Basis-encode the bit string 1011

Starting from $\lvert0000\rangle$, prepare the basis encoding of the bit string $x=x_0x_1x_2x_3=1011$:

$\lvert1011\rangle=\lvert1\rangle\otimes\lvert0\rangle\otimes\lvert1\rangle\otimes\lvert1\rangle=e_{11}\in\mathbb C^{16},$

the column vector with a $1$ in position $k=\sum_{j=0}^{3}x_j2^{3-j}=8+0+2+1=11$ (counting from $0$) and $0$ everywhere else. Qubit $j$ carries bit $x_j$, and qubit 0 is the leftmost, most significant bit.

Only $X$ gates are allowed, at most three of them. The grader computes the fidelity $F=\lvert\langle1011\vert\psi\rangle\rvert^2$ of your final state $\lvert\psi\rangle$ and requires $F\ge1-10^{-6}$.