12 problems

Let $\mathbf{TS}^*$ be a proposed categorical spectrum of topological stabilizer codes, with $\mathbf{TS}^n$ its degree-$n$ component, and let $\mathbf Q^*(\mathrm{pt})$ denote the…

Let $\Omega$ and $\Omega'$ be immersed regions in the $n$-sphere $\mathbf{S}^n$, with axioms ${\bf A0}$ and ${\bf A1}$ satisfied everywhere on the reference state. Let…

Let ${\mathcal L}$ be an immersed annulus, let ${\mathcal C}_{\mathcal L}$ be the superselection sectors detected by it, and let $d_\mu$ be the quantum dimension of $\mu$. Transpor…

Let $\Omega$ and $\Omega'$ be immersed regions in the sphere $\mathbf{S}^2$, and let $\Sigma(\Omega)$ denote the associated information convex set. Strong isomorphism conjecture. I…

Let $X_8$ be the immersed figure-8 annulus in the sphere, let ${\mathcal C}_8$ be the set of superselection sectors detected by $X_8$, and let $d_\mu$ denote the quantum dimension…

Let a two-dimensional Hamiltonian on a spin system satisfy the assumptions denoted by … , and let $\mathfrak A$ be its net of boundary algebras. Write $\mathsf{DHR}(\mathfrak A)$ f…

Let $\mathcal{S}$ be a connected component of the space of two-dimensional gapped Hamiltonians realizing a fixed topological order. Let invertible states be identified under equiva…

FDQC equivalence conjecture. The Hamiltonians $H$ and $H'$ are FDQC equivalent if and only if their surface topological orders in the presence of a gapped boundary are Witt equival…

A state-sum Hamiltonian schema is obtained from a topological state-sum construction: for a cellulation $\Delta$ of a space manifold $Y$, the state-sum on $Y\times I$ defines an id…

A lax-topological $D$-dimensional Hamiltonian schema satisfies $TQO0$, $TQO1$, and $TQO2$, and there exist constants $\alpha$ and $\beta$ depending only on $D$ such that … for ever…

Let ${\cal C}$ be a topological order, and let ${\cal C}_{\boldsymbol a,K}$ and ${\cal C}_{\boldsymbol a',K'}$ be topological orders constructed from ${\cal C}$ using anyon data…

Let $p$ be a prime, and let $\mathfrak C(D,p)$ denote the group of translation-invariant Clifford quantum cellular automata in spatial dimension $D$, modulo Clifford circuits and s…