Micro Blossom: Accelerated Minimum-Weight Perfect Matching Decoding for Quantum Error Correction

Abstract: Minimum-Weight Perfect Matching (MWPM) decoding is important to quantum error correction decoding because of its accuracy. However, many believe that it is difficult, if possible at all, to achieve the microsecond latency requirement posed by superconducting qubits. This work presents the first publicly known MWPM decoder, called Micro Blossom, that achieves sub-microsecond decoding latency. Micro Blossom employs a heterogeneous architecture that carefully partitions a state-of-the-art MWPM decoder between software and a programmable accelerator with parallel processing units, one of each vertex/edge of the decoding graph. On a surface code with code distance $d$ and a circuit-level noise model with physical error rate $p$, Micro Blossom's accelerator employs $O(d^3)$ parallel processing units to reduce the worst-case latency from $O(d^{12})$ to $O(d^9)$ and reduce the average latency from $O(p d^3+1)$ to $O(p^2 d^2+1)$ when $p \ll 1$. We report a prototype implementation of Micro Blossom using FPGA. Measured at $d=13$ and $p=0.1\%$, the prototype achieves an average decoding latency of $0.8 \mu s$ at a moderate clock frequency of $62 MHz$. Micro Blossom is the first publicly known hardware-accelerated exact MWPM decoder, and the decoding latency of $0.8 \mu s$ is 8 times shorter than the best latency of MWPM decoder implementations reported in the literature.