Work-efficient parallel union-find: Work-efficient parallel union-find

Simsiri, Natcha; Tangwongsan, Kanat; Tirthapura, Srikanta; Wu, Kun-Lung

doi:10.1002/cpe.4333

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 \name can optimize for resource efficiency by decoding $$d=51$ on a Xilinx VCU129 FPGA with an average latency of 544 ns per measurement round.

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