Quantum Curriculum Innovation - Considerations and Examples

Quantum Curriculum Innovation Consider… a) …targeting multiple skill areas with as much of your included content as possible in the overall course. b) …the background of your students and targeted skills in relation to their previous skill sets. c) …drawing attention to interconnections between the skill areas, like considering hardware restrictions when designing quantum algorithms. Theory & Analytics •Reason logically within quantum theory. •Calculate the outcome of quantum processes analytically. •Connect quantum to classical theory in, e.g., Physics or Information Science. Computation & Simulation •Program simulations of and real quantum computers. •Approximate and simulate quantum systems and processes. •Simulate quantum networks and information distribution. Experiment & Application •Develop and set up quantum technological experiments. •Utilise classical experimental techniques. •Discuss the real-world challenges of different qubit platforms. 2) Targeted skills We model Quantum curriculum innovation on five dimensions: 1) Content, 2) Targeted skills, 3) Targeted level of cognitive ability, 4) Multiple Representations, and 5) Teaching approach. Each of these dimensions contains considerations a, b, c (and d) to constitute a total number of 17 considerations. Note that one consideration is not necessarily more important or more valuable than another and not everything needs to be considered. Any QT topic and subtopic can be taught targeting any of the following three skill areas: European Commission: Directorate-General for Communications Networks, Content and Technology, Greinert, F. and Müller, R., European competence framework for quantum technologies (CFQT) – Reference framework for planning, mapping and comparing QT-related educational activities, personal qualification and job requirements, Publications Office of the European Union, 2024, https://data.europa.eu/doi/10.2759/389764 The Competence Framework for Quantum Technologies (CFQT) divides QT into eight content domains that can be mapped to three proficiency areas. The domains include various subdomains, topics and subtopics. Consider… a) …Qualification profiles: which proficiency level (A1 Awareness to C2 Innovation) your students achieve in the proficiency areas: (I) Quantum Concepts (II) QT hardware & software engineering (III) QT applications & strategies b) …involving your students and their career visions and goals in your curriculum planning. c) …including interconnections between the eight domains. d) …updating the content to the newest advances in the field. e) …covering subdomains of valorisation (domain 8) like responsibility, ethics, and awareness of diversity, equity and inclusion. 1) Content Jonas Bley, Simon Goorney, Aurél Gábris, Stefan Küchemann, Stefan Heusler, Artur Widera, and Jacob Sherson 05th November 2025 For example, if teaching Quantum Teleportation to Physics students, you may want to thematize quantum optical ideas of spontaneous down-conversion and Bell measurements first, and then continue with practical design of the protocol, before describing the more abstract analytics and programming of the algorithm, and discussing practical challenges and applications. For example, after discussion with your Master‘s students, you may decide to aim for the QT engineering professional at the end of the programm (B1in concepts, B2 in hardware & sofware engineering, and A2 in applications). Your content should be designed with this goal in mind, should cover various of the content domains and their interactions, updated to the state-of-the-art (e.g., deep-dives into recent advances in different quantum computing architectures), and include ethical conversations and big-picture discussions. more details at [5] Simon Goorneyet al 2024 Eur. J. Phys. 45 065702 DOI 10.1088/1361-6404/ad7e60 1 05th November 2025 more details at [5] Simon Goorney et al 2024 Eur. J. Phys. 45 065702 DOI 10.1088/1361-6404/ad7e60 2 Quantum Curriculum Innovation Jonas Bley, Simon Goorney, Aurél Gábris, Stefan Küchemann, Stefan Heusler, Artur Widera, and Jacob Sherson •Bloom‘s taxonomy describes different levels of cognitive ability, each being based on the one before. •Action verbs can be mapped to the taxonomy. Example action verbs include: Remember: arrange, outline, identify; Understand: articulate, express, give examples, Apply: implement, modify, demonstrate; Analyse: conclude, diagram, compare; Evaluate: criticise, contrast, rate; Create: hypothesise, invent, design. •In QIST, higher orders of thinking are often necessary for understanding. Newton, P. M., Da Silva, A., & Peters, L. G. (2020). A Pragmatic Master List of Action Verbs for Bloom’s Taxonomy. Frontiers in Education, 5. doi:10.3389/feduc.2020.00107 When designing exercises, consider… a) …thoughtful formulation of exercises such that, starting from the bottom, diversity in levels of cognitive ability is achieved. b) …connections to the other dimensions of this framework, like utilization of multiple representations to foster understanding, or all considerations of dimension 5 for reaching higher levels of Bloom‘s taxonomy. c) …being transparent with the students about the targeted level of cognitive ability for learning units. 3) Targeted Level of Cognitive Ability For example, for each subtopic (dim. 1) and targeted skill (dim. 2), you can design exercises on all levels of Bloom‘s taxonomy. When doing so, consider the qualification profiles you/your students are targeting. You can provide different representations, illustrations and visualizations to highlight different aspects of the protocol (dim. 4) and utilize scaffolding and cooperative learning to help with especially higher levels of Bloom‘s taxonomy (dim. 5). Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198. https://doi.org/10.1016/j.learninstruc.2006.03.001 When designing content, consider… a) …the functions of MERs: using MERs to complement each other, e.g. the Bloch sphere in addition to formulas for gate operations, to constrain interpretation, e.g. to use diagrams when describing an experimental apparatus more precisely, or to construct deeper understanding, e.g. by abstracting quantum circuits with CX calculus. See the next page for example visualizations. b) …designing MERs to reduce unnecessary cognitive load, considering design principles and learner & representational characteristics. c) …utilize scaffolds (see dim. 5) by including visual aids (colors, arrows, etc.), fostering understanding of the representations (representational competence) of your students, or enabling interactivity. 4) Multiple Representations External Representations include, e.g., graphs, text, illustrations, formulas, and audio. It has been shown that under the right conditions, using multiple external representations (MERs) leads to improved learning outcomes. Functions Complement each other •representations support different processes or cognitive strategies •representations show different information Constrain Interpretation •some representations are more precise than others (e.g., most representations are more precise than text) •some representations are more familiar than others Construct Deeper Understanding •using different levels of abstraction •showing relations/connections •some representations as extensions of others Design Number: How many MERs to use Distribution of Information accross MERs Form: E.g. visual, written text or audio Sequence: The order in which to present MERs Translate: Show connections between MERs Cognitive tasks depend on characteristics of the representations and the learners Reduce unnecessary cognitive effort by: •integrating the students and their competence with the representations •using multiple modalities (e.g., visual and audio) •refraining from too much redundancy •reducing spatial & temporal separation Tasks Quantum Curriculum Innovation 05th November 2025 Multiple Representations using the example of Quantum Teleportation The complete protocol in the BEADS representation[1]: In the BEADS representation, single-qubit states are visualized as spheres equivalent to the Bloch sphere (the red pole pointing along the 𝑧axis corresponds to the state 0, the green pole to state 1), and entanglement-based correlation functions are shown with additional spheres (blue for anticorrelation, yellow for correlation). It is embedded into the circuit representation, enabling direct translation between the theoretical protocol and the actions of the gates on the three-qubit quantum states. All possible measurement outcomes are displayed. Last step before measuring in the Dimensional Circle Notation (DCN) In Circle Notation[2], amplitudes in the computational basis are visualized as blue circles (absolute value) with gauges (complex phase). In dimensional notations, every qubit is assigned an axis in space[3]. In Quantum Teleportation, information is transferred from qubit #1 (blue) to qubit #3 (yellow) using only operations qubit #1 and #2. Entanglement can be seen as asymmetry along a particular qubit axis in regard to the corresponding plane (green means separable, red entangled)[4]. All the representations shown on this page complement the text and mathematical symbolism to help students construct deeper understanding. [1] Huber, D., & Glaser, S. J. (2025). BEADS: A canonical visualization of quantum states for applications in quantum information processing. New Journal of Physics, 27(9), Article 094509. https://doi.org/10.1088/1367-2630/ae0514 [2] E. R. Johnston, N. Harrigan, and M. Gimeno-Segovia, Programming Quantum Computers: Essential Algorithms and Code Samples (O'Reilly Media, Sebastapol, 2019). [3] B. Just, Quantum Computing Compact, 2nd ed. (Springer, Berlin, 2023) [4] Bley, J., Rexigel, E., et a. (2024). Visualizing entanglement in multiqubit systems. Physical Review Research, 6(2), Article 023077. https://doi.org/10.1103/PhysRevResearch.6.023077 An illustration of the abstract protocol shows the flow of information and gives an idea of the overall processes involved in the protocol[5]. The more concrete schematic of the experiment shows the necessary experimental elements while still describing the temporal sequences and flow of information[5]. Jonas Bley, Simon Goorney, Aurél Gábris, Stefan Küchemann, Stefan Heusler, Artur Widera, and Jacob Sherson more details at [5] Simon Goorneyet al 2024 Eur. J. Phys. 45 065702 DOI 10.1088/1361-6404/ad7e60 3 Quantum Curriculum Innovation a) …Inquiry-based Learning (IBL) Utilising IBL is essential to promote scientific thinking. •Use the 5E‘s cycle of the scientific method involve 1) Engagement, 2) Exploration, 3) Explanation, 4) Elaboration, and 5) Evaluation. •Inquiry can be more confirmational (e.g., using these given methods, verify that…) or more open (e.g. find out how a given system behaves under certain conditions). •Confirmational inquiry is useful to obtain conceptual and subject knowledge. •Open inquiry is useful to promote scientific thinking. •Digital Modules such as the Quantum Composer, Quantum Odyssey, QuBeads, or QC-SLIM can be used for IBL. b) …Scaffolding Scaffolding is on-demand and personalised support (not giving away answers). •It includes promoting student interest, controlling frustration, providing feedback, helping with prioritisation, offering models of expert processes and encouragement of reflection. •Just the right amount of support should be given, e.g. to reach the next step in Bloom’s taxonomy. •First and foremost, the tasks need to be thoroughly understood. •Forms of scaffolding include One-to-One scaffolding, Peer scaffolding, and Computer (including AI)-based scaffolding. •Interactivity is a type of scaffolding, because it is based on instant feedback. c) …Cooperative Learning Effective cooperative learning improves learning outcomes and teaches essential group-working skills. •It necessitates and promotes a diversity mindset and psychological safety. •Diverse teams are more objective and innovative. •Foster effective cooperative learning in your students by encouraging five elements: 1) positive interdependence, 2) face-to-face promotive interaction, 3) individual accountability and personal responsibility, 4) frequent use of small group social skills, and 5) frequent, regular group discussion of current function. Friesen, S., & Scott, D. (2013). Inquiry-based learning: A review of the research literature. Alberta Ministry of Education, 32, 1-32. Belland, B. R. (2017). Instructional scaffolding in STEM education: Strategies and efficacy evidence (p. 144). Springer Nature. Lee Manning, M., & Lucking, R. (1991). The What, Why, and How of Cooperative Learning. The Social Studies, 82(3), 120–124. https://doi.org/10.1080/00377996.1991.9958320 5) The Teaching Approach: Consider… 05th November 2025 Jonas Bley, Simon Goorney, Aurél Gábris, Stefan Küchemann, Stefan Heusler, Artur Widera, and Jacob Sherson An example teaching approach to a lesson on Quantum Teleportation for an introductory course in quantum technologies for Physics students is described in the following. The lesson may also include other topis. The approach utilizes the 5E cycle and focusses on the skill area of experiment & application with some necessary skill targeting in theory & analytics. The approach utilizes open inquiry, letting students define their own research questions. •Consider previous knowledge: students know about quantum key distribution with the BB84 protocol, Bell states and Bell state mesurements, entangled photon-pair creation and were introduced to Dirac notation and appropriate visualizations. •Engagement: The students listen to an engaging, visual introduction to the Quantum Teleportation protocol (optionally amongside other topics). •Exploration and Explanation: Students work alone to understand the theory of quantum teleportation protocols, and apply analytical knowledge to calculate the gates that are necessary to complete the protocol after measurement (Engagement and Exploration), and work through the Physics of the experimental implementation. •Elaboration: Students then come together in groups to resarch about and discuss real world applications (e.g., for quantum key distribution in quantum networks) and challenges, culminating their discussion in a white paper and a presentation. •Evaluation: The white paper is given to the rest of the class and peer-reviewed. The presentation are held and further scientific discussions and rounds of feedback follow. If other groups have been given other topics, the process is repeated for those. •Scaffolding: Students are given introductory material that is designed to fit their previous knowledge, papers to consider for research, are instructed on possible structures for the white paper and the presentations, and are given instructions for peer-review, e.g., discussions should be based on scientific interest, feedback should be constructive. The educator(s) is/are available for questions during the whole process. more details at [5] Simon Goorneyet al 2024 Eur. J. Phys. 45 065702 DOI 10.1088/1361-6404/ad7e60 4