**Self correcting quantum memories with a polynomial energy barrier** - Kamil Michnicki

The ferromagnetic hard disc drive is a paradigmatic example of a self-correcting classical memory. It uses natural thermalization to passively protect against errors by encoding information in the ground state of a hamiltonian. Local errors must pass through a large energy barrier to perform a global bit flip error. Self-correcting quantum memories have the further restriction that both bit flip and phase errors must simultaneously be protected. The previous highest energy barrier for a 3-d quantum code is O(log N) where N is the number of qubits in the lattice. Whether quantum codes with power law energy barriers exist or not has been an open problem before this result. A primitive called welding is introduced which like concatenation is a method for creating new stabilizer codes from pre-existing stabilizer codes. The procedure of welding is applied to a 3-d toric code, with rough and smooth boundaries, to produce a stabilizer code with a power law minimum energy barrier, an exponential improvement over previous results.