Build the SWAP test

The register has three qubits, all starting in $\lvert0\rangle$; qubit $0$ is the most significant bit, so $\lvert c\,a\,b\rangle$ has index $4c+2a+b$.

• qubit $0$ is the ancilla;
• qubit $1$ holds $\lvert\psi\rangle=R_Y(\pi/3)\lvert0\rangle=\frac{\sqrt3}2\lvert0\rangle+\frac12\lvert1\rangle$, prepared by the locked first operation $R_Y(1,\pi/3)$, which you must not edit or remove;
• qubit $2$ holds $\lvert\phi\rangle=\lvert0\rangle$.

Append the SWAP test so that the probability of measuring the ancilla in $\lvert0\rangle$ equals

$P(0)=\frac12\big(1+\lvert\langle\psi\vert\phi\rangle\rvert^2\big)=\frac12\Big(1+\cos^2\frac\pi6\Big)=\frac78=0.875.$

Allowed gates after the preparation: $H$, $\mathrm{CSWAP}$ (control first, then the two swapped qubits), $\mathrm{CNOT}$ and $\mathrm{CCX}$; at most $5$ gates; no measurements (the grader reads the exact pre-measurement state).

p-ancilla: the marginal distribution of qubit $0$ must be $\big(\frac78,\frac18\big)$ within $10^{-6}$.

z-ancilla: the expectation value $\langle Z\otimes I\otimes I\rangle=P(0)-P(1)$ must be $\frac34$ within $10^{-6}$; it carries the same information as the marginal and is used for targeted feedback.