The recent paper \cite{chatterjee2026bipartite} showed that deciding whether a bipartite graph has a perfect matching can be reduced to deciding whether a determinant, whose value may be assigned to any sufficiently large field $\mathbb{F}$, equals to zero. In the second part of their work, \cite{chatterjee2026bipartite} also generalized the algebraic method ... more >>>

In this note, we introduce the notion of ranked spreadness, a strengthening of the usual spread condition in which the elements of each member can be ordered so that their one-coordinate marginals decay geometrically with their rank. This additional structure removes the dependence on the maximum set size in random-containment ... more >>>

It is a major challenge in quantum fault-tolerance to obtain low-overhead protocols for performing non-Clifford gates. In this vein, we construct quantum codes with low-weight stabilizers that support transversal (i.e. low-depth) implementations of the non-Clifford $C^{r-1}Z$ gate, for every constant $r\geq 3$. In particular, we obtain length-$n$ quantum LDPC ... more >>>