A local automaton for the 2D toric code

We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and G'acs. Such a decoder is realized as a circuit of strictly local quantum channels that preserves the logical subspace of the toric code for exponential time in the presence of (below threshold) circuit-level noise without the need for non-local classical computation or communication. Our 2D construction is not translation invariant in spacetime, but can be made time-translation invariant in 3D.

Speaker: Margarita Davydova, Massachusetts Institute of Technology