4 problems

Linear-graph connection optimality conjecture. No other graph on $n$ qudits requires more connections to form an $\epsilon$-approximate $t$-design than the linear graph, which requ…

Let $G_{\star}$ be a star graph with $n_{\star}$ vertices, local dimension $q$, and moment $k$, and let $\Delta(G_{\star},n_{\star},k)$ denote its spectral gap. Higher-moment star-…

For a star graph $G_{\star}$ with $n_{\star}$ vertices, let $\Delta(G_{\star},n_{\star},k)$ denote the spectral gap of its Hamiltonian at moment $k$. Low-moment star graph conjectu…

Let … be the Hamiltonian associated with a one-dimensional local random circuit, where $T_k^{(i,i+1)}$ acts on neighboring sites. Let the circuit have open boundary conditions, and…