Can a CNOT Gate Affect the Control Qubit? Student Resources for Understanding CNOT and Entanglement

TL;DR

This study investigates how students understand the CNOT gate in quantum computing, identifying key reasoning resources and common misconceptions through think-aloud interviews.

Contribution

It reveals the cognitive resources students use to reason about CNOT and how these can lead to correct or incorrect conclusions, informing teaching strategies.

Findings

Students rely on procedural, qualitative, and control qubit invariance resources.

Use of these resources can lead to correct or incorrect reasoning about CNOT.

Students' reasoning varies when using Dirac notation, superpositions, and entanglement.

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.