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The challenging task of investigating student thinking: an example from quantum computing

Josephine C. Meyer, Steven J. Pollock, Bethany R. Wilcox, Gina Passante

Abstract

Physics education research (PER) studies how students learn physics, yet the nuances of student reasoning can be notoriously difficult to probe even for PER practitioners. This article presents the story of Item 15 on the Quantum Computing Conceptual Survey (QCCS). This assessment item underwent more revision and discussion within the team than the remaining 19 assessment questions combined. This paper provides a behind-the-scenes look at the development of this assessment question: a story that reveals not only interesting findings about student reasoning in quantum computing (specifically, the phenomenon of phase kickback) but provides a cautionary tale for any instructor or researcher attempting to evaluate student reasoning in physics through a multiple-choice test item.

The challenging task of investigating student thinking: an example from quantum computing

Abstract

Physics education research (PER) studies how students learn physics, yet the nuances of student reasoning can be notoriously difficult to probe even for PER practitioners. This article presents the story of Item 15 on the Quantum Computing Conceptual Survey (QCCS). This assessment item underwent more revision and discussion within the team than the remaining 19 assessment questions combined. This paper provides a behind-the-scenes look at the development of this assessment question: a story that reveals not only interesting findings about student reasoning in quantum computing (specifically, the phenomenon of phase kickback) but provides a cautionary tale for any instructor or researcher attempting to evaluate student reasoning in physics through a multiple-choice test item.
Paper Structure (17 sections, 1 equation, 5 figures, 2 tables)

This paper contains 17 sections, 1 equation, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Quantum Computing Conceptual Survey
  3. A primer on quantum computing
  4. Understanding phase kickback
  5. CNOT gate
  6. Phase kickback
  7. Our assessment objectives
  8. Designing high-quality multiple-choice items
  9. Context
  10. Statistical metrics
  11. Results and discussion
  12. QCCS version 1.0 (fall 2023)
  13. QCCS version 2.0 (spring 2024)
  14. QCCS version 2.1 (fall 2024)
  15. QCCS version 2.2 (spring/fall 2025)
  16. ...and 2 more sections

Figures (5)

  • Figure 1: A sample quantum circuit diagram. Here, $|\psi_{in}\rangle$ and $|\psi_{out}\rangle$ are unknown states. An ancilla qubit is initialized in the $|0\rangle$ state and then a series of unitary gates $U$, $V$, and $W$ are applied: $U$ is applied only to the bottom qubit, $V$ is a 2-qubit gate, and $W$ is separately applied to each qubit. Accordingly, at time $t_0$, the system is in the state $(W\otimes W)V(I\otimes U)[|\psi_{in}\rangle\otimes|0\rangle]$ where $I$ denotes the identity. Finally, the ancilla qubit's state is measured, collapsing the top qubit back into a single-qubit state $|\psi_{out}\rangle$. In general, $|\psi_{out}\rangle$ depends on the value of the measurement, a useful property in algorithms.
  • Figure 2: Piloted versions of Item 15 during the initial fall 2023 pilot semester (v1.0).
  • Figure 3: Piloted version of Item 15 during the spring 2024 pilot semester (v2.0), featuring two distinct but parallel subitems and a modified circuit diagram with specified input state.
  • Figure 4: Piloted version of Item 15 during the fall 2024 pilot semester (v2.1).
  • Figure 5: Piloted version of Item 15 during the 2025 pilot semester (v2.2).