Let $F_k(G)$ be the $k$-token graph of $G$, which has: * ${n \choose k}$ vertices, represented by $S \subseteq [n]$ of size $|S| = k$ * each edge $(S,T)$ is where the symmetric difference of S and T is an edge of $G$.
Suppose $G$ has $m$ edges. Prove that the eigenvalues of the Laplacian of $F_k(G)$ are all at most $m + k$.
As discussed by APS25, this bound would imply better algorithms for the Quantum Maximum Cut problem.