  Fault-tolerant quantum computing requires classical hardware to perform the
decoding necessary for error correction. The Union-Find decoder is one of the
best candidates for this. It has remarkably organic characteristics, involving
the growth and merger of data structures through nearest-neighbour steps; this
naturally suggests the possibility of its realisation using a lattice of simple
processors with nearest-neighbour links. In this way the computational load can
be distributed with near-ideal parallelism. Here we show for the first time
that this strict (rather than partial) locality is practical, with a worst-case
runtime $\mathcal O(d^3)$ and mean runtime subquadratic in the surface code
distance $d$. A novel parity-calculation scheme is employed which can simplify
previously proposed architectures, and our approach is optimised for
circuit-level noise. We compare our local realisation with one augmented by
long-range links; while the latter is of course faster, we note that local
asynchronous logic could negate the difference.
