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

2012/08/16 by Michnicki, Kamil · 2 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1208.3496

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(L³),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.

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