Parallel Minimum-Weight Parity Factor Decoding for Quantum Error Correction

The Minimum-Weight Parity Factor (MWPF) de-coder is renowned for its accuracy in Quantum Error Correction (QEC) for various space-time codes, including surface codes and quantum LDPC codes. This work explores the scalability of MWPF decoders through parallelization, similar to parallel MWPM decoders. We introduce a dynamic fusion graph to schedule fusion operations in dynamic quantum circuits. It allows parts of the decoding graph to be solved and fused at a later stage, without having the full fusion tree at the very beginning. It also reduces the overhead caused by the traversing of the fusion tree. The dynamic fusion graph represents a novel and efficient method for real-time QEC decoding, providing enhancements in throughput and scalability for fault-tolerant quantum computing.