Proves Θ(log N) routing number for Ramanujan (d,r)-regular hypergraphs via clique expansion matchings and develops applications to neutral atom qubit routing including virtual overlays, entanglement assistance, and hierarchical methods.
A new proof of Friedman's second eigenvalue Theorem and its extension to random lifts
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abstract
It was conjectured by Alon and proved by Friedman that a random $d$-regular graph has nearly the largest possible spectral gap, more precisely, the largest absolute value of the non-trivial eigenvalues of its adjacency matrix is at most $2\sqrt{d-1} +o(1)$ with probability tending to one as the size of the graph tends to infinity. We give a new proof of this statement. We also study related questions on random $n$-lifts of graphs and improve a recent result by Friedman and Kohler.
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quant-ph 1years
2026 1verdicts
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Permutation Routing on Ramanujan Hypergraphs with Applications to Neutral Atom Quantum Architectures
Proves Θ(log N) routing number for Ramanujan (d,r)-regular hypergraphs via clique expansion matchings and develops applications to neutral atom qubit routing including virtual overlays, entanglement assistance, and hierarchical methods.