A local automaton for the 2D toric code
read the original abstract
We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and G\'acs. Our decoder is a circuit of strictly local quantum operations preserving a logical state for exponential time in the presence of circuit-level noise without the need for non-local classical computation or communication. Our construction is not translation invariant in spacetime, but can be made time-translation invariant in 3D with stacks of 2D toric codes. This solves the open problem of constructing a local topological quantum memory below four dimensions.
This paper has not been read by Pith yet.
Forward citations
Cited by 3 Pith papers
-
Proof of a finite threshold for the union-find decoder
Union-find decoder for surface code achieves finite threshold under circuit-level stochastic errors with quasi-polylog parallel runtime bound.
-
Quantum Memory and Autonomous Computation in Two Dimensions
A two-dimensional dissipative quantum cellular automaton achieves passive quantum error correction with a nonzero noise threshold and supports fault-tolerant universal computation.
-
High-performance cellular automaton decoders for quantum repetition and toric code
SCALA is a signaling cellular automaton with local attraction that achieves ~7.5% threshold and p_L proportional to p^{d/4} scaling for toric codes while keeping computation strictly local and robust to measurement an...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.