Topological stabilizer codes with a power law energy barrier via welding

Kamil Michnicki, MIT
Event Date and Time: 
Thu, 2013-04-04 10:00 - 11:00
Hennings 309B
Local Contact: 
Robert Raussendorf
Intended Audience: 
A high energy barrier for logical errors in local stabilizer code Hamiltonians is essential for the development of self-correcting quantum memories. These devices would have an unbounded storage time as a function of the total number of qubits. We introduce a new primitive, called welding, for combining two stabilizer codes to produce a new stabilizer code for which the resulting shape of the logical operators is the combination of the former two shapes. 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.
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