Sum of quadratic residues

Let $\displaystyle p$ be a prime, $\displaystyle \[p \equiv 1\bmod 4\]$ and consider $\displaystyle \[{\mathbb{Z}_p}\]$.

Let $\displaystyle Q_{p}$ be the set of all quadratic residues (non-zero squares) in $\displaystyle \[{\mathbb{Z}_p}\]$.

I would like to know if there is a way to list down the elements of $\displaystyle Q_{p}$ in such a way that the difference of any two consecutive elements in the list is also a quadratic residue.

Is this already a theorem? Or are there any theorems that might be relevant in finding a solution for this?

Thanks in advance.