  A fault-tolerant quantum computer must decode and correct errors faster than
they appear to prevent exponential slowdown due to error correction. The
Union-Find (UF) decoder is promising with an average time complexity slightly
higher than $O(d^3)$. We report a distributed version of the UF decoder that
exploits parallel computing resources for further speedup. Using an FPGA-based
implementation, we empirically show that this distributed UF decoder has a
sublinear average time complexity with regard to $d$, given $O(d^3)$ parallel
computing resources. The decoding time per measurement round decreases as $d$
increases, the first time for a quantum error decoder. The implementation
employs a scalable architecture called Helios that organizes parallel computing
resources into a hybrid tree-grid structure. Using a Xilinx VCU129 FPGA, we
successfully implement $d$ up to 21 with an average decoding time of 11.5 ns
per measurement round under 0.1\% phenomenological noise, and 23.7 ns for
$d=17$ under equivalent circuit-level noise. This performance is significantly
faster than any existing decoder implementation. Furthermore, we show that
Helios can optimize for resource efficiency by decoding $d=51$ on a Xilinx
VCU129 FPGA with an average latency of 544ns per measurement round.
