Visualizing Quantum States: A Pilot Study on Problem Solving in Quantum Information Science Education (2406.16556v2)

Abstract: In the rapidly evolving interdisciplinary field of quantum information science and technology, a big obstacle is the need to understand high-level mathematics to solve complex problems. Current findings in educational research suggest that incorporating visualizations in settings of problem solving can have beneficial effects on students' performance and cognitive load compared to solely relying on symbolic problem solving content. Visualizations like the (dimensional) circle notation enable us to represent not only single-qubit but also complex multi-qubit states, entanglement, and quantum algorithms. In this pilot study, we aim to take a first step to identify in which contexts students benefit from the presentation of visualizations of single- and multi-qubit systems in addition to mathematical formalism. For this purpose, we propose test items and a complete 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 but more concrete studies in the future. Specifically, we compare two approaches: using the mathematical-symbolic Dirac Notation alone and using it accompanied by the (dimensional) circle notation. Analyzing time and performance, we find that most of the test items are appropriate for a heterogeneous target group as they can differentiate between the participants in regard to 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 respect to length and feasibility. Future studies should, however, be more restricted in context because of the observable student and context dependence, with special interest lying in the further investigation of the Hadamard gate, the CNOT gate, and entanglement in multi-qubit systems.