Existence of disentangling QCAs for bulk-trivial commuting projector Hamiltonians

Let $H$ be a local commuting projector Hamiltonian with no bulk order. A disentangling QCA is a quantum cellular automaton that maps the ground state of $H$ to a trivial product-state ground state. Two such QCAs are equivalent when the Hamiltonians whose ground states they disentangle have equivalent surface data, with Witt equivalence defined in the categorical Witt group.

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 Hamiltonians they disentangle admit Witt-equivalent surface topological orders.

This conjecture extends known constructions for particular Walker–Wang and related models to general local commuting projector Hamiltonians without bulk order. It would imply that nontrivial QCAs connect the finite-depth-circuit equivalence classes of these Hamiltonians, but existence and the claimed classification remain open.