For this problem, we follow the procedure given in the "Measurements in Arbitrary Orthogonal Bases" section of the Kata.
As noted in the solution of the "Distinguishing Orthogonal States: 2" exercise, the gate $R_x(-\theta)$, with $\theta = 2\alpha$ transforms the $\ket A/\ket B$ states to the $\ket 0/\ket 1$ states:
$$R_x(-\theta) \ket A = \ket 0,$$
$$R_x(-\theta) \ket B = \ket 1.$$
Hence, we first apply $R_x(-\theta)$ to the qubit. Next, we measure in the computational basis using the `M` operation.
If the `M` operation returned `Zero`, we get measurement outcome $A$, and if it returned `One`, we get measurement outcome $B$.

After the measurement, we apply the inverse of the $R_x(-\theta)$ gate, which is the $R_x(\theta)$ gate.
The final rotation ensures that the state of the qubit is in the state corresponding to the measurement outcome.

@[solution]({
    "id": "single_qubit_measurements__a_b_basis_measurements_solution",
    "exerciseId": "a_b_basis_measurements",
    "codePath": "Solution.qs"
})
