Sparse-graph quantum codes and non-local spin models Leonid Pryadko, Associate Professor, Department of Physics & Astronomony (University of California, Riverside) Locality is one of the fundamental principles used to construct physical models. For example, in the Ising model, each Hamiltonian term corresponds to a bond between nearest neighboring spins on a given lattice. What happens if we omit the locality condition? I will answer this question on the example of disordered spin models related to the decoding threshold for sparse-graph quantum error-correcting codes, also known as quantum LDPC codes. Both traditional local spin models (Ising model, Z2 lattice gauge theory) and non-local spin models not studied previously can be obtained this way. Ordered phase in such models corresponds to a deep minimum of the free energy. Transition to disordered phases happens by proliferation of "post-topological" extended defects generalizing the notion of a domain wall. Several families of quantum LDPC codes with finite rates (finite overhead per encoded qubit) are known. In the corresponding spin models the number of extended defect classes is exponentially large. In such models one can have a phase transition driven by the entropy of extended defects, where the analog of line tension for each defect type remains finite. A. A. Kovalev and L. P. Pryadko, "Spin glass reflection of the decoding transition for quantum error correcting codes", arXiv:1311.7688