Let $\mathcal{C}_L$ be a family of geometrically local CSS stabilizer codes on lattices of linear size $L$, with stabalizer group \[ S^X=\langle S^x_1, \dots S^x_n\rangle \qquad S^Z=\langle S^z_1, \dots, \dots S^z_n\rangle \]
What are the neccesary and sufficient conditions for $\mathcal{C}_L$ to admit a construction by a linear depth sequential quantum circuit (i.e a geometrically local circuit of $O(L)$ depth in which acts on each bit with only $O(1)$ gates) that maps a trivial product state to a ground state of the code.