7 problems

A graph state is a stabilizer state associated with a graph, and two stabilizer states are LU-equivalent if they differ by a tensor product of single-qubit unitary operators, while…

Let $G$ be a graph, let $V_G$ denote its vertex set, and let $|\chi\rangle$ be a magic graph state whose parameters are varied over the collection $\{\theta_{ij}\}$. Let…

Let $\mathcal{F}$ be a proper vertex-minor-closed class of graphs, let $G$ be an $n$-vertex graph in $\mathcal{F}$, and let $\omega$ be an upper bound on the clique number of $G$.…

Let $G$ be an $n$-vertex circle graph, and let $\operatorname{CZ}(G)$ denote its CZ-distance. Circle-graph lower-bound conjecture. There exist $n$-vertex circle graphs $G$ with … T…

The CZ-distance and CZ-complexity of a graph are the two graph-state preparation measures defined in the paper, with CZ-complexity additionally allowing arbitrarily many measuremen…

Let $G$ be sampled uniformly from graph states, and let $d4af$ be the set of eigenstates of the operators $X+Y$ and $X-Y$. For an $n$-qubit product state, write…

Graph-state representation conjecture. Every $n$-qubit Clifford state is equivalent to a state that can be represented with a graph. In particular, it is equivalent to a state that…