5 problems

Chiral-semion QCA nontriviality conjecture. The QCA $\alpha_1$ is nontrivial, because otherwise there would exist a standalone two-dimensional commuting projector Hamiltonian reali…

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…

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…

Gapped-boundary conjecture. ALCPHs can realize precisely those topological phases that support gapped boundaries.

A local commuting projector Hamiltonian is a Hamiltonian expressed as a sum of mutually commuting local projectors, and its ground state is a trivial product state when it is a ten…