Introducing Ambiguity Clustering: An Accurate and Efficient Decoder for qLDPC Codes

We introduce Ambiguity Clustering, a new decoder for general quantum low-density parity check codes. On the recently proposed bivariate bicycle codes we find an order of magnitude speedup compared to the state-of-the-art BP-OSD decoder with no reduction in logical fidelity at physically realistic error rates. In particular, a single-threaded CPU implementation of Ambiguity Clustering is fast enough to decode the 144-qubit Gross code in real time for neutral atom and trapped ion systems.