8 problems

Clifford bound conjecture. The cardinality of any unitary 2-design is at least

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 $n$ be the number of qubits in the brickwork model, let $t$ denote the circuit depth or number of layers, and let…

Let $K_n$ be the complete graph on $n$ vertices, and consider a gadget associated with a family of 2-local gates having parameter $a=\frac{5}{9}$ in the notation of the paper. Let…

Let $n\geq 3$, let $\mathcal{G}$ be a fixed connected graph, and let $\mathcal{E}$ be a 2-local unitary circuit ensemble. Write…

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…