Year: 2026
Type: preprint
Abstract: 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 $\operatorname{PSL}_2(\mathbb{F}_{p})$ for $p$ which is an even power of $q$, through the odd irreducible subrepresentation of the Weil representation of $\operatorname{SL}_2(\mathbb{F}_{p})$. 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 $2\sqrt{D-1}/D$ singular value bound exactly without any additive error.
Source: arXiv (Cornell University)
Author: Jain, Siddhartha
Institution: The University of Texas at Austin
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214988857