Introducing quantum information and computation to a broader audience with MOOCs at OpenHPI

Abstract

Quantum computing is an exciting field with high disruptive potential, but very difficult to access. For this reason, many approaches to teaching quantum computing are being developed worldwide. This always raises questions about the didactic concept, the content actually taught, and how to measure the success of the teaching concept. In 2022 and 2023, the authors taught a total of nine two-week MOOCs (massive open online courses) with different possible learning paths on the Hasso Plattner Institute’s OpenHPI platform. The purpose of the platform is to make computer science education available to everyone free of charge. The nine quantum courses form a self-contained curriculum. A total of more than 17,000 course attendances have been taken by about 7400 natural persons, and the number is still rising. This paper presents the course concept and evaluates the anonymized data on the background of the participants, their behaviour in the courses, and their learning success. This paper is the first to analyze such a large dataset of MOOC-based quantum computing education. The summarized results are a heterogeneous personal background of the participants biased towards IT professionals, a majority following the didactic recommendations, and a high success rate, which is strongly correlatated with following the didactic recommendations. The amount of data from such a large group of quantum computing learners provides many avenues for further research in the field of quantum computing education. The analyses show that the MOOCs are a low-threshold concept for getting into quantum computing. It was very well received by the participants. The concept can serve as an entry point and guide for the design of quantum computing courses.

1 Introduction

Quantum technologies are considered to be one of the most important technologies of the near future. Recently, the sub-area of quantum computing and quantum communication has increasingly come into focus, see Sect. 2 for a brief glance at the literature. Many companies have launched initial innovation projects in order not to miss out on these technologies. However, a major problem is the lack of skilled workers, particularly in the field of quantum computing. Universities have now set up relevant courses, but the number of graduates will not meet the expected demand for specialists. Politicians have recognized this and have launched various programs. The Federal Ministry of Education and Research in Germany (BMBF) has therefore initiated the “Quantum Future of Education” funding measure for 2021. The aim was to “develop innovative, interdisciplinary concepts and programs for education and training in quantum technologies”.

As part of this project, an innovative MOOC (Massive Open Online Courses) curriculum on topics related to quantum computing was developed by the authors of the present paper in cooperation with the Hasso Plattner Institute (HPI). The curriculum consists of nine courses and is explicitly addressed to an audience with little prior knowledge of the subject. The aim was to pick up participants at their level of knowledge and use innovative didactic concepts to convey a sound understanding of various areas of quantum computing. The focus was not on quantum physics or mathematics but on applications of the underlying concepts. As this was a BMBF project and was primarily aimed at a German audience, the MOOC content is in German with an ongoing process of English subtitles being added. The knowledge acquired in the MOOCs is intended to serve as a starting point for further individual specialized professional training.

To make it easier for participants to get started, they are offered various learning paths. This allows participants to put together an individual learning profile depending on their previous knowledge and interests. On January 17th, 2024, when the data for this paper was exported, 7413 participants had attended the MOOCs, who had taken an overall of 17,157 courses in the curriculum. The topic of this paper is to analyze the learning behavior of these participants within the MOOCs. Therefore, the following research questions are addressed:

• RQ 1: What kind of audience attended the MOOCs? What are the specific backgrounds and interests of the participants?

• RQ 2: What specific topics or subject areas did the participants choose when selecting the courses offered? Which topics are the participants particularly interested in?

• RQ 3: Which competences could be acquired by the participants through the course concept? To what extent did the course concept support the participants?

This paper is organized as follows. Section 2 provides a brief (and necessarily selective) overview of the enormous amount of literature on quantum computing education. Section 3 presents the didactic concept of the curriculum under consideration in this paper, as well as the course’s contents. The content is also categorized with respect to the European Competence Framework for Quantum Technologies [1]. Section 4 evaluates the data collected by HPI during the courses with respect to the three research questions mentioned above. In Sect. 5, based on the results of Sect. 4, we draw conclusions concerning the research questions, the lessons learned, and point out topics for further research.

2 Literature review

While quantum technologies have recently gained prominence in educational research, the investigation into quantum physics pedagogy is longstanding [2]. Bitzenbauer’s literature review spanning 2000 to 2021 encapsulates 1520 works on this subject.

Research in imparting skills and competencies for quantum technologies has primarily centered on university education, particularly Bachelor’s and Master’s degree programs [3]. Aiello’s work discusses 18 programs dedicated to training in quantum information science and engineering, emphasizing the necessity for corresponding investments across various stakeholders.

A targeted approach to teaching quantum technology and computing at US universities, especially within Historically Black Colleges and Universities (HBCUs), have been noted [4]. Lee’s research addresses issues of Black representation and workforce diversity in quantum information science and engineering.

Bungum’s study focuses on developing a quantum course for master’s level information technology students, drawing insights from participant interviews [5]. Similarly, Stump’s analysis explores student difficulties and misunderstandings regarding quantum topics [6].

An evaluation of interdisciplinary approaches to teaching quantum information science is detailed in Meyer’s work, highlighting the influence of instructors and the need for diverse perspectives [7]. The presentation of a 1D quantum simulation and visualization tool by Zaman Ahmed aims to enhance understanding of quantum phenomena from the students’ perspective [8].

Delgado’s examination of the effects of the COVID-19 pandemic on quantum information science education underscores the evolving landscape of online teaching modalities [9]. Lastly, Hasanovic’s account of the NSF-funded EdQuantum project highlights efforts to develop a curriculum for future quantum technicians [10].

In contrast to tertiary education, educational research on quantum topics focussing on elementary and secondary schools just started a few years ago.

The study of Bondani et al. [11] is initiated by the European QTEdu CSA project, a component of the “Quantum Flagship”, wherein courses on quantum physics and the application of quantum technologies are devised, implemented, and evaluated among approximately 250 students. Freericks et al. [12] already 2017 developed MOOCs for teaching quantum mechanics to over 28.000 non-scientists.

The work by Angara et al. [13], Santanassi et al. [14, 15], Pospiech [16], Sutrini et al. [17] investigate the possibilities to include basic quantum algorithms (e.g. teleportation) into physics classes. In addition, Sutirini et al. [17, 18] investigated how training courses for physics teachers can be set up.

The training in both school and university settings on quantum technologies ultimately aims to address the anticipated global demand for skilled professionals in these domains. This foreseen need is compellingly expounded upon by Venegas-Gomez and Plunkett [19, 20].

Several works specifically tackle the imperative of cultivating a requisite national and international workforce in quantum domains. Fox et al. [21] conclude that the commercialization of quantum technologies necessitates an adequately trained workforce, drawing insights from a qualitative study involving 21 US companies. Asfaw et al. [22] chart a roadmap for developing a commensurate workforce through the establishment of a quantum engineering education program, informed by a survey of 480 researchers across US universities, government agencies, industry, and research laboratories.

Although the aforementioned studies primarily center on the US landscape works such as those by Greinert (nee Gerke) et al. [1, 23, 24], contribute to the formulation and presentation of a European competence framework. This framework underpins the development of training programs aimed at nurturing the future quantum workforce. Such initiatives were integral to the European project QTEdu CSA, which began to establish a framework for second-generation quantum technologies - activities that are now continuing as part of QUCATS, the current Quantum Flagship CSA.

The education and training of specialists in quantum technologies necessitate broader dissemination of these subjects in academic institutions alone. Engagement with individuals already employed in companies is imperative. Additionally, initiatives must cater to students and schoolchildren lacking adequate educational provisions thus far.

Quantum-related online courses were introduced at the European Research Center CERN in 2020, as evaluated in Combarro’s report [25], which examines participant demographics and course outreach.

Maldonado-Romo’s study reports on a Spanish-language quantum online event featuring introductory workshops and hackathons, engaging 220 participants from Latin America, with two-thirds being beginners [26].

The integrated approach presented in the present paper, which encompasses fundamental quantum concepts, quantum computing, and quantum cryptography, is echoed in Aithal’s work [27]. Notably, Aithal underscores synergies among various topics within the realm of Information, Communication, and Computing Technologies (ICCT).

3 The OpenHPI quantum channel and the curriculum on quantum computing

Since 2012, the Hasso Plattner Institute (HPI) has operated the online educational platform OpenHPI (https://open.hpi.de). The platform offers free access to MOOCs in the field of information technology. A MOOC at OpenHPI usually consists of around 20 concise videos (approximately 10-15 minutes each), 10 self-tests to assess participant learning progress and one final examination test. The self-tests and the final examination tests are carried out online and are multiple-choice tests with more than one choice possible for the questions. The self-tests consist of about 10 questions each, the final exam of 20 questions.

Each course is conducted within a specified timeframe. Participants can repeat self-tests as needed, but the final exam can only be taken once online at the end of the time frame and has to be finished within 120 minutes.

The time frame of a MOOC normally is two weeks since studies in the literature support the determination that a two-week module with integrated self-tests and a final exam is optimal [28].

Throughout the course’s timeframe, participants can engage in discussions and pose questions within a forum moderated by the instructor. Answers to questions and comments are usually provided within one day. A course can be completed in two ways. If participants have accessed more than 50% of the items (videos, self-tests, additional material), they receive a certificate of attendance. If participants have more than 50% of the points achieved in the final examination, they receive a qualification certificate. It should be noted that it is not necessary to access any of the items to obtain a qualification certificate. It is sufficient to pass the final exam. These are the commen rules for all the courses at openHPI.

Even after the MOOCs have ended, the courses are still available to new interested parties. However, the forums are closed, and the final exam cannot be taken anymore. The videos can now be viewed on the platform without registering. However, registered participants can access the self-test and old forum entries. Participants can still complete the course successfully by accessing 50 % or more of the items. Then they will also receive a certificate of attendance.

In the present paper, a distinction between so-called course learners and self-learners is made. Course learners attend the course during the timeframe and are able to interact with the course instructor and fellow students. Self-learners register for the course after the end of the timeframe. They can only attend the course in a non-interactive way.

In 2022, a dedicated channel for quantum computing was established on OpenHPI (https://open.hpi.de/channels/quantum). The channel features 15 MOOCs addressing various aspects of quantum computing. The kernel is an introductory curriculum of nine interconnected and thematically coordinated MOOCs developed by the authors of the present paper from June 2022 to July 2023. Concurrently, six additional quantum MOOCs were developed as specialized, independent courses. These courses cover diverse topics such as quantum computing for school pupils, a general introduction to Qiskit, or advanced topics like simulating quantum systems (Quantum Computing for Natural Sciences). The present paper discusses and evaluates the curriculum of the nine interconnected quantum MOOCs forming the kernel of the channel.

3.1 Didactic concept

The didactic concept aims to give participants with no prior knowledge of mathematics or physics a sound introduction to quantum information. The broad field is structured by three pillars “introduction”, “cryptography” and “algorithms”. However, it is not required to work through these pillars one by one. Instead, a series of self-contained learning paths is offered, so that participants can set their own priorities and not have to deal with topics outside their area of interest. In the end, they are able to use the acquired knowledge to face the quantum computing topics occurring in their proper professional practice.

The learning paths are illustrated in Fig. 1. The nine courses are categorized into three sections: three introductory courses (Intro 1, Intro 2, and Intro 3), three courses focusing on quantum cryptography (Crypto 1, Crypto 2, and Crypto 3), and three courses on quantum algorithms (Algo 1, Algo 2, and Algo 3). Intro 1 does not require any prior knowledge. Intro 2 requires Intro 1, but with Intro 1 alone it is already possible to understand Crypto 1. In general, it is possible to understand a course with the knowledge of the courses prior to it in Fig. 1. For instance, Algo 2 can be understood with the knowledge of Intro 1, Intro 2, Intro 3 and Algo 1. Especially, the pillars about crypto and algorithms are distinct one from the other, so participants who want to deepen their knowledge in quantum cryptography need nothing to learn about (advanced) quantum algorithms, and vice versa. A proposed learning path is a subset of the courses following the arrows in Fig. 1 and with each course also containing its predecessors. Information on the structure of the curriculum and the structure of the learning paths is given in the first video of each course, thus providing an orientation on where the course is located in the curriculum, and also information on where to get prior knowledge if necessary for a more advanced course in the curriculum. When useful, also the last video of a course provides this information as a review and outlook. The modular structure allows participants to customize their learning paths based on their interests and pre-existing knowledge. For course-learners, the learning path for all 9 courses was determined by the order of the courses’ timeframes: Intro 1, Crypto 1, Intro 2, Crypto 2, Algo 1, Intro 3, Crypto 3, Algo 2, Algo 3. (Algo 2 and Algo 3 were merged together for practical reasons). They could of course attend subsets of the courses, but in the timeframes’ order. Self-learners can work through the courses in any order of their choice, but it is recommended to complete the previous courses in Fig. 1 before attending a new course.

Figure 1

Structure of the curriculum with nine courses and self-contained learning paths

In designing the individual courses, the authors drew on their experience of teaching at Universities of Applied Sciences. The aim here is always to assume as little prior knowledge as possible, minimize the theoretical background, use graphical representations, and activate the participants through integrated exercises. Repetitions of the same topic in different courses from different perspectives are also intentionally included to deepen the participants’ understanding.

Special didactic features in the course pillars are as follows:

• In the introductory courses, the “quantum cube” is used throughout to illustrate quantum register states and the effect of quantum gates. This model was developed by Just [29, 30] and since then has been studied and used as an intuitive tool for visualizing quantum entanglement and quantum computation [31–33]. It was applied to the more advanced topics of quantum oracles and quantum phase kickback for the first time in the courses under consideration and is presented in greater detail in the appendix of this paper.

• The focus on quantum cryptography and quantum algorithms use Qiskit [34] to provide easy, hands-on access for the participants. The code is made available to the participants, so they can also experiment independently of the course.

• The quantum cryptography series of courses largely dispenses with formal mathematical formulations and uses many examples to illustrate the concepts and mechanisms. For example, simulation examples and graphical diagrams demonstrate entanglement swapping and purification very well.

• In the algorithmic course series, the focus is on the practical implementation and less on analytical investigations of the algorithms. Access to the quantum algorithms via programming has the advantage that complex calculations can be omitted, and a strong emphasis can be placed on demonstrations.

In addition to the MOOCs, twenty participants were selected by the HPI to participate in a workshop associated with the courses. The workshop was guided by members of the HPI Academy and the authors of the present paper. It used the design thinking method (for further information see e.g. [35]) and aimed to develop tangible applications of quantum technologies. The workshop took the style of a business game. A fictitious company had to be made “quantum-ready” by the participants. There were no limits to the imagination. Since only a few selected participants could attend the workshop, its evaluation is not the topic of the present paper.

3.2 Course content

The biggest challenge for the content design of the courses was the different and heterogeneous prior knowledge of the participants. As the courses are aimed at such an audience, only minimal mathematical and physical knowledge could be required. On the other hand, the aim of the course series was for participants to have a deeper understanding and overview of current topics after successfully completing the curriculum. The bridge between minimal prior knowledge and deeper understanding at the end of the curriculum was built by choosing the contents of the courses as follows.

In the introductory course series, the first course (Intro 1) introduces logical qubits, the elementary gates X, Z, H, and CNOT, and the gate model for the description of algorithms. Since the cube model for illustration [29, 30] (see appendix) is used, this very quickly familiarized the participants with quantum phenomena known from the press such as superposition and entanglement. In the second course (Intro 2), the algorithm for teleportation is presented. Then elementary mathematical description tools ($2^{n} \times 2^{n}$-matrices, the operations of matrix multiplication and tensoring, and complex numbers) are introduced. Formal definitions are deliberately omitted. The focus is on examples and applications to give the participants an intuitive understanding of the concepts. The third course (Intro 3) deals with quantum oracles and the phenomenon of phase kickback, again taking advantage of the quantum cube for visualizing abstract algorithmic concepts. These two concepts form the basis of many classical quantum algorithms. A brief excursion into adiabatic quantum computing concludes the introductory course series.

In the course series on quantum cryptography, the first course (Crypto 1) explains elementary concepts from classical cryptography using examples. The somewhat inaccessible terms computationally secure and perfectly secure are also introduced. It is shown how quantum computers attack common asymmetric encryption methods. The BB84 key exchange protocol [36] is discussed in detail (including simple error correction and privacy amplification) and its physical implementation and attack possibilities are explained. In the second course (Crypto 2) the central topic is the property of entangled quantum systems (in particular bipartite systems, Schmidt decomposition, partial trace) and the key exchange protocol derived from this. Instead of mathematical calculations, simulations with Qiskit [34] or quantum games (CHSH-Inequality) [37, 38] are used. The ideas on the security proofs of the protocols are also explained. The third course (Crypto 3) discusses the concept of a quantum internet and the associated technological challenges (repeaters and error correction).

In the first course of the series on quantum algorithms and programming (Algo 1), the implementation of the gate model with Qiskit [34] is presented. The classic quantum algorithms [39] such as teleportation, Deutsch’s algorithm, Deutsch-Jozsa’s algorithm, and Grover’s algorithm are presented using Qiskit. In the second course (Algo 2), somewhat more sophisticated algorithms such as the quantum Fourier transform, the Shor algorithm [40] and the HHL algorithm [41] are explained step by step using example implementations. The third part (Algo 3) deals with current NISQ algorithms [42], which can also run on existing error-prone hardware. In addition to Monte Carlo simulations, VQE and QAOA for solving optimization problems and algorithms are presented, see e.g. [43].

3.3 Mapping to quantum competencies

The three Tables 1, 2 and 3 show which course teaches which competence up to which level, with the domains of possible knowledge and skills taken from the European Competence Framework for Quantum Technologies [1]. The framework defines six proficiency levels: A1 Awareness, A2 Literacy, B1 Utilisation, B2 Investigation, C1 Specialisation, and C2 Innovation.

Table 1 Competence Domains: Concepts and Foundation

Table 2 Competence Domains: Quantum communication and networks

Table 3 Competence Domains: Quantum Computing and Simulation

It can be seen that the curriculum covers a wide range of quantum information technology skills, mostly at level A1 of the European Competence Framework, and sometimes at level A2. This is in line with the aim of not assuming any prior knowledge, while still enabling participants to deepen their knowledge according to their needs and prior knowledge.

4 Evaluation of the data collected

To analyze the field of participants and the success of the courses, the anonymized participant data provided by HPI is used. These data consist of two types of data sets:

Dataset 1::

Once registered at OpenHPI, a pseudo ID is assigned to each participant, which is the same for all courses attended. Now for each course enrolment, there is an automatically generated data record with the pseudo ID, the date of enrolment in the course, and information on the number of course items taken (i.e. videos, self-test, and final exam), the number of posts in the forum and the success in the final exam, if this was taken. Information on the age of the participant is also sometimes included if disclosed by the participant.

Dataset 2::

In addition, when registering for a course, each participant is asked to take part in a questionnaire on their personal background. This includes questions about gender, current professional activity, and previous education. Participation in this survey is anonymous and voluntary.

Across all courses in the curriculum under consideration, there are till January 2024 a total of 17,157 course attendances of 7413 distinct participants. Among those 6232 participants were already registered on OpenHPI; 1181 created a new account on the same day they enrolled in their first course.

4.1 RQ 1: What kind of audience attended the MOOCs? What are the specific backgrounds and interests of the participants?

In this section, the personal and professional background of the participants is analyzed. The information provided voluntarily by the participants is used for this purpose. Thus, the information relates to about 5700 of 17,147 registrations, and participants who attended several courses may have answered more than once. Nevertheless, the analyses provide good indications of the spectrum of participants present and of frequently occurring characteristics.

The following criteria are analyzed:

• age (Dataset 1)

• gender (Dataset 2)

• status of employment (i.e. student, employee, pensioner) (Dataset 2)

• professional area (i.e. IT, administration, education) (Dataset 2)

• highest educational qualification (Dataset 2)

It turns out that the typical participant in a course is between 50 and 59 years old, male, employed in IT, and has a university degree. These characteristics are mentioned in between 30% and 80% of registrations. But often there is a wide variety of answers for the non-typical participants. The courses were therefore also attended by hundreds to thousands of participants who are female, do not work in IT, or do not have a university degree.

Figures 2-6 provide detailed information: In Fig. 2 we show the distribution of age groups over all participants, without double countings of participants. Unfortunately, the majority (4747 participants) did not disclose their age. Of those who revealed their age, a majority of participants are in the 50-59 age group.

Figure 2

Distribution of age groups over all participants. Participants in the survey: 2732

Figure 3 shows the distribution of genders. At over 80%, the proportion of men is even higher than is typically observed in STEM subjects, where the proportion of men is regularly around 2/3.

Figure 3

Distribution of different genders. Registrations in the survey: 5767

Figures 4-6 reveal information about professional characteristics. Over 60% of survey participants described their employment status as employed, followed by retired people (approx. 17%) and students at universities and others (approx. 7% each). Unsurprisingly, around 58% of participants categorize themselves in the IT sector, followed by other (around 16%), education (around 14%), and engineering (around 12%). However, it was also possible to reach people from administration and marketing/sales. In terms of professional qualifications, the MA degree (this also includes the former German diploma degrees) dominates with approx. 54%, followed by a Bachelor’s degree (approx. 18%) and a doctorate (approx. 17%). Around 15% of respondents stated that they had a non-academic professional qualification.

Figure 4

Staus of Employment. Registrations in the survey: 5652

Figure 5

Professional Area of the participants. Registrations in the survey: 5303

Figure 6

Professionl qualification. Registrations in the survey: 5331

4.2 RQ 2: What specific topics or subject areas did the participants choose when selecting the courses offered? Which topics are the participants particularly interested in?

In this section, we look at the learning behavior of the participants. The data basis is the automatically generated, anonymized data records, i.e. there is a complete data basis without double counting (Dataset 1). A data record refers to one participant in a course, with each participant having an unchanging pseudo ID across all courses. The following criteria are analyzed:

• Number of course registrations per participant

• Number of course registrations per course

• Items visited per participant and course

• Number of registrations per learning path

It turns out that many participants specifically selected one or a few courses and did not decide to complete the entire program with all the courses.

Among the courses, the number of enrolments for Intro 1 is the highest, followed by Intro 2, Crypto 1, and Algo1. The number of participants then decreases within the three areas. This order of enrolments also holds for the two subgroups here considered separately, namely enrolments during the course and enrolments for self-study after the course was finished.

When analyzing the items attended per course, after deducting the no-shows who were only enrolled and did not attend any items at all, the largest group of participants attended 75% to 100% of the items. The second-largest group only attended less than 25% of the items. It turns out that only a small percentage of participants visited an average number of items between 26% and 75%.

When analyzing the learning paths, only participants who attended at least 25% of the items in the courses are considered, as only here can the effect of the didactic concept unfold. It turns out that the majority of these participants followed the recommended learning paths.

Figures 7-10 show the details. Figure 7 shows that many participants specifically selected one or a few courses and did not decide to complete the entire program with all courses. The number of participants enrolling in one course, two courses, ..., and all nine courses can be seen.

Figure 7

Number of participants taken one, two, …, nine courses

Figure 8 shows the registrations per course. Summed up over all nine courses, there are 17,157 registrations until January 2024. 12,468 are course learners and 4689 are self-learners. The courses continue to be open for self-learners, so the number of self-learners is still increasing.

Figure 8

Registrations per course, subdivided to course learners and self-learners

Figure 9 displays for each course initially how many participants visited how many items. Participants are divided into 5 groups: the no-shows (participants who registered but did not visit any course item), and then the 4 groups of participants who visited between 1% and 25%, between 26% and 50%, between 51% and 75%, and more than 75% of the items. In all courses, the middle participant groups, those with shares between 26% and 75%, were by far the smallest groups. The other groups are roughly equal in size, with variations between individual courses.

Figure 9

Number of participants using percentage of the items

Figure 10 shows which participants took which learning paths. Here, only course participations with at least 25% of visited items are considered, these are 2036 participants. The most visited learning path consists of the course Intro 1 only, with 720 participants. This is followed by the learning path Intro 1 and Crypto 1 with 316 participants, and then the learning path with all courses with 119 participants. Only in exceptional cases course selections outside the recommended learning paths were made.

Figure 10

The 16 most frequently used learning paths embedded to the untranslated German curriculum

4.3 RQ 3: Which competencies could be acquired by the participants through the course concept? To what extent did the course concept support the participants?

To check the success of course participation, we split the 17,157 data records into 12,468 data records from course learners (CLs) and 4689 data records from self-learners (SLs). The distinction between course learners and self-learners was made in the data records based on the enrolment date for the course.

Course learners used the same learning items as self-learners, except that they also had the opportunity to exchange ideas and ask questions in the forum. They also took a final exam.

The learning success of course learners is derived from the result of the final examination. This is passed if 50% of the questions are answered correctly. These participants get a “Record of Achievement”. All participants who visited at least 50% of the items in a course get a “Confirmation of Participation”.

It can be seen that of the 12,468 course learners, 4550 are no-shows, 3145 did not reach the 50% items threshold and 4773 successfully completed the course. This corresponds to 38% of all course learners.

To gain more insights on which the points percentage (total score) of the course learners may depend, we model this with a simple regression model where the points percentage depends linearly on the percentage of items visited, see Fig. 11. Here, besides the data points, the linear model with slope and intercept as well as the $R^{2}$ can be seen. While only a few participants achieved a high overall score despite having attended fewer learning items, the majority showed a clear positive correlation between the two variables as seen by the value of $R^{2}=0.27$. Note, that as a global model, the linear regression interpolates smoothly between different regimes of the data.

Figure 11

Points percentage (=total score) of the course learners vs. percentage of items visited. 3299 data points are included

Aggregated over all courses, 3299 participants tried the final exams and are included in this analysis. This underlines the significance of the learning materials visited for course success.

When dividing the dataset into the three course blocks, Intro 1 to 3, Crypto 1 to 3, and Algorithms 1 to 2/3, we observe a qualitatively similar dependence on points percentage and items visited percentage: Participants using the content of the courses more actively performed better in the final exam. This is shown in Figs. 12 to 14.

Figure 12

Courses Intro 1, Intro 2 and Intro 3: Points percentage (=total score) of the course learners vs. percentage of items visited. 1667 data points are included

Figure 13

Courses Crypto 1, Crypto 2 and Crypto 3: Points percentage (=total score) of the course learners vs. percentage of items visited. 1051 data points are included

Figure 14

Courses Algo 1 and Algo 2/3: Points percentage (=total score) of the course learners vs. percentage of items visited. 581 data points are included

For the course learners, we can furthermore relate the success of the final exam to the items visited. Figure 15 gives an overview on the results achieved in the final exams. In Fig. 16 we show that the mean of the number of items visited is significantly larger for the top performers of the courses (top 5%, top 10% and top 20% of the participants) compared with the remaining participants. Here “topx” means that a participant has achieved one of the x highest percentage results. Surprisingly, the Top 5 performers attended slightly fewer items than the Top 10 and Top 20 performers. This may be due to the fact that some quantum professionals also attended the courses to relate them to their professional knowledge or to use the structure of the courses. Overall, the top performers visited more than 92% of the items on average.

Figure 15

Number of participants achieving points percentage of the final examination

Figure 16

Percentage of the items visited by Top Performers (Top 20, Top 10, Top 5) and the other course-learners

It can be seen that of the 4689 self-learners, 1369 were no-shows, 2181 did not visit 50% of the items and 1139 finished the course with success, so roughly a portion of 24% of the participants starting the course completed it with a certificate of attendance.

Figure 17 gives an overview and the details on course registrations for course learners and self-learners, the no-shows, the unsuccessful, and the successful participants. Across all courses and participants, 5912 completed the course; in 11,245 cases the courses were not completed. It should be noted here that individual participants are counted separately in each course they attended.

Figure 17

Divided between course and self-learners the number of no-shows, successful and unsuccessful participants are displayed

5 Conclusions and topics for further research

In the previous section, we analyzed the participant’s data and the data of their learning behavior in the core courses on quantum computing on the OpenHPI platform that took place in the period from June 2022 to July 2023. This provides answers to the following research questions

• RQ 1: What kind of audience attended the MOOCs? What are the specific backgrounds and interests of the participants?

• RQ 2: What specific topics or subject areas did the participants choose when selecting the courses offered? Which topics are the participants particularly interested in?

• RQ 3: Which competencies could be acquired by the participants through the course concept? To what extent did the course concept support the participants?

It should be emphasized once again that all data included in the analyses is anonymized so that no conclusions can be drawn about individual participants.

RQ1: Our analyses show that the quantum MOOCs were attended by an audience with different backgrounds and interests. All age groups were represented, with the majority being over forty. Most participants had an IT background, but participants from non-technical professions are also a considerable part of the audience. The majority of participants have a university degree. As is often the case in technical and scientific fields, male participants also predominated in our courses. The analyses show that people not directly associated with a university are also interested in quantum computing. An enlarged audience with different professional and personal characteristics could therefore be addressed.

RQ2: As the field of quantum computing is very broad, various learning paths were suggested to the participants. With the MOOC platform’s help, the participants’ learning behavior could be tracked in detail. The analyses show that the recommended learning paths were often followed. Most participants attended an introductory course in each subject area (Intro 1, Crypto 1, Algo 1). Depending on their interests, they remained loyal to the topic and completed more advanced courses. A not inconsiderable number of participants also attended courses on several topics. More than 140 people completed all nine core MOOCs. The data shows that the recommendation of learning paths was highly accepted. Thus, there seems to be evidence that it is important to suggest learning paths to participants for better orientation when dealing with complex topics.

RQ3: The generally recognized European Competence Framework for Quantum Technologies [1] was used to select material. All content taught and tested in the examinations could be assigned to categories in the reference framework. Over 80% of exam participants passed the final exam, 50% even with a good to excellent result. It also shows that the success rate correlates with the number of learning materials consumed (videos, self-study tests, forum discussions). It can be stated that the learning elements provided by the MOOC platform are sufficient to teach participants the necessary skills.

In conclusion, one can say that the quantum MOOCs at OpenHPI were a big success and up to January 2024 reached more than 7400 participants from different age and professional groups. The MOOCs help to bring the topic of quantum computing closer to an audience outside of universities and research departments. The MOOCs are a good opportunity for anyone interested in quantum computing to delve deeper into the topics. The structure and content of the courses might also be a good point of reference and starting point for persons who would like to hold quantum computing courses. Depending on the desired learning objectives, teachers can build their own courses along the proposed learning paths, since the learning paths provide a self-contained arrangement of quantum computing topics. The teachers then can deepen quantum topics according to their specialization, and insert additional topics according to their preferences.

As the courses are in high demand, the openHPI has now started to provide the videos with English subtitles to make them accessible to a non-German-speaking audience. However, as the slides shown are still in German, the reach of the courses is likely to remain limited. In hindsight, it would have been better to formulate the slide content directly in English. The project schedule (start, milestones, end) required by the project organizer meant that the timing of the courses was not always optimal. Some courses were held very close together, while other courses were sometimes several months apart. When organizing an extensive series of courses, care should be taken to ensure that the courses are evenly distributed, giving the participants enough time to catch up on their work, but that the breaks between the courses are not too long.

The experience gained from running the MOOCs shows that many concepts of quantum computing can be explained to an interested audience without complex mathematical and physical descriptions. Presenting the various topics using examples and applications that are closer to everyday life has proved useful. Mathematical descriptions were only used when there was an intuitive understanding based on the application. Such an approach lowers the entry barrier to the topic and leads to less frustration among learners. Mathematical and physical descriptions and concepts should only be introduced and used once a basic understanding and curiosity have been aroused.

In addition to the results discussed in the present paper, further research questions can be investigated based on the available data. It would be interesting to see, how exactly the participants worked with the video tutorials. For example, were the videos paused in between to better understand complicated details? Did the sometimes detailed discussions in the forum motivate the participants to engage with the topic? Another interesting question could deal with possible specific learning differences between male and female participants. More generally, the learning behavior of different subgroups could be analyzed in relation to age, professional situation, or educational attainment. The professional and personal backgrounds of the Top Performers could also be analyzed in more detail. Since the amount of data is large, the subgroups usually consist of hundreds of participants with respect to various characteristics, so that statistical analyses are meaningful.

Appendix:  The “quantum cube” for visualizing entanglement in multi-qubit-registers and the effect of quantum gates

In the introductory MOOCs of the curriculum, the “quantum cube” is used throughout to illustrate quantum register states and the effect of quantum gates.

The model was developed by Just [29, 30] and since then has been studied and used as an intuitive tool for visualizing quantum entanglement and quantum computation [31–33]. The quantum cube represents the state of an n-qubit register by providing one dimension in n-dimensional Euclidean space to each qubit. It then utilizes the standard n-dimensional cube with corners $(0,\ldots,0)$ up to $(1,\ldots,1)$. For a given register state, it places the amplitudes of the basis states (in any suitable representation of numbers, i.e. digits, arrows, squares, cubes, or circles) at the corresponding corners of the n-dimensional cube. See Fig. 18 for an example with two qubits, and the effect of Pauli-X-gate operating on the first of them.

Figure 18

Visualizing the state $\sqrt{\frac{1}{16}}e^{i290^{o}}|00\rangle + \sqrt{\frac{4}{16}}i|01 \rangle + \sqrt{\frac{5}{16}}|10\rangle + \sqrt{\frac{6}{16}}e^{i200^{o}}|11 \rangle$ of a 2-qubit-register and the effect of Pauli-X operating on the first qubit with the quantum cube model. The first qubit is provided with the left-right direction in 2-dimensional space, the second qubit with the down-up direction. The amplitudes are placed at the corresponding corners of the n-dimensional unit cube, which in 2 dimensions is the unit square. The representation of the complex amplitudes here follows Feynman’s QED [44]. Pauli-X on the first qubit interchanges the amplitudes along the left-right lines of the “cube”. The resulting state is $\sqrt{\frac{5}{16}}|00\rangle + \sqrt{\frac{6}{16}}e^{i200^{o}}|01 \rangle + \sqrt{\frac{1}{16}}e^{i290^{o}}|10\rangle + \sqrt{ \frac{4}{16}}i|11\rangle$

The application of quantum gates to a quantum register can generally be visualized as a swapping, rotation, or mixing of the numbers at the corners of the cube. This has been done by Just [29, 30] for the teleportation algorithm, see Fig. 19.

Figure 19

The CNOT-Hadamard-Measurement-steps of the teleportation algorithm as in [29]. For didactical reasons, only real amplitudes are considered. Green squares indicate positive amplitudes, red squares indicate negative amplitudes. The state of a register with three qubits is visualized in a 3-dimensional cube. Each qubit is provided with one dimension in space: The first qubit with the left-right dimension, the second qubit with the down-up direction, the third qubit with the front-back direction

For the purpose of the quantum MOOCs at openHPI, the cube model for the first time was applied to more advanced quantum algorithmic features, such as quantum error correction, see Fig. 20, quantum oracles, see Fig. 21, and quantum phase kickback, see Fig. 22. Based on the MOOCs, the visualization of some abstract algorithmic concepts with the quantum cube model is summarized and demonstrated in [45].

Figure 20

The decoding in bit flip correction code, visualised with the quantum cube model. The CNOT gate with the first qubit as control-bit is applied two times, first with the second qubit as target-bit (down-up interchangement of amplitudes when first qubit equals $|1\rangle$), then with the third qubit as target-bit (front-back interchangement of amplitudes when first qubit equals $|1\rangle$). It can be seen how the amplitudes α and β of the first qubit (left-right direction) are rearranged to one specific state of the syndrome qubits (down-up and front-back direction)

Figure 21

A quantum oracle for a boolean function of three bits, in this example $f(x_{1}, x_{2}, x_{3})=1$ if and only if $(x_{1}, x_{2}, x_{3})$ is $(0,0,0)$ or $(1,0,1)$ or $(1,1,1)$. The oracle $U_{f}$ in general interchanges the amplitudes of the $|x_{0}\rangle$ and $|x_{1}\rangle$ states, if and only if $f(x)=1$. The initial state in this figure is prepared as it is done in the algorithms of Deutsch-Jozsa and Bernstein-Vazirani

Figure 22

Illustrating quantum phase kickback für a controlled-U. The unitary U operating on two qubits changes the amplitudes of a register from orange to grey (which could mean anything), but in the case of an eigenstate, this means turning all of them by the same angle. Controlled-U operating on three qubits applies U to the states where the control-qubit is 1, hence to those at the left-sided square of the cube. Applied to an eigenstate, controlled-U just turns the amplitudes of the left-sided square of the cube all by the same angle