Purify a mixed qubit

Starting from $\lvert00\rangle$, build a circuit with at most four gates from $\{R_Y,R_X,R_Z,H,X,\mathrm{CNOT},\mathrm{CZ}\}$ whose output $\lvert\psi\rangle$ is a two-qubit pure state with reduced state on qubit 0

$\rho_0=\mathrm{Tr}_1\lvert\psi\rangle\langle\psi\rvert=\begin{pmatrix}\tfrac34&0\\0&\tfrac14\end{pmatrix}.$

Qubit 0 is the leftmost bit, and the components of the partial trace are $(\rho_0)_{aa'}=\sum_b\psi_{(a,b)}\overline{\psi_{(a',b)}}$. The check computes the trace distance $T(\rho_0,\sigma)=\tfrac12\sum_i\lvert\lambda_i(\rho_0-\sigma)\rvert$ to the target $\sigma$ and accepts $T\le10^{-6}$.