Picturing The Future Quantum Workforce: Visual Thinking May Help Break Quantum Education Barrier

Insider Brief

• A new study found that high school students can learn core quantum computing concepts using diagram-based instruction without prior knowledge of advanced mathematics.
• The Quantum Picturalism (QPic) method enabled 82% of students to pass a post-training exam, with 48% achieving distinction after eight weeks of tutorials.
• Researchers concluded that QPic reduces cognitive barriers and increases student motivation, suggesting it could broaden access to quantum education and support STEM workforce development.

If the quantum era does take hold, it will need more people who are proficient in quantum science. Now, a new study suggests high school students can master the principles of quantum computing without learning complex mathematics, if the material is taught in pictures.

Researchers from Quantinuum, University of Oxford, and University College London tested a new teaching framework called Quantum Picturalism (QPic), which replaces traditional equations with diagrams. In an eight-week training program for 54 students aged 16 to 18, 82% passed a post-training exam and nearly half achieved distinction. The findings, detailed in a study uploaded to arXiv, point to a promising alternative for expanding access to quantum science education and building a broader STEM talent base.

“This study demonstrates that a complex theory, often perceived as intimidating or highly mysterious, can be taught rigorously in a fun and engaging way,” the researchers write. “It could also play a pivotal role in mitigating workforce shortages by accelerating the integration of learners and developers into emerging computational domains.”

Diagrams Instead of Dirac Notation

Quantum mechanics is typically reserved for university students with advanced training in math. The standard method — a system based on linear algebra called Hilbert space formalism — requires fluency in vectors, matrices, complex numbers and linear algebra. These barriers leave most high school students locked out of learning real quantum information science and technology (QIST).

QPic takes another approach by using diagrammatic reasoning, drawing from the ZX calculus, a form of category theory, which helps model complex structures through diagrams and logic. Each diagram corresponds to a matrix, and diagrammatic rules allow students to manipulate quantum operations visually. The result: students can perform quantum teleportation and understand entanglement without solving matrix equations.

“Its significance lies in that a field as complex as Quantum Information Science and Technology (QIST), for which educational opportunities are typically exclusive to the university level and higher, can be introduced at high school level,” the researchers report.

The approach has already been used in university courses across Oxford, Amsterdam, Cambridge and Indiana University, and in programs at Google and Quantinuum for tasks like quantum circuit optimization. But the educational efficacy of QPic for pre-university students had never been formally tested — until now.

Methods and Participants

The study recruited 75 UK students through an application process, with 54 ultimately completing the course. The program ran from June to August 2023 and consisted of 16 hours of live tutorials over eight weeks. Students studied one to four hours a week and came from a mix of public and private schools, with more than half attending government-funded state schools.

Most students had little to no prior knowledge of QIST, and many were unfamiliar with the mathematical tools typically required. Despite this, they were able to complete advanced quantum reasoning problems through QPic’s diagram-based system.

The study explains that just eight rules in the ZX calculus are sufficient to express all of qubit quantum mechanics, including concepts like decoherence and the Stern-Gerlach experiment.

Final assessment included a rigorous exam, double-blind marked by quantum computing professors. The average score was 58%, significantly above chance, with 48% of participants scoring above 70%. Canary questions ensured participants had a real grasp of the material.

Wider Access and Workforce Impact

The implications extend beyond pedagogy. By eliminating advanced math as a prerequisite, QPic could make quantum education more equitable and widespread. Fewer than 5% of UK state school students take Further Mathematics, where matrices are taught. QPic bypasses this bottleneck entirely.

The study’s findings support national and international calls to address the quantum workforce gap by starting earlier and reducing cognitive barriers. A majority of students said the course increased their motivation to study QIST and pursue STEM careers. Those with initially little knowledge of quantum concepts showed marked improvement and increased confidence.

“QPic has the potential to facilitate new cross-skilling opportunities for both developers and learners,” the authors noted.

Educational and Cognitive Foundations

The study highlights that the benefits of QPic may come from deep cognitive processes. The authors link the method to principles from Gestalt psychology and dual coding theory, suggesting diagrams align better with how the human brain organizes and processes information—through visual structure rather than symbolic language alone.

This theory—that diagrammatic reasoning taps into nonlinguistic parts of the brain—may explain why students could grasp quantum principles usually deemed inaccessible without years of mathematics. Follow-up neuroimaging studies are being planned to explore this hypothesis further.

Limitations and Next Steps

As this is just a proof-of-concept study, there’s room for future research and refinements, the team points out. For example, the sample size was small and not globally representative. Some students found the tutorials rushed or wished for more practice problems. And while many found the material engaging, a third of students still reported uncertainty about their motivation or confidence levels after the course.

Without a similar study of students using traditional quantum learning methods, it’s difficult to assess the results accurately.

Replications are already underway in other countries, and future work will explore longer courses, different teaching environments, and integration into formal curricula. The researchers also aim to further test QPic’s impact on gender gaps, socio-economic barriers, and long-term interest in quantum careers.

“Although this study serves as proof of concept, we recognize the necessity of substantial data required from diverse age and ability groups across various cultures to thoroughly discuss its educational efficacy. We should highlight that several experiments replicating the present study are currently underway across different countries,” the researchers write.

The study was conducted by Selma Dündar-Coecke, Caterina Puca, Lia Yeh, Muhammad Hamza Waseem, Thomas Cervoni, Vincent Wang-Maścianica, Peter Sigrist, Vincent Anandraj, Ilyas Khan, and Bob Coecke, from Quantinuum in Oxford, United Kingdom; Selma Dündar-Coecke is also affiliated with the Centre for Educational Neuroscience at University College London. Lia Yeh, Stefano Gogioso, and Aleks Kissinger are from the Department of Computer Science at the University of Oxford, while Muhammad Hamza Waseem is also affiliated with the Department of Physics at the University of Oxford. Emmanuel M. Pothos is from the Department of Psychology at City, University of London. Sieglinde M.-L. Pfaendler is with IBM Research in Rüschlikon, Switzerland. Stefano Gogioso is also affiliated with Hashberg Ltd in London. Ferdi Tomassini is with Moth Quantum in London, and Bob Coecke is also affiliated with the Perimeter Institute in Waterloo, Canada.

For more technical detail, read the study on arXiv. Researchers use arXiv and other pre-print servers as a way to receive swift feedback on their work. However, it is not officially peer reviewed, a critical step in the scientific method.