Institute for Quantum Information Seminar

A high energy barrier for logical errors is essential for the development of self-correcting quantum memories in the Hamiltonian framework. These devices would have an unbounded storage time at a fixed temperature as a function of the total number of qubits. In order to find a codes with large energy barriers 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. Despite the large energy barrier, this code is unlikely to serve as a self-correcting quantum memory.