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

The controlled-not () 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 gate to understand students’ “ toolbox”—the strategies and cognitive resources students use when reasoning about the effect of the gate. We identify three cognitive resources related to the gate: (1) the procedural resource of applying to specific states, (2) a qualitative description of ’s effect on the target qubit given the control qubit, and (3) the idea that the control qubit is not changed when 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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