In quantum error correction quantum information is encoded across multiple quantum subsystems in such a way that one can diagnose and fix the most likely errors that occur to the system. This error correcting step is achieved by performing a measurement that does not disturb the encoded quantum information but does diagnose what error has occurred on the system. These error diagnosing measurements are often, but not always, of observables that are non-trivial over nearly the entire quantum system containing the encoded quantum information. The exceptions to this rule are topological and color quantum codes where the diagnosing measurements involve only a small number of spatially local subsystems (that is, involve only measurements over a constant sized neighborhood on some D-dimensional lattice.) These spatially local codes are much better suited to most realistic physical implementations of quantum computers. In this talk I will describe work (joint with Jonathan Shi) that shows how to convert a large class of quantum error correcting codes, all stabilizer codes, into spatially local codes. These codes are subsystem codes derived from measurement based quantum computing and have the same distance and rate as the original code, at the cost of using more qubits. The best of these codes have distances that scale as an area in two out of three spatial dimensions, and have ill-defined distances in the remaining dimension. |