Ramanujan quantum expanders from the Weil representation

For every odd prime power $q$ and $D=q+1$, we construct an infinite family of Ramanujan quantum expanders of degree $D$. The construction transfers Morgenstern’s Ramanujan Cayley graphs on ${\mathrm{PSL}}_2({\mathbb{F}}_p)$ for $p$ which is an even power of $q$, through the odd irreducible subrepresentation of the Weil representation of ${\mathrm{SL}}_2({\mathbb{F}}_p)$. For a quantum expander of dimension $N$, our implementation uses $O({\log }^{2}N)$ elementary gates, and $O(\log N)$ ancilla qudits, using a fixed finite gate set depending on $q$. An advantage compared to the previous work of Iyer, Jain, Jordan, and Somma (FOCS 2026) is that assuming the quantum circuit is implemented exactly, we satisfy the $2\sqrt{D-1}\mathrm{/}D$ singular value bound exactly without any additive error.