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Making Error Correction Spatially Local

Dave Bacon, University of Washington

(Session 2 : Thursday from 7:30pm-8:00pm)

Abstract. In quantum error correction quantum information is encoded across multiple 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. An example of the contrary case 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.) Here we show 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 properties similar to toric and surface codes.