High-performance cellular automaton decoders for quantum repetition and toric code

arXiv:2604.21866v2 Announce Type: replace Abstract: Execution of quantum algorithms on large-scale quantum computers will require extremely low logical error rates and scalable decoding architectures. Local decoders are promising candidates for this task because they avoid the communication and data-processing bottlenecks inherent in global decoding strategies. Here, we present SCALA (Signaling CA with Local Attraction), a non-hierarchical cellular automaton decoder for quantum repetition and toric codes, and compare it with the hierarchical CA decoder proposed by Harrington. SCALA combines constant local memory and simple nearest-neighbor signaling with a system-size-dependent global reset schedule. We find a code-capacity threshold estimate of $p_c\simeq7.40(5)\%$ and sub-threshold scaling approaching $p_L\propto p^{d/4}$ for the toric code. For the finite system sizes accessible numerically, and despite numerical evidence for the absence of a finite critical threshold, SCALA also provides strong logical-error suppression under phenomenological noise while retaining its low local computational overhead. SCALA furthermore remains robust when its internal signals are themselves noisy. Together with its simple local dynamics, this makes SCALA particularly interesting for low-overhead real-time decoding and motivates its exploration as a quantum cellular automaton for measurement-free quantum error correction.