Train a one-qubit variational classifier

The circuit is fixed: $R_Y$ with the angle given by the data symbol $x$ (parameter x, not trainable), followed by $R_Y$ with the angle given by the weight $\theta$ (parameter theta). Only the value of theta may change; the gates, their order and the parameter x are locked.

The grader binds $x$ to each of the four training points, simulates the state $R_Y(\theta)R_Y(x)\lvert0\rangle$, and predicts $\hat y=\mathrm{sign}\,\langle Z\rangle$:

The check passes when the accuracy is $1$, i.e. all four predictions equal their labels (an output of exactly $0$ counts as wrong). In the lesson it is shown that $\langle Z\rangle=\cos(x+\theta)$, so you need $\cos(x+\theta)<0$ at $x=0.3,\,0.9$ and $\cos(x+\theta)>0$ at $x=1.8,\,2.2$. At the initial value $\theta=0$ the accuracy is $0$.