Visualizing quantum states: A pilot study on problem solving in quantum information science education

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.