3D Topological Quantum Memory with a Power-Law Energy Barrier

We discuss energy barriers and their relationship to self-correcting quantum memories. We introduce the solid code, a 3D version of Kitaev's surface code, and then combine several solid codes using a technique called welding. The resulting code is a [O(L³),1,O(L(4/3))] stabilizer code with an energy barrier of O(L(2/3)), which is an exponential improvement over the previous highest energy barrier in 3D. No-go results are avoided by breaking microscopic translation invariance.