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Can a controlled-not gate affect the control qubit? Student resources for understanding controlled-not

Soren S. Plueger1, Bethany R. Wilcox1, Steven J. Pollock1, and Gina Passante2,*

  • *Contact author: gpassante@fullerton.edu
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Phys. Rev. Phys. Educ. Res. 22, 020145 – Published 9 October, 2026

DOI: https://doi.org/10.1103/6tn7-klxh

Abstract

The controlled-not (cnot) gate is essential to algorithms in quantum computing for its ability to entangle qubits. As such, it is important to understand how students learning quantum computing reason around the function and use of this critical quantum gate. To investigate this, we conducted think-aloud interviews in which students solved problems involving the cnot gate to understand students’ “cnot toolbox”—the strategies and cognitive resources students use when reasoning about the effect of the cnot gate. We identify three cognitive resources related to the cnot gate: (1) the procedural resource of applying cnot to specific states, (2) a qualitative description of cnot’s effect on the target qubit given the control qubit, and (3) the idea that the control qubit is not changed when cnot is applied to computational basis states. We find that students’ use of the first resource is foundational to their understanding of the second and third, that the second and third resources can sometimes lead students to incorrect conclusions, and that students can use each of these resources separately or in tandem. We also explore how students use these resources in conjunction with Dirac notation, superposition states, and entanglement to reason both productively and unproductively about quantum computing problems.

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Phys. Rev. Phys. Educ. Res. 22, 020145– Published 9 October, 2026
  • Received 17 April 2026
  • Accepted 4 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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