Cellular Automaton Quantum Memory Decoders

Local space-time syndrome rules and their logical suppression thresholds. The main concepts are local CA updates, measurement history, percolation. Each must be defined in the context of a concrete physical model, mathematical representation, or experimental task. Terminology alone does not establish the behavior of the system.

A cellular automaton decoder uses local update rules on a syndrome lattice rather than a global optimization run after every fault. Locality can reduce wiring and latency, but finite propagation speed can also restrict correction of widely separated faults. The code geometry, dimension, repeated measurement noise and boundary treatment are essential to any claimed threshold. A rule performing well with perfect stabilizer measurements may fail when detection events fluctuate across time.

Construct a three-dimensional space-time syndrome history for a two-dimensional stabilizer code, implement an explicit local update schedule and measure the logical failure probability over a physical-error grid. Compare against minimum-weight matching at matched rounds, resources and latency. Verify that success does not arise only from postselected trajectories or underrepresented correlated errors.