Abstract The field of Quantum Information Science and Technology (QIST) education presents unique challenges for both students and educators, such as the necessity of understanding abstract properties of quantum systems. To provide a more intuitive understanding of quantum systems, a multitude of qubit representations have been developed in recent years. Given the diversity of the field, a specific representation may be more suitable in one content area of than in another. Consequently, the choice of representation may vary considerably depending on the course orientation. However, no exhaustive analysis has been conducted into the differences between the representation of single- and multi-qubit systems in higher education QIST courses. Furthermore, the factors which influence the selection of a suitable representation remain open. To close this gap, we conducted an online survey with 25 educators at different German and Austrian universities on their use of representations in QIST-related courses. The results confirm the pivotal role of mathematical formalism in QIST education regardless of the specific course characteristics but also reveal an untapped potential for enhancing student learning through the intentional and comprehensive use of multiple external representations (MERs), especially in the case of multi-qubit systems. The findings are discussed within the context of the field of QIST and current insights into learning with MERs.
Abstract The field of Quantum Information Science and Technology (QIST) education presents unique challenges for both students and educators, such as the necessity of understanding abstract properties of quantum systems. To provide a more intuitive understanding of quantum systems, a multitude of qubit representations have been developed in recent years. Given the diversity of the field, a specific representation may be more suitable in one content area of than in another. Consequently, the choice of representation may vary considerably depending on the course orientation. However, no exhaustive analysis has been conducted into the differences between the representation of single- and multi-qubit systems in higher education QIST courses. Furthermore, the factors which influence the selection of a suitable representation remain open. To close this gap, we conducted an online survey with 25 educators at different German and Austrian universities on their use of representations in QIST-related courses. The results confirm the pivotal role of mathematical formalism in QIST education regardless of the specific course characteristics but also reveal an untapped potential for enhancing student learning through the intentional and comprehensive use of multiple external representations (MERs), especially in the case of multi-qubit systems. The findings are discussed within the context of the field of QIST and current insights into learning with MERs.
The rapid growth of quantum information science and technology (QIST) presents unique educational challenges as it brings together students and researchers from many disciplines. This work presents findings from in-depth interviews with leading quantum researchers who are also educators, whose perspectives provide guidance for developing a framework for interdisciplinary QIST teaching and builds on our earlier paper that focused on QIST courses and curricula. We discuss quantum educators’ reflections on three critical aspects of QIST education: (1) the development of a common interdisciplinary language, (2) determining appropriate levels of abstraction and physical detail for diverse student populations from various disciplines, and (3) why students should pursue courses, degrees, and careers in this rapidly evolving field. Our analysis reveals that the emergence of linguistic evolutions such as “qubits” and “measurement bases”, rather than a focus on measurement of physical observables and their corresponding Hermitian operators, has begun to create a unifying framework that transcends disciplinary boundaries. Nevertheless, educators face ongoing challenges in balancing the level of abstractness with physical details as well as mathematical rigor with conceptual accessibility, particularly when teaching foundational QIST courses to an interdisciplinary group of students. The experts emphasize that successful QIST education for an interdisciplinary student body not only requires a shift from traditional quantum mechanics pedagogy for physics majors, but careful consideration of students’ diverse prior conceptual and mathematical foundations overall. They encourage students to pursue QIST related courses, degrees, and careers, highlighting the unique historical opportunity to participate in creating transformative quantum technologies while developing transferable skills for an evolving technological landscape. These findings provide valuable guidance for developing a framework for interdisciplinary QIST teaching especially useful for foundational courses.
In the rapidly evolving interdisciplinary field of quantum information science and technology, a major obstacle is the need to understand advanced mathematics to solve complex problems. Current findings in educational research suggest that incorporating visualizations into problem-solving settings can have beneficial effects on students’ performance and cognitive load compared to relying solely on symbolic problem-solving content. Visualizations like the (dimensional) circle notation enable us to represent not only single-qubit but also more complex multiqubit states, entanglement, and quantum algorithms. In this pilot study, we aim to take an initial step toward identifying the contexts in which students benefit from the presentation of visualizations of single- and multiqubit systems in addition to mathematical formalism. For this purpose, we propose a set of test items and a comprehensive methodology to assess students’ performance and cognitive load when solving problems. This is a pilot investigation with a large breadth of questions intended to generate hypotheses and guide larger-scale, more focused studies in the future. Specifically, we compare two approaches: using the mathematical-symbolic Dirac notation alone and using it in combination with the (dimensional) circle notation. In surveys in one-, two- and three-qubit systems, we gather qualitative data from five, five and two think-aloud interviews, identifying problems that students encounter and their problem-solving strategies. In addition, we analyze quantitative data (performance and cognitive load) from 23, 27, and 17 participants in surveys on one-, two-, and three-qubit systems recruited mainly from our quantum computing lectures. We find that most of the test items are appropriate for a heterogeneous target group, as they can differentiate between participants in terms of performance and time taken. In general, the A-B crossover structure of the study is suitable for investigating the benefits of visualization for problem solving with regard to length and feasibility. Future studies should, however, be narrower in scope, given the observable dependence on student characteristics and context, with particular interest lying in the further investigation of the Hadamard gate, the gate, and entanglement in multiqubit systems.
Abstract The revolutionary new field of quantum computing (QC) continues to gain attention in industry, academia, and government in both research and education. At educational institutions, there is a proliferation of introductory courses at various academic levels signaling a growing interest and recognition of the significance of this field. A crucial and often overlooked aspect is the development of research-based materials and pedagogical approaches to effectively teach the complexities of QC to diverse cohorts of learners across multiple disciplines. There is a great need for empirical investigations of the effectiveness of learning materials and pedagogical approaches in this new interdisciplinary field. We present an empirical investigation done at an R1 institution using the multiple case study method. We compare a case study on students in an introductory QC course without research-based mini-tutorials to a study of students taking the QC course with research-based mini-tutorials. We compare the strengths and difficulties of students in the two courses, discuss the general strengths and difficulties of students across both courses, postulate the effectiveness of the mini-tutorials and discuss how they can be revised. Strengths across both classes include the ability to apply single-qubit and two-qubit gates, favoring application of Dirac notation, and a reasonable understanding of normalization, probability and teleportation described qualitatively. Difficulties across both classes included use of matrix representation, use of rotation gates, and an ability to recall and analyze quantitatively a circuit representing teleportation. We postulate that the mini-tutorials on gates, normalization, probability and a qualitative description of teleportation may have been effective in increasing students’ understanding of the concepts. We also identify mini-tutorials that may need revision.
Quantum mechanics (QM) has taken on a paradigmatic role in how physics describes and builds new knowledge about the world. It also has a growing role in our society thanks to recent and rapid developments in the field of new quantum technologies. These are becoming increasingly important in our society, in the world of work and which will also decisively influence future socio-economic choices. Also for this reason QM has an increasing role in the education of young people and has been introduced in many different ways also in secondary school in all continents. The change in the theoretical and cultural frame has profound implications that are often not intuitive, which involve the appropriation of a specific way of thinking. Neither macroscopic phenomenology, nor intuition help, because there is no simple evidence of how quantum objects must be thought to interpret that unobservable microscopic world and for which we must enter another interpretative paradigm even if we want to limit ourselves to describe it. PER has carried out several studies on the learning of key concepts, on the learning nodes, the ways of reasoning, the difficulties of the students, their spontaneous ideas, according to two main strands: above all at university level, conceptual difficulties and misunderstandings often linked to a formal approach, which, moreover, underpins the very nature of the entities involved; at secondary school level in relation to how students acquire a quantum view of phenomena on the basis of specific approaches adopted to address QM. In particular, a vast literature, which has increased considerably and especially in relatively recent times, has studied how university students deal with certain concepts such as that of state, superposition, measurement in quantum mechanics rather than how quantum quantities evolve over time. These studies are based on the use of questionnaires that allow to explore different levels: the verbal, formal and representative one, with different representations (eg. wave function, Dirac notation), rather than different representative modes (eg. Graphs of probability amplitudes, or probability distributions). At the secondary school level, the most important studies on student learning were instead conducted evaluating the educational impact and outlining the learning paths of students who had followed formative activities based on differentiated innovative research-based educational paths. In particular, the learning outcomes were compared to those activated by proposals based on the historical reconstruction approach of quantum physics. This approach is privileged in traditional curricula and school texts and consequently in the ways of teachers approaching the topic. It was developed in schools with a narrative or descriptive dimension of solutions based on old physics of quanta for the interpretation of phenomena not explained by classical physics. The innovative approaches instead make use of contexts whose formal treatment is simple (quantum properties described in a two-state space such as polarization or spin) with the aid of simulations that compensate for the problem of students” limited mathematical-formal skills, avoiding any historical reference. In particular, there is a significant difference between the survey tools and the survey contexts in the high school environment compared to surveys conducted with university students. This paper presents a review of the research literature, focusing in particular on the learning processes of secondary school students and outlining how research perspectives have evolved.
Abstract As the field of quantum information science and engineering (QISE) continues its rapid growth, there are increasing concerns about the workforce demands and the necessity of preparing students for quantum-related careers. Given the interdisciplinary nature of the field, it is necessary to offer diverse educational opportunities to ensure that students are well-prepared for careers emerging from the second quantum revolution. In this paper, we present our findings from a qualitative study involving semi-structured interviews with university QISE educators, who have taken on the challenges and opportunities in developing QISE courses and curricula for undergraduate and graduate students from different academic backgrounds. Our findings focus on common themes across undergraduate and graduate QISE education, as well as advising and mentoring students to prepare them for research in the field. The interviewees discussed the various strategies they had implemented, such as incorporating hands-on lab activities, integration of Python coding with Qiskit, and including project-based learning experiences. Furthermore, their reflections on mentorship and advising students emphasized the importance of recognizing students’ prior preparation, providing targeted resources, and supportive learning environments. Our findings are meant to provide guidance for educators looking to implement effective QISE educational strategies that address the changing landscape of quantum information revolution.
[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of QISE, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a Quantum Interactive Learning Tutorial, on the basics and applications of quantum computing. These include an overview of key quantum mechanical concepts relevant to quantum computation (including ways a quantum computer is different from a classical computer), properties of single- and multiqubit systems, and the basics of single-qubit quantum gates. The tutorial uses guided inquiry-based teaching-learning sequences. Its development and validation involved conducting cognitive task analysis from both expert and student perspectives and using common student difficulties as a guide. For example, before engaging with the tutorial, after traditional lecture-based instruction, one reasoning primitive that was common in student responses is that a major difference between an N -bit classical and N -qubit quantum computer is that various things associated with a number N for a classical computer should be replaced with the number 2 N for a quantum computer (e.g., 2 N qubits must be initialized and 2 N bits of information are obtained as the output of the computation on the quantum computer). This type of reasoning primitive also led many students to incorrectly think that there are only N distinctly different states available when computation takes place on a classical computer. Research suggests that this type of reasoning primitive has its origins in students learning that quantum computers can provide exponential advantage for certain problems, e.g., Shor’s algorithm for factoring products of large prime numbers, and that the quantum state during the computation can be in a superposition of 2 N linearly independent states. The inquiry-based learning sequences in the tutorial provide scaffolding support to help students develop a functional understanding. The final version of the validated tutorial was implemented in two distinct courses offered by the physics department with slightly different student populations and broader course goals. Students’ understanding was evaluated after traditional lecture-based instruction on the requisite concepts and again after engaging with the tutorial. We analyze and discuss their improvement in performance on concepts covered in the tutorial. Published by the American Physical Society 2024