Citation: Stephen, David T., et al. "Non-local finite-depth circuits for constructing SPT states and quantum cellular automata." arXiv preprint arXiv:2212.06844 (2022).
Web: https://arxiv.org/abs/2212.06844
Tags: SPT/SETs, No-go
This paper shows that QCAs can be trivialized under finite-support non-local finite depth unitary circuits. QCAs are defined to be mappings on the space of operators on a D-dimensional lattice, modulo finite depth local unitary circuits. Here, it is very important that local means geometrically local. The operators must act on some ball of radius O(1).
The question is whether or not these states can be trivialized when one allows unitary operators which still have finite support, but act on a non-geometrically local set of states. It is shown in this paper that, with non-geometric locality, QCAs can be trivialized.