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We discuss energy barriers and their relationship to self-correcting quantummemories. We introduce the solid code, a 3-d version of Kitaev's surface code,and then combine several solid codes using a technique called welding. Theresulting code is a $[[O(L^3),1,O(L^{\frac{4}{3}})]]$ stabilizer code with anenergy barrier of $O(L^{\frac{2}{3}})$, which is an exponential improvementover the previous highest energy barrier in 3-d. No-go results are avoided bybreaking microscopic translation invariance.

3-d topological quantum memory with a power-law energy barrier