Build the product state |+⟩ ⊗ |1⟩

Starting from $\lvert00\rangle=\lvert0\rangle\otimes\lvert0\rangle$, prepare

$\lvert\psi\rangle=\lvert+\rangle\otimes\lvert1\rangle=\frac{1}{\sqrt2}\begin{pmatrix}1\\1\end{pmatrix}\otimes\begin{pmatrix}0\\1\end{pmatrix}=\frac{1}{\sqrt2}\begin{pmatrix}1\cdot0\\1\cdot1\\1\cdot0\\1\cdot1\end{pmatrix}=\frac{1}{\sqrt2}\begin{pmatrix}0\\1\\0\\1\end{pmatrix}=\frac{1}{\sqrt2}\big(\lvert01\rangle+\lvert11\rangle\big).$

Convention: qubit $0$ is the most significant bit, i.e. the left tensor factor, so basis state $\lvert q_0q_1\rangle$ has index $2q_0+q_1$ and a gate $A$ on qubit $0$ with $B$ on qubit $1$ acts as $A\otimes B$.

Allowed gates: $H, X, Y, Z$ (single-qubit only, at most $4$ gates, no two-qubit gates). The grader requires fidelity $\lvert\langle\psi_{\text{target}}\vert\psi\rangle\rvert^2\ge1-10^{-6}$.