form of quantum computing, this new paradigm poses signif-
icant advances and challenges for computer science. Even though
modern computer systems are already built on the principles of
quantum physics, only more recent developments of the so-called
“second quantum revolution” have the potential to inuence our
society. This leads to new opportunities and challenges. For ex-
ample, future developments in quantum technologies may aect
information security and privacy of citizens, governments, or com-
panies. Sensitive data can already be tapped from networks without
quantum-resistant encryption, stored, and potentially decrypted
at a later time by quantum computers. At the same time, quantum
cryptography creates new possibilities for tap-proof transmissions.
Another important application area of quantum computing is sim-
ulation. Here, quantum computers promise increased eciency,
for example in drug research or meteorology. Thus, quantum tech-
nologies bring both great opportunities and risks for society that
require an informed public debate.
Despite the increasing presence in the media and growing needs
in science, economy, and society, quantum computing as a subject
area of computer science education is still at an early stage – in
contrast to the importance of quantum theory in physics. The aim
of this paper is to present quantum computing as a topic and task
of computer science education. To this end, it provides an initial
approach to core terms, ideas, and suitable explanations based on a
survey of experts and literature.
2 RELATED WORK
Information processing based on quantum physics diers from
the conventional way of digital information processing in many
ways: While a traditional computer represents information with bits
valued either 0 or 1, a quantum computer uses so-called qubits. A
qubit can also take the value 0 or the value 1. But in addition, it can
be in a so-called superposition. In this case, the qubit has a certain
probability to be measured as 0 or as 1. However, this measurement
“destroys” the superposition – i. e. any further measurement would
reveal the same result: If a qubit has a 50% chance to be measured as
0 and a 50% chance to be measured as 1 and the rst measurement
yields 0, the second measurement will also yield 0 100% of the time.
Moreover, qubits can be entangled – i. e., made dependent on each
other – which enables the creation of arbitrary quantum states, and

WiPSCE ’21, October 18-20, 2021, Stefan Seegerer, Tilman Michaeli and Ralf Romeike
thus achieving quantum superiority. Taking advantage of superposi-
tion and entanglement, quantum algorithms attempt to solve certain
problems such as prime factorization [
31
], database searching [
15
],
or simulations [
38
] much faster than traditional supercomputers:
While
𝑛
traditional bits can only be in one of the 2
𝑛
possible states,
𝑛
qubits can be used to represent 2
𝑛
states simultaneously, with
each state assigned a specic probability: So while a traditional
computer could only represent one state with 4 bits (e.g. 1001),
a quantum computer can represent all 16 possible combinations
of 0 and 1 with length 4, with each combination having a certain
probability to be measured. Traditional computers use gates – prim-
itive logical functions – such as AND, OR or NAND (not and) to
process data stored in bits. Quantum algorithms manipulate qubits
by applying special quantum gates in such a way that a correct
result is measured at the end with high probability.
The three sciences directly involved, physics, mathematics, and
computer science, can contribute to the understanding of quantum
technologies, and each can serve as a perspective and entry point
into the subject area. Thus, there are various educational concepts
to address the basics of quantum physics in school, e. g., by starting
with the double-slit experiment to illustrate central contents and
questions of quantum physics [
21
], with light experiments [
11
] or
by providing students the possibilities to experiment in dierent
laboratory settings [
12
]. A physics education approach to quan-
tum computing exists, for example, for high school students [
28
].
However, this approach requires in-depth mathematical knowledge.
If we consider quantum computing as a topic of computer science
education, approaches are limited and there are only a handful of
educational concepts. Quantum computing can be found in certain
university courses in bachelor’s (e. g., [
20
]) or master’s computer
science programs (e. g., [
22
,
33
]). Billig [
4
] addresses quantum com-
puting for secondary school students concerning their mathematics
skills, e. g., by simplifying the central concepts and avoiding com-
plex numbers. To illustrate the potentials of quantum computing,
traditional computer systems and cryptographic methods are rst
described. Then, the special features, strengths, and challenges of
quantum technology are highlighted. A rst proposal for key con-
cepts of quantum information science is presented by QISLearners
[
1
]. Other secondary school curricula consider the STEM context
[
29
], use problem-based learning and the IBM Quantum Circuit
Designer [
26
], or propose quantum computing activities to support
regular lessons [
32
]. Wootton [
36
] describes an approach to getting
started using a brain game app that allows interested individuals
ages 5 and up to learn about qubits and quantum gates in a playful
manner. In addition, several videos explain quantum computing by
teaching the basics of quantum technologies at dierent levels. To
our knowledge, there are no scientic studies or research ndings
on the aforementioned approaches, which are primarily devoted to
the preparation of content.
3 METHODOLOGY
In the following, an initial didactical analysis of the topic of quan-
tum computing will be undertaken. For this purpose, we will rst
(1) identify central terms and concepts as well as relevant questions
and needs for clarication based on relevant literature, (2) utilize
a focus-group-interview with experts to determine candidates for
core ideas of quantum computing, and (3) analyze and contrast ex-
isting explanatory approaches for the resulting core ideas to collect
and discuss existing pedagogical approaches.
(1) Clarication and Analysis Of the Subject Area. In the rst step,
in an explorative literature analysis, relevant terms and concepts
within literature were gathered. Furthermore, open questions and
needs for further clarication were identied. The corpus com-
prises a total of 17 documents (children’s books, textbooks, school
curricula, and popular science books dealing with the topic of quan-
tum computing), see table 1. This allows for an initial clarication
and analysis of the subject area, providing the basis for the expert
interviews.
Target audience # Documents Documents
Children 2 [13, 23]
Students 5 [4, 25, 26, 29, 35]
Professional audience 4 [5, 16, 17, 27]
Interested general public 6 [6, 10, 18, 19, 34, 37]
Table 1: Document corpus
(2) Focus group interview with experts. To discuss and evaluate
the concepts and issues identied in the rst step, an expert sur-
vey in the form of a focus group interview was conducted. Due
to its exploratory and discursive character aiming at reaching a
consensus, this survey method is particularly suitable for our re-
search interest [
14
]. The experts were approached via the German
Informatics Society’s (GI) working group “quantum computing”.
They are characterized by both technical expertise in the research
area of quantum computing as well as corresponding teaching ex-
perience. For the online workshop, 9 people could be recruited. As
preparation, the experts were surveyed using a semi-structured
questionnaire on central terms, possible applications, and social im-
pact of quantum computing beforehand. The results of this written
survey were then analyzed and summarized to provide the basis
for the actual group discussions within the workshop. Thus, the
structure of the questionnaire also served as an interview guide for
the focus group. Within the workshop, those results were discussed.
Based on the central terms of the eld, the method of pile sorting
was applied to develop and rate core ideas of quantum computing.
In addition, follow-up interviews were conducted with selected
participants.
(3) Explanatory approaches. In the third step, explanatory ap-
proaches for the previously-identied core ideas of quantum com-
puting were elaborated, categorized, and contrasted with the help
of a literature analysis. For this purpose, the corpus of step 1 (cf.
table 1) was examined with the help of a structuring qualitative
content analysis according to Mayring [
24
]. As a deductive category
system, we used the resulting core ideas of step 2. This way, recur-
ring patterns in the explanatory approaches for the corresponding
ideas could be identied.

antum Computing As a Topic in Computer Science Education WiPSCE ’21, October 18-20, 2021,
4 RESULTS
4.1 Clarication and Analysis Of the Subject
Area
To identify the core ideas of quantum computing important to
the context of computer science education, an initial overview of
the relevant concepts is needed. This overview was rst obtained
with the help of an exploratory analysis of relevant literature for
dierent target groups. The results show that there seems to be a
certain consensus regarding topics and terms relevant to the subject
area, which is reected in a group of recurring terms used similarly
in all analyzed documents (cf. the terms mentioned by experts in
Tab. 2). Furthermore, the terms were largely independent of the
literature’s target group. Due to their prominence in the literature, it
can be assumed that the terms are also central from the perspective
of computer science education and thus for the understanding of
quantum computing and can be used as a basis for identifying core
ideas.
Furthermore, it has proven to be purposeful to consider not only
the technological perspective but also the application-oriented and
socio-cultural perspective [
7
]. However, in literature, statements
almost exclusively came from a technological perspective. Possible
applications and also societal implications of quantum computing
were only hinted at, so that this question was also taken to the
expert panel.
4.2 Focus Group Interview With Experts
Central Terms. Terms can help dene, specify, and prioritize
learning content in a subject area. With this goal in mind, the
questionnaire asked participants to name what they considered to
be the seven most important terms regarding quantum computing
that everyone should know (see Tab. 2). These terms corresponded
with the term identied in the exploratory literature analysis. In
the focus group interview, these terms were initially grouped or
combined together. For example, the terms quantum parallelism,
quantum speed up, and quantum advantage were combined into one
concept. When multiple terms were combined into a single concept,
particular care was taken to ensure a similar level of abstraction for
all involved terms. In addition, the terms were prioritized: Terms
that contribute to a basic understanding and thus allow for access to
the eld were selected. For example, quantum internet and quantum
communication or quantum simulation, which focus mainly on
specic applications, were considered less relevant.
Core Ideas. Following the interviews, the concepts essential for
understanding were formulated in the form of ideas and validated
with follow-up interviews. The nal 5 candidates for these ideas
are as follows:
(1)
Superposition: Qubits in a superposition of 0 and 1 have a
certain probability of being measured as 0 and as 1, respec-
tively.
(2)
Entanglement: The state of multiple entangled qubits cannot
be described by specifying an individual quantum state for
each qubit.
(3)
Quantum computer: Quantum computers can solve certain
– but not all – problems more eciently than traditional
computers.
(4)
Quantum algorithm: In a quantum algorithm, quantum gates
are used to inuence the state of the qubits in such a way that
the probability of measuring a correct solution increases.
(5)
Quantum cryptography: Quantum cryptography uses the
fragility of qubits to enable tap-proof communication.
Application-oriented and Socio-cultural Perspective. . Three key
application or societal implications emerge from the experts’ re-
sponses. In the area of cryptography, on the one hand, there is a
threat to traditional methods such as RSA, but on the other hand,
there are opportunities for new, secure methods. At the same time,
the experts promise social implications in optimization problems,
for example in the eld of articial intelligence, which could be
solved better or faster in the future. Finally, quantum simulations
promise societal progress in biological, chemical, or physical re-
search and can thus help, for example, to develop new vaccines.
Nevertheless, with a few exceptions, such as the generation of ran-
dom numbers on smartphones, quantum information applications
have hardly been used in everyday life.
4.3 Explanatory approaches
In the following, the result of the literature analysis on explanatory
approaches is presented. The individual approaches do not neces-
sarily appear in isolation: Within a document, dierent explanatory
approaches were sometimes used for the same idea.
Superposition: Qubits in a superposition of 0 and 1 have a certain
probability of being measured as 0 and as 1, respectively. A popular
way to explain this idea is to use analogies such as the coin toss (or
the spin of a coin), where the coin in the air (or spin) is interpreted
as a superposition of heads and tails (cf. Fig. 1). Another approach is
represented by a physical explanation approach, in which concrete
realizations of qubits by photons or electron spins are used, as well
as experiments such as Stern-Gerlach. Furthermore, qubits in the
corpus are also explained mathematically-symbolically: the state
of one or more qubits is then represented by a vector. graphical
representations are also used for explanation, for example geomet-
rically via the Bloch sphere or unit circle, and schematically via
partially lled circles or squares for each state of a qubit in a system.
Moreover, qubits are introduced based on the bit notion with the
help of probabilistic bits and subsequently generalized to qubits,
i.e., building on traditional topics of computer science education.
Entanglement: The state of multiple entangled qubits cannot be
described by specifying individual quantum states for each qubit.
Similarly to the rst idea, entanglement is often explained by analo-
gies. For example, two entangled coins always land both on heads
or always both on tails (cf. g. 2). In another analogy, two colored
balls are packed in dierent boxes: even if it is not known which
color is in the boxes, both balls will have the same color. In addi-
tion, a mathematical-symbolic approach to the explanation is often
taken, in which it is proved computationally that an entangled two-
qubit state cannot be represented as two individual one-qubit states.
Moreover, entanglement is also explained via measurement of quan-
tum circuits when Hadamard and CNOT gates are combined, or
again starting from traditional topics of computer science education
via introducing probabilistic bits as an intermediate step.

WiPSCE ’21, October 18-20, 2021, Stefan Seegerer, Tilman Michaeli and Ralf Romeike
Begri # Begri # Begri #
Qubit 8 State 2
Quantum Information
processing
1
Entanglement 8 Measurement 2
Quantum communica-
tion
1
Quantum circuit /
-gate
5 Quantum simulation 2 Quantum speed up 1
Superposition 5 Decoherence 2 Bloch sphere 1
Quantum cryptogra-
phy
5 Teleportation 2 Supremacy 1
Quantum computer 4 Quantum internet 2 Quantum Advantage 1
Quantum algorithm 2 Error-prone 2 Photon 1
Quantum parallelism 2 Quantum information 1
Table 2: Core terms and number of responses by experts.
1
1
1
1
50%
50%
Coin analogy Unit circle Bloch sphere Photons Filled squares
0
q
1
1
0
00 10
01 11
Figure 1: Examples for explainaing qubits and superposition
Mathematical-symbolic
11
10 +
≠
a1)(a0
10 +b1)(b0
00
1
2
1
2
+
1
1
1 1
1
1
1
1
50%
50%
Coin analogy Measurement of
quantum circuits
H
X
0
0 1
1
Figure 2: Examples for explaining quantum entanglement in the context of quantum computing
Quantum computers: Quantum computers can solve certain – but
not all – problems more eciently than traditional computers. Again,
the analogy approach is often taken, describing quantum comput-
ers as operating in a highly parallel fashion. Another explanatory
approach uses set of states – often using concrete examples and
orders of magnitude: For example, 300 qubits can already represent
more states (about 10
90
) than particles that exist in the universe.
Another popular explanatory approach works with a concrete exam-
ple such as the Deutsch-Josza algorithm [
9
]. This way, the number
of steps necessary to solve the problem can be compared between
a traditional and a quantum computer.
Quantum algorithm: In a quantum algorithm, quantum gates are
used to inuence the state of qubits in such a way that the probability
of measuring a correct solution increases. For this concept, on the
one hand, a physical explanation approach is used, which describes
a concrete realization and manipulation of qubits (e.g. photons)
(cf. g. 4). To explain the eect of the dierent gates on the state
of one (or more) qubits, sometimes a graphical representation is
chosen. For example, a rotation is made on the Bloch sphere, a
vector is mirrored at a certain axis on the unit circle, or lled areas
are exchanged along certain edges of a cube in a schematic rep-
resentation. In the experimental explanation approach, the eects
of the gates are investigated by measurement – for this purpose,
one usually works directly with appropriate tools (usually simula-
tors for quantum computers). Lastly, in a mathematical-symbolic
explanatory approach, the quantum gates are used in their matrix
representation, where applying a gate corresponds to multiplying
the matrix by a vector, or mapped to a state transition diagram.
Quantum cryptography: quantum cryptography exploits the fragility
of qubits to enable tap-proof communication. Aconcrete example is
often chosen as an explanatory approach for the way quantum

antum Computing As a Topic in Computer Science Education WiPSCE ’21, October 18-20, 2021,
Analogy: "Operating
highly parallel" Set of representable
states Specific example
Conventional computer
1
0f(0)
f(1)
One qubit quantum computer
10 +ba f(1)f(0)+ ba
H
Oracle
H
01
Possible measurements
Figure 3: Examples for explaining why quantum computers can solve certain problems more eciently than classical com-
puters
Physical explanation Unit circle
mirroring
Bloch sphere
rotation
Experiments with
quantum circuits
0
q
1
1
0
H
X
0
0 1
0
(
(
1 1
1 -1
(
(
1
0
Hq =
1
2
Matrix-vector
multiplication
State transition
diagram
xx
H
H
x
x
(
(
1
0
(
(
0
-1
(
(
1
0
(
(
-1
0
(
(
-1
2
1
2
(
(
1
2
1
2
(
(
-1
2
-1
2
(
(
1
2
-1
2
Figure 4: Examples for explaining gates
cryptography works, in the form of the BB84 key exchange proto-
col [
3
], since this does not require entangled states and is overall
considered easy to understand. Furthermore, to illustrate the ad-
vantages of a quantum key exchange protocol, traditional topics of
computer science education such as symmetric encryption and the
one-time pad are also referenced.
5 DISCUSSION
Both the literature-based analysis and clarication of the subject
area and the expert interview show that quantum computing can be
made accessible via a core of central ideas. Similar to the beginnings
of computer science, mathematical foundations, physical realization,
and computational use of quantum computers are still very close
to each other. This has an impact on existing foci and teaching
approaches to quantum computing. The expert group agreed that
a specic computer science perspective exists and is important. A
particular challenge for computer science education is that there
are – as of now – hardly any concrete applications of quantum
computing. Therefore, applications and contexts used in teaching
must be limited to simulation and future scenarios, for example.
The same applies to the socio-cultural perspective: The potential
eects of quantum technologies already motivate several research
directions, such as (post-)quantum cryptography, but are not yet
noticeable in everyday life. However, since they are considered
to have the potential to change society, educational approaches
that are comprehensible to the general public are necessary for an
informed public discourse.
Looking at the analyzed explanatory approaches, it can be seen
that mathematical and physical views and approaches to quantum
technologies have dominated so far. Thus, in the corpus studied,
physical experiments were often described in the context of an
introduction to quantum computing. Furthermore, complex num-
bers or matrices were introduced to describe states and gates. The
corpus shows, however, that explanations of the ideas are possible
even without a corresponding foundation in physics or elaborate
knowledge of mathematics.
Furthermore, our data indicates that quantum computer science
ideas are often explained starting from traditional concepts of com-
puter science – or are contrasted to them. Thus, traditional contents
of computer science education, such as the representation of in-
formation by bits or the realization of information processing by
computers with the help of logic gates, represent an important basis
for the teaching of quantum computing.
Beyond that, the results show that – as usual in computer science
education – analogies are often used. Analogies can help, according
to a constructivist learning understanding, to clarify facts vividly,
but mostly reduce the idea to a single aspect. This results in special
challenges concerning misconceptions. For example, the analogy of
a coin toss for qubits in superposition has only limited validity, since
objects like coins do not behave according to quantum mechani-
cal laws: The result of a toss could be calculated if all parameters
were known exactly. These laws are subject to those of traditional
mechanics. A comparable problem appears with the analogy that
quantum computers – similar to traditional multiprocessor systems
– would operate in a highly parallel fashion. In fact, quantum com-
puters alter the probabilities of a large number of potential solutions
in such a way that a correct solution is very likely to be measured.
Accordingly, it can be seen as a task of research in computer science
education to explore which approaches and analogies are suitable
to develop helpful conceptions, which misconceptions should be
avoided, and which age-appropriate competencies students can and
should acquire concerning quantum computing.
6 CONCLUSION
The investigation of quantum computing as a rather young sub-
discipline of computer science shows that both the research eld

WiPSCE ’21, October 18-20, 2021, Stefan Seegerer, Tilman Michaeli and Ralf Romeike
as well as its educational discussion are still in an early stage. In
light of the expected enormous progress in the eld of quantum
computing and the resulting growing inuence on our everyday
life, quantum computing may become an increasingly important
subject and research area of computer science education.
The aim of this study was to present an analysis of quantum
computing as a topic in computer science education by providing an
initial approach to core terms, ideas, and suitable explanations. To
this end, we investigated literature and conducted a focus group in-
terview with experts of the subject area. Overall, our study provides
the following two major contributions:
Firstly, we identied 5 core ideas of quantum computing. Those
ideas make quantum computer science accessible for computing
education by structuring the eld with a focus on underlying princi-
ples relevant in the long term. This provides the basis for preparing
the topic for teaching or developing respective curricula.
Secondly, we categorize, contrast, and discuss dierent explana-
tory approaches used within the literature for those core ideas.
These approaches make the core ideas and the respective appli-
cations, and implications of quantum computing comprehensible,
constituting the foundation for teaching the subject area. Further-
more, they raise further tasks and questions for the computing ed-
ucation research community, for example regarding the suitability
of certain approaches or the relation and connection to traditional
topics of computer science education.
Even though quantum computing will not nd its way into K12
curricula in the near future, students should be given the oppor-
tunity to understand these exciting developments in the context
of extracurricular activities or within elective formats. This way,
they have the opportunity to develop an interest and perhaps be
enabled to help shape the future themselves.
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