Theta value passed as input to quantum phase estimation: qiskit textbook

Question

I'm trying to understand the Quantum Phase Estimation in the qiskit textbook https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html.

I know QPE is used to estimate the $\theta$ given the operator $U$ in $U|\psi\rangle = e^{2 \pi i \theta} |\psi\rangle$, but when I see the code for the problem in the same link further below, the theta is passed as input to the creation of the Controlled U gates (the variable 'angle' in the code snippet in the below link).

https://qiskit.org/textbook/ch-algorithms/quantum-phase-estimation.html#3.1-The-Problem-

We are trying to estimate the angle theta but then again we are passing the same as an input to the code. Isn't this cheating? What am I misunderstanding?

In the example, we know what the $\theta$ is but in the real world scenarios, will we not have only $\psi$ and no knowledge of $\theta$? How will it work? Please help me understand.

Answer 1

At a glance, it looks like your understanding is correct - they're cheating a bit, using a an operator $U$ which is most straightforwardly defined directly from its $HHHX$ eigenvalue $θ$. This is for pedagogical purposes, so that it's very easy to see on measurement that the program outputs the right answer.

I might suggest a better approach would have been to use a less-straightforward $U$, go through the steps to calculate the classical eigenvalue, then show how much easier it is to ask the quantum computer to do it. But there is a place for both.