I get stuck on the "Applying Hadamard Twice" lesson, which assertss "Applying Hadamard twice [on a qubit] returns the qubit to its initial state again. From this we can conclude that the information stored in the qubit has not been lost."
The article doesn't explain what a Hadamard Gate is actually physically doing to the qubit. Without that information, I do not draw the same conclusion that a qubit's storing and retaining any useful information. Instead, I'd assume that the Hadamard gate is (somehow?) sensing if a qubit is in a superposition or collapsed stated, and then it inverts that state (i.e. from a superposition to a collapsed state or from a collapsed state back into a superposition).
I'm not saying that's the correct assumption, I'm just pointing out some incomplete logic in the lessons that's prohibiting me from proceeding with this lesson plan until I can definitively rule out the possibility that the Hadamard gate itself is not introducing the information back into the qubit.
I supposed if you used an example of a 2 qubits (qbit A originally in a 50/50 superposition and qbit B in a 25/75 superposition), then showed that that the two H gates in series able to restore the original states every time - that would allow me to agree with your logical deduction that a qubit's information is not lost when H gates are applied. Since that's not included in this lesson, I'm going to need to exit and go hunt for that answer elewhere on the interwebs.
I do like this lesson set-up though. That's been my only hang-up thus far.
The article doesn't explain what a Hadamard Gate is actually physically doing to the qubit. Without that information, I do not draw the same conclusion that a qubit's storing and retaining any useful information. Instead, I'd assume that the Hadamard gate is (somehow?) sensing if a qubit is in a superposition or collapsed stated, and then it inverts that state (i.e. from a superposition to a collapsed state or from a collapsed state back into a superposition).
I'm not saying that's the correct assumption, I'm just pointing out some incomplete logic in the lessons that's prohibiting me from proceeding with this lesson plan until I can definitively rule out the possibility that the Hadamard gate itself is not introducing the information back into the qubit.