Simple question on the phrasing on a PBS Infinite Series video
The state of an $n$-qubit system is a superposition of the $2^n$ pure states
$$
\sum_{x \in \{0,1\}^n} \alpha_x \left| x \right\rangle,
$$
where the $\alpha_x$ are complex numbers satisfying $\sum_x |\alpha_x|^2 = 1$. The $2^n$-dimensional (complex) sphere is just
$$
\{ (\alpha_{0\dots0},\ldots,\alpha_{1\dots1}) \in \mathbb{C}^{2^n} : \sum_x |\alpha_x|^2 = 1 \}.
$$
I'm not sure what "finding" $\left|010001\right\rangle$ on the sphere means, though.