What The Controlled Not DoesThe CNOT operator does not create a cause-effect relationship. It does not even have a directed effect. It's only a simple swap of amplitudes. But one that produces Boolean logic, phase kickback, or entanglement, depending on how you look at it. look at what it is instead.October 7, 2025

Dear Quantum Machine Learner,

In the previous post, we looked at what the CNOT Operator Really is. Surprisingly, the controlled-Not operator is simply a swap of the two ampliutudes where the control qubit is in state

But this technical description does not explain the effects the CNOT seems to have. Apparently, we can use it to implement
• Boolean logic,
• Phase Kickback, and
• to create Entanglement.

In today's post, we shed light on these different effects the controlled-Not operator can have. Of course, I also prepared a PDF companion for this post.

—Frank ZickertAuthor of PyQML