Visualizing Quantum States: A Pilot Study on Problem Solving in Quantum Information Science Education

TL;DR

This pilot study investigates whether visualizations of quantum states (circle notation CN and dimensional circle notation DCN) augment problem solving and modulate cognitive load when used alongside traditional Dirac notation (DN) in quantum information science education. Using a mixed-methods design with three online MC tests (one-, two-, and three-qubit) and think-aloud interviews, the authors assess representational and connectional understanding, cognitive load, and time-to-solve across CN, DCN, and DN conditions. Results indicate context- and learner-dependent effects: some tasks show improved strategies and reduced cognitive load with visualization, especially for entanglement and multi-qubit operations, while other tasks show no benefit or even increased load or time, highlighting the importance of representational competence and task design. The study provides validated instruments and a framework for progressively targeted future work to identify when and how visualizations best support qist education, with implications for designing instructional materials and assessments that leverage multiple external representations. Overall, the findings suggest visualizations can be a valuable complement to symbolic problem solving in qist, particularly in multi-qubit contexts, but benefits depend on learner prerequisites, task demands, and careful integration with existing notation.

Abstract

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 multi-qubit 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 multi-qubit 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...

Figures (23)

• Figure 1: Overall structure of the study. In the two-, and three-qubit surveys, the participants were first grouped into cn or dcn randomly. During all surveys, the participant group(s) was/were split during the main parts of the studies into group vis-math or group math-vis, depending on whether they were presented with or without visualization first. The questions within one of the parts A or B only differed in whether they were with visualization or not. This results in two groups in the one-qubit survey and four groups in the two- and three-qubit surveys. $^*$Representational understanding was only tested in the one-qubit survey.
• Figure 2: The state $\ket{\psi}=\frac{1}{3}\ket{00}+\frac{1}{3}e^{i\pi/2}\ket{01}+\frac{1}{\sqrt{3}}e^{-i\pi/4}\ket{10}-\frac{2}{3}\ket{11}$ in cn (left) johnston_harrigan_gimeno-segovia_2019 and in dcn (right). The qubits are ordered in from right to left, $\ket{\#2\#1}$.
• Figure 3: The X, Z, and H gate in a single-qubit system in cn.
• Figure 4: Introductory example slide for the action of single-qubit gates in two-qubit systems visualized in dcn.
• Figure 5: Introductory example slide for measurements in two-qubit systems visualized in dn.