7 problems

Fidkowski's conjecture. $Y$ is a nontrivial QCA if the invertible phase it entangles has a nontrivial partition function on some orientable manifold.

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 $k$ be a field, let $\mathbf Q(\mathbb Z^3)$ be the QCA space in dimension three, and let $\mathrm{Witt}_k$ denote the Witt group of braided fusion $k$-linear categories. The Q…

For each spatial dimension $d$, let $\mathcal Q^*(\mathbb Z^d)$ be the group of quantum cellular automata and let $\mathcal C^*(\mathbb Z^d)$ be its normal subgroup of quantum circ…

For each spatial dimension $d$, let $\mathcal I(\mathbb Z^d)$ be the abelian group of invertible gapped phases, and let $\mathrm{IP}(\mathbb Z^d)$ denote a proposed space-level con…

Disentangling-QCA conjecture. For every such Hamiltonian $H$, there exists a QCA that disentangles its ground state. A pair of disentangling QCAs are equivalent if and only if the…

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…