3-d quantum stabilizer codes with a power law energy barrier

Abstract

We introduce a new primitive, called welding, for combining two stabilizer codes to produce a new stabilizer code. We apply welding to construct surface codes and then use the surface codes to construct solid codes, a variant of a 3-d toric code with rough and smooth boundaries. Finally, we weld solid codes together to produce a $(O(L^3),1,O(L^{4/3}))$ stabilizer code with an energy barrier of $O(L^{2/3})$, which solves an open problem of whether a power law energy barrier is possible for local stabilizer code Hamiltonians in three-dimensions. The previous highest energy barrier is $O(\log L)$. Previous no-go results are avoided by breaking translation invariance.

19 pages, 12 figures

References in corpus (3)

• Local stabilizer codes in three dimensions without string logical operators
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Topological order in a 3D toric code at finite temperature