PreprintCC BY 4.0arXiv
Ramanujan quantum expanders from the Weil representation
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 PSL2(๐ฝp) for p which is an even power of q, through the odd irreducible subrepresentation of the Weil representation of SL2(๐ฝp). For a quantum expander of dimension N, our implementation uses O(log2 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 2โ(Dโ1)/D singular value bound exactly without any additive error.
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BibTeX
@misc{jain2026ramanujan,
title = {{Ramanujan quantum expanders from the Weil representation}},
author = {Siddhartha Jain},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38075},
eprint = {2609.38075},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38075},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ramanujan quantum expanders from the Weil representation
AU - Siddhartha Jain
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38075
UR - https://arxiv.org/abs/2609.38075
AB - 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 PSL_2(๐ฝ_p) for p which is an even power of q, through the odd irreducible subrepresentation of the Weil representation of SL_2(๐ฝ_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 2โ(Dโ1)/D singular value bound exactly without any additive error.
ER -