Figure 2
From: Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
A family of rhombic dodecahedral lattices with boundaries. (a) Construction of the \(L=3\) lattice from the cubic lattice. We show the initial cubic lattice as well as the final rhombic dodecahedral lattice. (b) The \(L=3\) lattice. The front and back boundaries are smooth (syndromes must form closed loops) and the other boundaries are rough (open loops of syndrome can terminate). (c) An example of a open loop of syndrome terminating on one of the rough boundaries (light yellow edges). (d) A syndrome on the smooth boundary (light yellow edges). With the sweep direction \(\vec {\omega } = -(1,1,1)\), the ringed vertex does not satisfy the trailing location condition.
